# Time Value of Money

I would like someone to explaine the following problems

(See attached file for full problem description)

– Retirement savings
– Annuity Value
– Amortizing Loan

# Time Value of Money

Company makes a deposit of \$600,000 on 1/1/01 and a deposit of \$400,000 on 1/1/03 into an account that pays interst at 6% compounded semiannually. On 1/1/04, Company transfers the entire balance in the account to a new account that pays interest at 8% compounded quarterly. Company then deposits %500,000 into the account on 1/1/05. On 1/1/07, Company transfers the entire balance in the account to a new account that pays interest at 4% compounded annually. On this same day, Company makes the first of 4 equal annual withdrawals designed to deplete the account

**Compute the
1) amount transfered into the new account on 1/1/04
2) amount of interest earned by Company from 1/1/02 through 1/1/06
3) amount transfered on 1/1/07 to the new account
4) amount of the equal annual withdrawal
5) amount of interest earned during the year of 2007
6) balance in the account on 1/1/08, immediately after makin gthe 2nd equal annual withdrawal
7) amount of decrease in the balance of the account from 1/1/08 to 1/1/09

CLUE MUST MATCH::::The balance in the account at 1/1/07, immediately AFTER the 1st withdrawal, is approximately \$1,494,195.

# Time Value of Money

27. Lee Childs is negotiating a contract to do some work for Hass Corp. over the next five years. Hass proposes to pay Lee \$10,000 at the end of each of the third, fourth, and fifth years. No payments will be received prior to that time. If Lee discounts these payments at 8%, what is the contract worth to him today?

# Time Value of Money.

A 9 million dollar contract that stipulates equal payments to be made monthly over a period of five years. To determine what such a contract is worth today, you would need to use

Choices are

present value factors
future values factors
presnt value factors of an annuity
future value factors of an annuity

# Time value of money

1. Your brother has offered to give you \$100, starting next year, and after that growing at 3% for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in the local bank so that the account will generate the same cash flows as he is offering you. Your local bank will guarantee a 6% annual interest rate so long as you have money in the account.

a) How much money will you need to deposit into the account today?

b) Using Excel Spreadsheet, show explicitly that you can deposit this amount of money into the account, and every year withdraw what your brother has promised leaving the account with nothing after the last withdrawal.

2. You have decided to buy a perpetuity. The bond makes one payment at the end of every year forever and has an interest rate of 5%. If you initially put \$1000 into the bond, what is the payment every year?

# Time Value of Money

One
The Chinese government is conducting an auction for a joint project involving oil exploration. Because of a desire for U.S. dollars, they require the winning bidder to make an up-front, one-time payment for the rights to join the project and supervise the work. The Chinese government will use the proceeds to cover all of the expenses during the life of the project. The winning bidder will receive a single payment at the end of the ten-year life of the project. This payment, based on the amount of the winning bid, will pay either simple interest of 15 percent annually or 10 percent annually compounded quarterly. Blue Mesa Oil’s bid team has to help evaluate its \$47 million bid. First, find out the future value, on a per dollar basis, of each of the two interest payment options. Next, compute the future value of the \$47 million bid using each option, and determine which is bigger.

Two
Blue Mesa Oil Company is considering two projects. The As Is Project involves drilling for oil using existing technology. Given the estimated reserves, this project is expected to produce \$15.6 million at the end of year 3. Due to the relatively low level of risk involved, management’s required rate of return is 12.5 percent.
The Bedrock project involves using new technology to drill for oil from a field located beneath bedrock. Given the higher risk involved, this project must provide a rate of return of 14.6 percent. If the new technique works, the project is expected to produce \$12.4 million in only 2 years. Compute the present value of each project using annual compounding, and report on the relative values and the difference between the two.

# Time Value of Money

1. What interest rate would allow you to accumulate \$10,000 in 8 years if you saved \$60 per month and earned compounded interest monthly?

2. What amount of money should you pay each month to retire a \$12,000 debt in five years if the interest rate on money owed is 10%?

3. If the equivalent annual interest rate is 15% what is the monthly rate that would be compounded to achieve this?

# Time value of money

Sam was injured in an accident, and the insurance company has offered him the choice of \$49,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?

# Time value of money

SAC is considering the purchase of new equipment to manufacture specialty spark plugs.
The new equipment would allow the firm to manufacture 100,000 additional spark plugs per year and is expected to have a useful life of 5 years and to have no salvage value at that time.

SAC will depreciate the equipment using the straight-line method. Specialty spark plugs are selling for an average price of \$20 and are expected to cost \$8 to manufacture with the new equipment. Indirect costs are expected to remain the same.
The equipment will cost \$3,000,000 to purchase and install. SAC’s tax rate is 34%.

# Time Value of Money

Describe the following project evaluation processes: Payback, NPV, PI, IRR. Is any one evaluation process better the others? Why?

2. Group “A” will use 4% factors
A) Calculate the Future value of \$400 compounded annually for 5 years.
B) Calculate the Future value of \$400 compounded semi-annually for 5 years.
C) Calculate the Present value of \$500 received in 10 years. (annual discounting)
D) Calculate the Future value of a \$1,000 per year annuity for 10 years. (annual payments)

# Time Value of Money

Give appropriate solutions to the attached email.

1. How long will it take \$10,000 to reach \$50,000 if it earns 10% interest compounded semiannually?
a.) 17 years
b.) 33 years
c.) 16.5 years
d.) 8.5 years

2. You require an 8% annual return on all investments. You will receive \$1,000,
\$2,000, and \$3,000 respectively for the next three years (end of year) on a particular investment. What is the most you be willing to pay for this investment?
a.) \$5,022
b.) \$2,577
c.) \$6,000
d.) \$4,763

3. Your partners have promised to give you \$25,000 on your wedding day if you
Wait 10 years to get married. Your sister is getting married today. What amount should she receive in today’s dollars to match you gift? The appropriate discount rate is rate 12%.
a.) \$8,049
b.) \$10,000
c.) \$22,321
d.) \$25,000

4. You want to start saving for retirement. If you deposit\$2,000 each year at the end
Of the next 60 years and earn 11% on the investment, how much will you have when you retire?
a.) \$792,000
b.) \$1,048,114
c.) \$9,510,132
d.) \$10,556,246

5. What is the present value of a semi-annual ordinary annuity payment of \$7,000
made for 12 years with a required annual return of 5%?
a.) \$65,145
b.) \$128,325
c.) \$125,195
d.) \$62,043

6. You get a 25-year loan of \$150,000 with a 8% annual interest rate. What are the
annual payments?
a.) \$14,052
b.) \$2,052
c.) \$13,965
d.) \$13,427

7. Your grandmother is offered a series of \$6,000 starting one year from today. The
Payments will be made at the end of each of the next 10 years. Similar risk investments are yielding 7%. What should she pay for the investment?
a.) \$60,000
b.) \$45,091
c.) \$42,141
d.) \$30,501

8. Company XYZ purchased some machinery and gave a five-year note with a
Maturity value of \$20,000. The discount rate is 8% annually and the interest is discounted monthly. How much did the company borrow?
a.) \$13,612
b.) \$13,424
c.) \$19,346
d.) \$12,000

9. Your father loans you \$12,000 to make it through your senior year. His
Repayment schedule requires payments of \$1401.95 at the end of year the next 15 years. What interest rate is he charging you?
a.) 7.0%
b.) 7.5%
c.) 8.0%
d.) 8.5%

10. What is the future value of an annuity due if your required return is 10%, and
Payments are \$1,000 for 10 years?
a.) \$15,937
b.) \$16,145
c.) \$17,531
d.) \$11,000

11. You deposit \$10,000 in a bank and plan to keep it there for five years. The bank
Pay 8% annual interest compounded continuously. Calculate the future value at the end of five years.
a.) \$14,693
b.) \$15,000
c.) \$14,918
d.) \$14,500

12. Calculate the present value of \$100,000 received in six months. Use an annual
discount rate of 10%. Do not adjust the discount rate to a semi-annual rate. Keep it annual and adjust to the appropriate value.
a.) \$95,346
b.) \$56,447
c.) \$90,909
d.) \$100,000
13. You get a twenty-year amortized loan of \$100,000 with a 5% annual interest rate.
what are the annual payments?
a.) \$8,718
b.) \$37,689
c.) \$4,762
d.) \$8,024

14. What is the present value of \$100,000 received in fifteen years with an annual
Discount rate of 5% discounted monthly?
a.) \$25,000
b.) \$48,102
c.) \$47,310
d.) \$207,893

15. A gallon of milk cost \$3.59 today. How much will it cost you to buy a gallon of
milk for your grandchildren in 35 years if inflation averages 5% per year?
a.) \$3.77
b.) \$6.28
c.) \$12.34
d.) \$19.80

16. You borrow \$95,000 for 12 years at an annual rate of 12%. What are the monthly
Payments required to amortize this loan?
a.) \$1,248
b.) \$15,336
c.) \$11,400
d.) \$3,936

Next four years. You can earn an annual rate of 8% on your investments. How much can you withdraw each year (end of year) just using up the \$50,000?
a.) \$12,000
b.) \$11,096
c.) \$11,750
d.) \$15,096

18. You would like to retire on \$1,000,000. You plan on a 7% annual investment rate
(3.5% semi-annually) and will put away \$7,500twice a year at the end of each semi-annual period. How long before you can retire? Round to the nearest figure.
a.) 51years
b.) 25 years
c.) 35 years
d.) 66 years

19. What is the present value of an annual annuity payment of \$7,000 made for 12
Years with a required return of 5% with the first payment starting today?
a.) \$3,898
b.) \$65,145
c.) \$62,043
d.) \$11,200

20. What a deal! Your new car only cost \$28,300 after rebates and trade. If you
Finance it for 60 months at 6% annual interest, what will be you rmonthly payments?
a.) \$471.67
b.) \$544.40
c.) \$547.12
d.) \$1,751.08

Essay. Write your answer in the space provided or on a separate sheet of paper.

21. Sum the present values of the following cashflows to be received at the end of
each of the next six years \$1,500, \$3,500, \$\$3,750, \$4,250, \$5,000 when the discount rate is 4%.

22. How long it will take for \$2,500 to become \$8,865 if it is deposited and earns 5% per year compounded annually? (Calculate to the closet year.)

23. Company XYZ purchased equipment and gave a three-year note with maturity value of \$12,006. The annual discount rate for the note was 14% discounted semi-annually. Calculate how much they borrowed.

24. Calculate the resent value of each of the alternatives below, if the discount rate is 12%.
a.) \$45,000 today in one lump sum.
b.) \$70,000 paid to you in seven equal payments of \$10,000 at the end of each of the next seven years.
c.) \$80,000 paid in one lump sum 7 years from now.

25. A bank agrees to give you a loan of \$12,000,000 and you have t pay \$1,309,908
Per year for 26 years. What is your rate of interest? What would the payments be if this were a monthly payment loan?

# Time Value of Money

An insurer sells a very large number of policies to people who each have the following identical loss (claims) distribution

Loss/claim Probability
100,000 .005
60,000 .010
20,000 .020
10,000 .050
0 .915

1 A. Calculate the Expected claim cost per person.

1 B. Assume claims are paid out 1 year after premiums are received and the discount rate is 6%. Calculate the Present value of expected claim cost

1 C. Assume that the only administrative cost is the cost of processing an application which is \$100 per policy and that the fair profit loading is \$50. Calculate the Fair premium .

Redo problem 1, but include the expected costs of lost adjustment expenses (the cost of processing claims) assuming that loss adjustment expenses equal 12% of losses and are paid at the time that claims are paid.

2 A. Expected loss adjustment expenses =

2 B. Present value of expected loss adjustment expenses =

# TIME VALUE OF MONEY

1) Joe will receive \$175,000 in 50 years. His friends are jealous of him. What is his pot of gold worth today if the alternative investment rate is 14%

2) Sue will receive \$12,000 a year for the next 15 years as a result of her patent. Using a 9% rate , should she be willing to sell her future rights now for \$100,000.

3) Mike has been depositing \$2,500 in a savings account each December starting in 1991. The account earns 5% compounded annually. How much will he have in December 2000. (Assume a deposit is made in December 2000).

4) If you owe \$40,000 – payable at the end of seven years. How much should your creditor be willing to accept immediately if they could earn 12%.

5) Your rich uncle has offered you a choice of one of the three following alternatives
a) \$10,000 now
b) \$2,000 a year for 8 years – equal investments have earned 11%
c) \$24,000 at the end of 8 years – equal investments have earned 11%

6) John started a paper route 1/1/95. Every 3 months , he deposited \$500 in his bank account. The account earns 4% annually but is compounded quarterly. On 12/31/98 , he used the entire balance in his account to invest in a contract that pays 9% annually. How much will he have on 12/31/01?

7) Pete has just invested \$6,250 for his son (age 1). The money will be used for his son’s education in 17 years. He calculates that he will need \$50,000 for the first year of college. What rate of return does he need?

8) Jane has just retired after 25 years. Her total pension has an accumulated value of \$180,000. Her life expectancy is 15 more years. Her pension manager believes she can earn 9% on her assets. What will be her yearly income for the next 15 years?

9) You wish to retire in 18 years , at which time , you want to have accumulated enough money to receive an annuity of \$14,000 a year for 20 years of retirement. During the period before retirement , you can 11% annually. after retirement you can earn 8% annually. What annual contributions will allow you to receive \$14,000 annually.

10) If you borrow \$15,618 and are required to pay the loan back in 7 equal annual instalments of \$3,000. What is the interest rate associated with this loan?

11) If you borrow \$17,000 and are required to pay it back in 20 equal annual instalments of \$2,000 ; what is the approximate interest rate associated with the loan.

12) Joe Invests \$50,000 in a project that is expected to yield a return of 8%, compounded semi-annually over the next 5 years. He will then take the proceeds & provide himself with a 10 year annuity. Assuming a 10% annual interest rate, how much will the annuity be?

13) Joe will receive \$19,500 a year for the next 20 years as a payment for a song he has written. If a 10% rate is applied, should he be willing to sell out all future rights now for \$160,000?

# Time Value of Money

——————————–
Using the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns.

a) What is the amount of the payments that Ned Winslow must make at the end of each of 8 years to accumulate a fund of \$90,000 by the end of the eighth year, if the fund earns 8% interest, compounded annually? (Provide calculation as well)

b) Robert Hitchcock is 40 years old today and he wishes to accumulate \$500,000 by his sixty-fifth birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his fortieth through his sixty-fourth birthdays. What annual deposits must Robert make if the fund will earn 12% interest compounded annually? (Provide calculation as well)

c) Diane Ross has \$20,000 to invest today at 9% to pay a debt of \$47,347. How many years will it take her to accumulate enough to liquidate the debt? (Provide calculation as well)

d) Cindy Houston has a \$27,600 debt that she wishes to repay 4 years from today; she has \$19,553 that she intends to invest for the 4 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt? (Provide calculation as well)

# Time value of money

30. You are saving for retirement. To live comfortably, you decide you will need to save \$2 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a saving account. If the interest rate is 5%, how much must you set aside each year to make sure that you will have \$2 million in the account on your 65th birthday?

31. You realize that the plan in Problem 30 has a flaw. Because your income will increase over your lifetime, it would be more realistic to save less now and more later. Instead of putting the same amount aside each year, you decide to let the amount that you set aside grow by 7% per year. Under this plan, how much will you put into the account today? (Recall that you are planning to make the first contribution to the account today).

# Time value of money

1)
Calculate the future value of \$2000 in
a) 5 years at interest rate of 5% per year
b) 10 years at an interest rate of 5% per year
c) 5 years at an interest rate of 10% per year
d) why is the amount of interest earned in part (a) less than half the amount of interest earned in (b)

2)
You are thinking of retiring. Your retirement plan will either pay you \$250000 immediately on retirement or \$350000 five years after
date of retirement. Which alternative should you choose if interest rate is;
0% per year
8% per year
20% per year

3)
you have been offered a unique investment opportunity. If you invest \$10,000 today you will receive \$500 one year from now; \$1500 two years from now and \$10,000 ten years from now

what is the NPV of the opportunity if the interest rate is 6% per year? Should you take the opportunity?
what is the NPV of the opportunity if the interest rate is 2% per year? Should you take the opportunity?

4)
What is the present value of \$1000 paid at the end of each of the next 100 years if interest rate is 7% per year?

5)
you have found 3 investment choices for a one year deposit
****10% APR compounded monthly
****10% APR compounded annually
****9% APR compounded daily
Compute the EAR for each investment with 365 days in the year

6)Key Bank is offering a 30 year mortgage with an EAR of 5 and 3/8%. If I borrow \$ 150,000 what will be my monthly payment?

7)
if the rate of inflation is 5% what nominal interest rate is necessary for you to earn a 3% real interest rate on your investment

8) your best taxable investment has an EAR of 4%. Your best tax-free investment opportunity has an EAR of 3%.
If your tax rate is 30%, which opportunity provides the higher after-tax interest rate?

# Time Value of Money

Problem 1 chapter 4
You have just taken out a five-year loan from a bank to buy an engagement ring. The ring costs \$5000.You plan to put down \$1000 and borrow \$4000. You will need to make annual payments of \$1000 at the end of each year. Show the timeline of the loan from your prospective. How much would the timeline differ if you created it from the bank perspective?

Problem 3 chapter 5
Many academic institutions offer a sabbatical policy. Every seven years a professor is given a year free of teaching and other administrative responsibilities at full pay. For a professor earning \$70,000 per year who works for a total 42 years, what is the present value of the amount she will earn while on sabbatical if the interest rate is 6% (EAR)?

# Time Value of Money

There are 3 parts to this; part of this has been completed
1. Present value calculation
2. Future value of annuity: ordinary annuity and annuity due
3. Loan interest deductions

1. Present value calculation:
A PVIF &#61501; 1 &#61624; (1 &#61483; 0.02)4 &#61501; ??
B PVIF &#61501; 1 &#61624; (1 &#61483; 0.10)2 &#61501; ??
C PVIF &#61501; 1 &#61624; (1 &#61483; 0.05)3 &#61501; ??
D PVIF &#61501; 1 &#61624; (1 &#61483; 0.13)2 &#61501; ??

2. Future value of an annuity
a. Future value of an ordinary annuity vs. annuity due
(1) Ordinary Annuity (2) Annuity Due
FVAk%,n &#61501; PMT&#61472;&#61620;&#61472;(FVIFAk%,n) FVAdue &#61501; PMT&#61472;&#61620;&#61472;[(FVIFAk%,n&#61472;&#61620;&#61472;(1 &#61483; k)]
A FVA8%,10 &#61501; \$2,500&#61472;&#61620;&#61472;14.487 FVAdue &#61501; \$2,500&#61472;&#61620;&#61472;(14.487&#61472;&#61620;&#61472;1.08)
FVA8%,10 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: ?? Calculator solution: \$??
B FVA12%,6 &#61501; \$500&#61472;&#61620;&#61472;8.115 FVAdue &#61501; \$500 &#61620;( 8.115&#61472;&#61620;&#61472;1.12)
FVA12%,6 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$??
C FVA20%,5 &#61501; \$30,000&#61472;&#61620;&#61472;7.442 FVAdue &#61501; \$30,000&#61472;&#61620;&#61472;(7.442&#61472;&#61620;&#61472;1.20)
FVA20%,5 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$??
D FVA9%,8 &#61501; \$11,500&#61472;&#61620;&#61472;11.028 FVAdue &#61501; \$11,500&#61472;&#61620;&#61472;(11.028&#61472;&#61620;&#61472;1.09)
FVA9%,8 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$138,241.92
E FVA14%,30 &#61501; \$6,000&#61472;&#61620;&#61472;356.787 FVAdue &#61501; \$6,000&#61472;&#61620;&#61472;(356.787&#61472;&#61620;&#61472;1.14)
FVA14%,30 &#61501; \$?? FVAdue &#61501; \$??
Calculator solution: \$?? Calculator solution: \$??
b. The annuity due results in a ???? future value in each case. By depositing the payment at the beginning rather than at the end of the year, it has ???? year of compounding.

3. Loan interest deductions
Challenge
a. PMT &#61501; \$10,000 &#61624; (PVIFA13%,3)
PMT &#61501; \$10,000 &#61624; (2.361)
PMT &#61501; \$??
Calculator solution: \$??

b.
End of
Year Loan
Payment Beginning of
Year Principal Payments End of Year
Principal
Interest Principal
1 \$4,235.49 \$10,000.00 \$1,300.00 \$2,935.49 \$7,064.51
2 4,235.49 7,064.51 918.39 3,317.10 3,747.41
3 ?? ?? ?? ?? ??
(The difference in the last year’

# Time-value of money

Can you help? I’m stuck on a few True/False questions…

Chapter 1

1. A financial analyst is responsible for maintaining and controlling the firm’s daily cash balances. Frequently manages the firm’s short-term investments and coordinates short-term borrowing and banking relationships.

2. Finance is concerned with the process institutions, markets, and instruments involved in the transfer of money among and between individuals, businesses and government.

3. Financial services are concerned with the duties of the financial manager.

4. Financial managers actively manage the financial affairs of many types of business-financial and non-financial, private and public, for-profit and not-for-profit.

5. In partnerships, owners have unlimited liability and may have to cover debts of other less financially sound partners.

6. In partnerships, a partner can readily transfer his/her wealth to other partners.

7. The board of directors is responsible for managing day-to-day operations and carrying out the policies established by the chief executive officer.

Chapter 4
8. Since individuals are always confronted with opportunities to earn positive rates of return on their funds, the timing of cash flows does not have any significant economic consequences.

9. Time-value of money is based on the belief that a dollar that will be received at some future date is worth more than a dollar today.

10. Future value is the value of a future amount at the present time, found by applying compound interest over a specified period of time.

11. Interest earned on a given deposit that has become part of the principal at the end of a specified period is called compound interest.

12. The future value interest factor is the future value of \$1 per period compounded at i percent for n periods.

13. For a given interest rate, the future value of \$100 increases with the passage of time. Thus, the longer the period of time, the greater the future value.

14. The greater the potential return on an investment and the longer the period of time, the higher the present value.

# Time Value of Money

Sheila and Ed have approached you with their problems as highlighted situations 1-5.

Situation #1

Sheila and Ed have \$150,000 cash to invest with a bank offering a 4% interest rate. They are not sure whether to invest the cash with interest rate compounded quarterly, semi-annually, or annually. Calculate the balance at the end of 5 years generated by investing \$15,000 at 4% in an interest-bearing account that is compounded quarterly, semi-annually, or annually.

Situation #2

Shanghai Winters, one of BC’s biggest customers, has requested a loan with favorable terms. Sheila and Ed decide to offer this customer a \$70,000 five-year note receivable. You recommend that since this is your best customer, they offer a 4% interest rate rather than the 7% going rate.

Situation #3

Sheila would like to retire in 10 years. She estimates that her life expectancy upon retirement would be 17 years and she would require \$90,000 a year to live comfortably.

Situation #4

XYZ Corporation has a balloon payment coming due from a recent acquisition. They need to have \$200,000 set aside 5 years from now. They can either make payments into the fund at the beginning of the year or at the end of the year. The current discount rate is 6%.

Situation #5

Ed won the lottery! He can either take the \$10,000,000 prize now or receive the payments over the next 15 years.

Using your knowledge of the time value of money, offer them guidance in each situation. Include the following in your answer:

What TVM concept(s) is represented in the situation?
What is the value of the money represented by the situation?
How did you arrive at the value?
To structure the task, use the format below for each situation:

Situation #__
TVM concept represented:
Value:
Explanation:

# Time Value of Money

1. B.J. Industries has a current ratio of 2.5, with \$2.5 million in current assets. Due to sales growth, the company wants to expand accounts receivable and inventories by taking on additional short-term debt. If B.J. Industries wants to maintain a minimum current ratio of 2.0, what is the maximum additional short-term funding it can borrow?

a.\$750,000
c. \$150,000
b. \$350,000
d. \$500,000

2. You are comparing two investment options. The cost to invest in either option is the same today. Both options provide you with \$20,000 of income. Option A pays five annual payments of \$4,000 each. Option B pays five annual payments starting with \$8,000 the first year followed by four annual payments of \$3,000 each. Which one of the following statements is correct given these two investment options?
a. Both options are of equal value given that they both provide \$20,000 of income.
b. Option A has a higher present value than option B given any positive rate of return.
c. Option B has a higher present value than option A given any positive rate of return.
d. Option B has a lower future value at year 5 than option A given a zero rate of return.

3. Mr. Moore will be 35 years at the end of the month and he wishes to retire in 25 years. He plans to invest in a mutual fund earning 7.5 percent annual return compounded monthly and have a \$1.5 million retirement fund at age 60. How much must be deposited at the end of each month to achieve his goal?

a. \$2,850 c. \$1,449
b. \$8,514 d. \$1,710

4. You are the manager of an annuity settlement company. Jim Patton just won the state lottery which promises to pay him \$1,000 per year for 20 years, starting from today, and \$2,000 per year for years 21-45, given a 9% discount rate. Your company wants to purchase the proceeds from the lottery from Jim. What is the most that your company can offer?
a. \$13,770.90
b. \$18,680.95
c. \$23,721.01
d. \$12,633.85

5. Jean Cleveland currently has \$5,750 in a money market account paying 5.65 percent compounded semi-annually. She plans to use this amount and her savings over the next 5 years to make a down payment on a townhouse. She estimates that he will need \$15,000 in 5 years. How much should she invest in the money market account semi-annually over the next 5 years to achieve this target?
a. \$ 886.28
b. \$ 757.25
c. \$ 650.97
d. \$ 610.79

6. You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum amount of \$50,000 today, or receive payments of \$641 a month for 10 years. You can earn 6.5% on your money. Which option should you take and why?

a. You should accept the payments, because they are worth \$56,452 today.
b. You should accept the payments, because they are worth \$56,737 today.
c. You should accept the \$50,000 because the payments are worth only \$47,758 today.
d. You should accept the \$50,000 because the payments are worth only \$47,808 today.

# Time value of money

Can you help with this??

1. In two to three paragraphs, explain why the concept of present value is so important for corporate finance and is often the very first topic taught in any finance class.

2. Calculate the future value of the following:

a. \$500 if invested for five years at a 4% interest rate

b. \$150 if invested for three years at a 9% interest rate

c. \$9100 if invested for seven years at an 3% interest rate

d. \$1000 if invested for ten years with a 0.5% interest rate

3. Calculate the present value of the following:

a. \$7700 to be received three years from now with a 5% Interest rate

b. \$1500 to be received five years from now with a 7% interest rate

c. \$7200 to received two years from now with a 11% interest rate

d. \$680,000 to be received eight years from now with a 9% interest rate.

4. Suppose you are to receive a stream of annual payments (also called an “annuity”) of \$3000 every year for three years starting this year. The interest rate is 3%. What is the present value of these three payments?

5. Suppose you are to receive a payment of \$5000 every year for three years. You are depositing these payments in a bank account that pays 2% interest. Given these three payments and this interest rate, how much will be in your bank account in three years?

# Time Value of Money

1. I am getting ready to buy a new car. I plan on spending \$35,000 for the car and I believe my current car has a \$17,000 trade-in value and I make no additional downpayment. I keep my vehicles 5 years but would like a three-year loan.

What will my monthly car payment be at the end of each month if the annual interest rate is 12%?

2. My firm is hunkering down and we anticipate a long tough year. We believe that over the winter months, we will need the following funds:

End of Month Shortfall
November \$25,000
December \$30,000
January \$32,000
February \$28,000
March \$15,000

(a) We are coming off the summer flush with cash by the end of October. How much should we make as a single deposit today to cover the budget shortfalls next winter if we can earn 12% annually on the funds?

(b) If we could earn more than 12% on the funds, what effect would that have on the amount of the single deposit we make today?

3. My husband and I are planning to retire in exactly 10 years. Considering our social security benefits and income from other investments, we have decided that we will need an additional \$35,000 per year to be able to travel and explore the world. We believe that we will need these funds for 25 years following retirement (after that, we’ve got long-term care insurance). We anticipate earning 7% on our retirement funds for the 25 years we’ll be active and retired and would like this money available at the end of each year.

We don’t want to worry about depositing into this fund after we retire 10 years from now.

(a) How much must our fund be when we retire in 10 years to provide our 25-year, \$35,000 annuity with no worries?

(b) My husband and I discussed things further and decided that we want to set aside the amount we will need to have in the fund today to get it out of the way and we won’t have to worry about anything. How much will we need if we can earn 4% on those funds from now through our 10 years-from-now retirement plan?

(c) What effect would an increase in the rate we can earn both during and prior to retirement have on the values you calculated in (a) and (b)? Explain fully!

4. My firm has an outstanding issue of \$1,000 par-value bonds with a 7% coupon interest rate. We pay interest on this issue annually and we have 10 years to its maturity date.

(a) If bonds of similar risk are currently earning a 5% rate of return, how much should our bonds sell for today?

(b) Why would bonds with similar risk to ours be currently earning a return below our 7% coupon interest rate?

(c) What would the current value of our bond be if the required return were at 7% instead of 5%? Contrast this finding with your results from (a) above and explain.

# Time Value of Money

1.) You have just purchased a car and taken out a \$50,000 loan. The loan has a five year term with monthly payments and an APR of 6%.

a.) How much will you pay in interest, and how much will you pay in principal, during the first month, second month, and first year? (Hint: complete the loan balance after one month, two months and one year).

b.) How much will you pay in interest, and how much will you pay in principal, during the fourth year (i.e., between three and four years from now)?

2.) When you purchased your car, you took out a five year annual payment loan with an interest rate of 6% per year. The annual payment on the car is \$5000. You have just made a payment and have now decided to pay the loan off by repaying outstanding balance. What is the payoff amount if

a) You have owned the car for one year (so there are four years left on the loan)?

b) You have owned the car for four years (so there is one year left on the loan)?

# Time Value of Money

Pierre borrowed \$100,000 from his grandfather for college expenses. The interest rate is to be 5% annually (and compounded annually). The plan is that he will graduate in four years and start making payments at the end of the fifth year.
a. How much will Pierre owe just before he makes his first payment?
b. If he wants to pay off the loan in 10 years, what would his annual payment be?
c. How long would it take to pay off the loan after he graduates if he pays his grandfather \$15,000 annually.

# Time Value of Money

Apply the concept of present value to Second Life. Suppose Second Life is selling a bond that will pay you \$1000 in one year from today. Keep in mind that if Seconbd Life has financial difficulties in one year you might not get your full \$1000 back. Given that a dollar one year from now is always worth less than a dollar today, you most certainly would not pay a full \$1000 for this bond. Given the concepts of the time value of money, answer the following questions:

1. How much would you pay for this bond today? Take into consideration your own personal risk preferences, interest rates, inflation, and the probability your company will not be able to pay you back in one year.

2. Based on your answer to the previous question, what would be your discount rate for this bond? Use the present value formulas from the background materials and show your work.

3. Pick two other companies in the same industry as your SLP company. One should be one that you would pay less for a \$1000 bond than you would from your SLP company and another one that you would pay more for a \$1000 bond from your SLP company. Explain why you would pay more or less for their bonds.

# Time Value of Money

Explain the concept of the time value of money. You will need to include and define/explain the concepts of “future value”, annuities, present value, cash flows, compound interest and opportunity cost in your answer

# Time value of money

You were selected as the new Chief Executive Officer of OHC Medical Center, a 600-bed hospital in the suburbs of a city with a population of over 1.5 million. The hospital board recently decided to investigate ways to increase revenues. The facility has the benefit of different revenue streams including patient revenue and money from investments.

The hospital recently sold property for \$100,000. The hospital board wants to invest \$50,000 at 5% in an ordinary annuity and receive annual payments of 10,000 over the next five years. What is the future value of this ordinary annuity investment?

The board is considering other options for investing the remaining money. They want to double their investment of \$50,000 over the next 10 years by using conventional securities with a projected return of 8%. Does the present value of the investment indicate that this is possible?

What is the future value of this ordinary annuity investment?
Does the present value of the investment indicate that this is possible?

Restate the scenario in your response
Identify the key components (PV, FV, i, n)
Present the results as part of your response to these questions.

# Time Value of Money

If you put up \$21,000 today in exchange for a 9.25 percent, 17-year annuity, the annual cash flow will be \$ . (Round your answer to 2 decimal places. Omit the “\$” sign in your response.)

Your company will generate \$61,000 in cash flow each year for the next 9 years from a new information database. The computer system needed to set up the database costs \$292,000. (Round your answer to 2 decimal places. Omit the “\$” sign in your response.)
If you can borrow the money to buy the computer system at 8.5 percent annual interest, the present value of the savings is \$ .

The present value of the revenue greater than the cost, so your company afford the equipment

If you deposit \$1,700 at 8 percent interest at the end of each of the next 18 years you will have \$ in the account. If you make deposits for 36 years, you will have \$ in the account at the end of 36 years. (Round your answers to 2 decimal places. Omit the “\$” sign in your response.)

Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs \$15,000 per year forever. If the required return on this investment is 10 percent, you will pay \$ for the policy. (Round your answer to 2 decimal places. Omit the “\$” sign in your response.)

Present Value and Multiple Cash Flows
Ancelet Co. has identified an investment project with the following cash flows. If the discount rate is 9 percent, the present value of these cash flows is \$ . If the discount rate is 17 percent, the present value of these cash flows is \$ . If the discount rate is 28 percent, the present value of these cash flows is \$ . (Round your answers to 2 decimal places. Omit the “\$” sign in your response.)

Year Cash Flow
1 \$ 1,000
2 700
3 800
4 1,680
________________________________________

Calculating Annuities Due
Suppose you are going to receive \$20,000 per year for twelve years. The appropriate interest rate is 17 percent. (For each step, you must insert rounded answers as directed in the problem. However, when doing the calculations for the next steps, use the complete number (without rounding) for the calculations.)

Requirement 1:
(a) What is the present value of the payments if they are in the form of an ordinary annuity? (Round your answer to 2 decimal places. Omit the “\$” sign in your response.)

Present value \$

Present value \$

Requirement 2:
(a) Suppose you plan to invest the payments for twelve years. What is the future value if the payments are an ordinary annuity? (Round your answer to 2 decimal places. Omit the “\$” sign in your response.)

Future value \$

Future value \$

Requirement 3:
(a) Which has the highest present value, the ordinary annuity or annuity due?

Annuity due

Ordinary annuity

(b) Which has the highest future value?

Annuity due

Ordinary annuity

Calculating Perpetuity Values
Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs \$13,000 per year forever. The policy costs \$202,000. The interest rate that would make this a fair deal is percent.
(Input answer as a percent rounded to 2 decimal places, without the percent sign).

# Time Value of Money

2. The present value of a single sum of \$100 to be received in 10 years and discounted at a annual 12% rate on a semi-annual basis is:

a. \$32.19
b. \$31.18
c. \$100
d. \$310.58
3. The best way to compare two sums to be received at different times in the future is to compute:

a. The present value of each sum.
b. The future value of each sum
c. Compare each sum directly without regard to compound interest
d. None of these

4. Which factor would you use when computing the present value of a series of rent payments, assuming the rent is paid at the beginning of each period as in a standard lease:

a. PVIFA(periods, rate)
b. FVIFA(periods, rate)
c. PVIFA(periods, rate) x (1+rate)
d. PVIF(periods, rate)

# Time Value of Money

Present Value, Future Value and Annuity Due.

1. You will receive \$5,000 three years from now. The discount rate is 8 percent.

a. What is the value of your investment two years from now? Multiply
\$5,000 x .926 (one year’s discount rate at 8 percent).

b. What is the value of your investment one year from now? Multiply your answer to part a by .926 (one year’s discount rate at 8 percent).

c. What is the value of your investment today? Multiply your answer to part b by .926 (one year’s discount rate at 8 percent).

d. Confirm that your answer to part c is correct by going to Appendix B (present value of \$1) for n = 3 and i = 8 percent. Multiply this tabular value by
\$5,000 and compare your answer to part c. There may be a slight difference due to rounding.

2. If you invest \$9,000 today, how much will you have:
a. In 2 years at 9 percent?
b. In 7 years at 12 percent?www.mhhe.com/bhd13e
c. In 25 years at 14 percent?
d. In 25 years at 14 percent (compounded semiannually)?

3. Your uncle offers you a choice of \$30,000 in 50 years or \$95 today. If money is discounted at 12 percent, which should you choose?

# Time Value of Money

The Stein family wants to buy a small vacation house in a year and a half. They expect it to cost \$75000 at that time. They have the following sources of money.

1. They have \$10000 currently in a bank account that pays 6% compounded monthly.
2. Uncle Murray has promised to give them \$1000 a month for 18months starting today.
3. At the time of purchase, they’ll take out a mortgage. They anticipate being able to make payments of about \$300 a month on a 15-year, 12% loan.

In addition, they plan to make quarterly deposits to an investment account to cover any shortfall in the amount required. How much must those additions be if the investment account pays 8% compounded quarterly?

# Time Value of Money

5. Describe the concept of Time Value of Money (TVM). What are its components? why is it a foundational principle of finance? How do organizations and individuals use it ever day

# Time Value of Money

1. Find the present value of a payment stream of \$100 per year for the first fifteen years and \$200 per year for the next five years, given a 12% discount rate.

2.A company stock was priced at \$15 per share two years ago. The stock sold for \$13 last year and now it sells for \$18. What was the total return for owning this company stock during the most recent year? Assume that no dividends were paid and round to the nearest percent.

3.Stock A has a required return of 18% and a beta of 1.4. The expected market return is 14%. What is the risk-free rate?

4.A company is putting out a new product. The product will pay out \$25,000 in the first year, and after that the payouts will grow by an annual rate of 2.5 percent forever. If you can invest the cash flows at 7.5 percent, how much will you be willing to pay for this perpetuity?

5. To pay for school a student need \$12,000 at the end of four years. She can invest a certain amount at the beginning of each of the next four years in a bank account that will pay her 6.8 percent annually. How much will she have to invest annually to reach her target?

6. I plan to start saving for retirement. I will invest \$5,000 at the end of each year for the next 45 years in a fund that will earn a return of 10 percent. How much will I have at the end of 45 years?

7.A renter will be making lease payments of \$3,895.50 for a 10-year period, starting at the end of this year. If the renter uses a 9 percent discount rate, what is the present value of this annuity?

8.A company has generated a net income of \$161,424 this year. The firm expects to see an annual growth of 30 percent for the next five years, followed by a growth rate of 15 percent for each of the next three years. What will be the firm’s expected net income in eight years?

# Time value of money

1.If Ryan who is 27 years old, wants to have one million dollars(today dollars) when he retires at age 65, how much should he save in equal monthly deposits from the end of the next month. Assume his savings earn a rate of 7% per year (A.P.R)

2. If Ryan who is 27 years old, wants to have one million dollars(today dollars) when he retires at age 65, how much can he withdraw each month( beginning one month after his retirement) in equal dollars, if he lives up to age 85. Assume that this investment fund yields a nominal rate of return of 7% per year.

# Time value of money

1-An investment will pay \$ 100 at the end of each of the next 3 years, \$ 200 at the end of Year 4, \$ 300 at the end of Year 5, and \$ 500 at the end of Year 6. If other investments of equal risk earn 8% annually, what is its present value? Its future value?

2- You want to buy a car, and a local bank will lend you \$ 20,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 12% with interest paid monthly. What will be the monthly loan payment? What will be the loan’s EAR?

# Time value of money

? Annsley deposits \$1,000 today into a savings account that pays 3% annual interest. How much will she have in 15 years with annual compounding?

? What is the present value of \$20,000 to be received in 30 years if the appropriate discount rate is 9%?

? How do we determine the appropriate discount rate to use when computing the present value of a certain amount of cash to be received at a certain future point in time?

? For a 4-year car loan in the amount of \$35,000 with an annual interest rate of 6% and monthly payments, what will be the remaining balance on the loan immediately after the first month’s payment is made?

? Suppose you invest \$3,000 per year into an IRA every year for 25 years beginning today. If you earn 7% per year on your investments, what will be the value of your IRA in 25 years?

? Suppose you want to have \$2,000,000 when you retire in 30 years. Assume you will earn 8% per year on your investments. How much would you have to invest at the end of each year for the next 30 years to reach your \$2,000,000 goal?

# Time value of money

Future value: Chuck Tomkovick is planning to invest \$25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years?

5.30 Patrick Seeley has \$2,400 that he is looking to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick’s brother to deliver on his promise?

6.18 Growing perpetuity: You are evaluating a growing perpetuity product from a large financial services firm. The product promises an initial payment of \$20,000 at the end of this year and subsequent payments that will thereafter grow at a rate of 3.4 percent annually. If you use a 9 percent discount rate for investment products, what is the present value of this growing perpetuity?

6.22 Computing annuity payment: Gary Whitmore is a high school sophomore. He currently has \$7,500 in a money market account paying 5.65 percent annually. He plans to use this and his savings over the next four years to buy a car at the end of his sophomore year in college. He estimates that the car will cost him \$12,000 in four years. How much should he invest in the money market account every year for the next four years if he wants to achieve his target?

# Time Value of Money

Bob invested \$2,000 in an investment fund on his 21st birthday. The fund pays 7% interest compounded semiannually. Bob is celebrating his 50th birthday today. Bob decides he wants to retire on his 60th birthday and he wants to withdraw \$75,000 per year, the first withdrawal on his 60th birthday and the last withdrawal on his 90th birthday. Bob expects to receive \$100,000 from his employer on his 55th birthday in recognition of his long service to the company.

Assume Bob has not taken any money out of his investment fund since he initially funded it on his 21st birthday, and that he will deposit the \$100,000 from his employer into the investment fund on his 55th birthday. The investment fund will be used to pay for Bob’s retirement.

a) If Bob makes no additional deposits into his investment fund, how much will be available for retirement at age 60?

b) Since the amount in (a) is insufficient to meet his retirement goals, Bob decides to deposit equal annual amounts into the investment fund beginning on his 51st birthday and ending on his 59th birthday, so that he can meet his retirement goals. How much will each deposit be?

# Time value of money

Hello,
I need some assistance with the attached questions regarding my financial accounting studies.

For example:

P3-6. PV = FVn x (PVIF i%,n)

a. PV = \$ 20,833.50

b. PV = 21,114.00

c. PV = 19,840.00

Please use the above format and provide your answers to the following questions, found in Chapter 4 (Gitman, 2009) pp. 208 – 211:

1. Single payment loan repayment. A person borrows \$200 to be repaid in 8 years with 14% annually compounded interest. The loan may be repaid at the end of any earlier year with no prepayment penalty.

a. What amount will be due if the loan is repaid at the end of year 1
b. What is the repayment at the end of year 4?
c. What amount is due at the end of the 8th year?

2. Present value concept. Answer each of the following questions

a. What single investment made today, earning 12% annual interest, will be worth \$6000 at the end of 6 years?
b. What is the presnet value of \$6000 to be received at the end of 6 years if the discount rate is 12%?
c. What is the most you would pay today for a promise to repay you \$6000 at the end of 6 years if your opportunity cost is 12%?
d. Compare, contrast, and discuss your findings in parts a through c.

3. Time value and discount rates. You just won a lottery that promises to pay you \$1,000,000 exactly 10years from today. Because the \$1,000,000 payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate single cash payment.

a. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 10-year period?
1. 6%
2. 9%
3. 12%

b. Rework part a under the assumption that the \$1,000,000 payment will be received in 15 rather than 10 years
c. On the basis of your findings in parts a and b, discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum.

4. Future value of an annuity. For each case in the accompanying table, anser the questions that follow

Case Ammount of Annuity Interest reate Deposit period (years)
A \$2500 8% 10
B \$500 12% 6
C \$30000 20% 5
D \$11500 9% 8
E \$6000 14% 30

a. Calculate the future value of the annuity assuming that it is
1. an ordinary annuity
2. an annuity due
b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity-ordinary or annuity due-is preferable? Explain why

5. Value of a retirement annuity. An insurance agent is trying to sell you an immediate retirement annuity, which for a single amount paid today will provide you with \$12000 at the end of each year for the next 25 years. You currently earn 9% on low risk investments comparable to the retirment annuity. Ignoring taxes, what is the most you would pay for this annunity?

——————————-

Henderson Electric Inc., a maker of electronic surveillance equipment, is considering selling to a well-known hardware chain the rights to market its home security system. The proposed deal calls for the hardware chain to pay Henderson \$30,000 and \$25,000 at the end of years 1 and 2 and to make annual year-end payments of \$15,000 in years 3 through 9. A final payment to Henderson of \$10,000 would be due at the end of year 10.

a. Lay out the cash flows involved in the offer on a time line.

b. If Harte applies a required rate of return of 12% to them, what is the present value of this series of payments?

c. A second company has offered Henderson an immediate one-time payment of \$100,000 for the rights to market the home security system. Which offer should Henderson accept and why?

# Time Value of Money

Ashley Cambry is planning for her retirement. She already has \$12,500 in a retirement plan and will deposit \$500 a month for the next 20 years. Her account manger says she will be earning 8.00% on an annual basis on this account at the time of retirement and Ashley plans to withdraw a sum each month during her 15 retirement years and then leave \$120,000 to the College at the end of 15 ears to furnish a student lounge. During retirement her account will be earning a 6.00% return on an annual basis.

a. How much will Ashley be able to withdraw each month during retirement?

b. Instead of 6.00% what would Ashley’s rate-of-return after retirement have to be so that she could withdraw \$3,500 a month and still leave the same amount for the student lounge?

# Time value of money

1) If you borrow \$20,000 at the interest rate of 10%, what are the end-of-year payments if the loan is for five years? If the interest rate is 12.5% would the monthly payment be higher/lower

** I cant figure out the monthly payments at 12.5%. I have \$5,275 a year for the first part

2) If you want to have \$800,000 for retirement in 20 years and have only \$100,000 saved today, how much do you need to put away at the end of each year until retirement if your assets can earn 8% per year?

3) If a stock is paying \$2.50 per year in dividends, and is expected to continue this indefinitely, with a required rate of return of 8% what is the value of the stock

# Time Value of Money

What is the “time value of money” and how does it affect a financial manager’s decision regarding cash flows?

What is an annuity? Why might annuities be useful to a corporation?

In computing the cost of capital, do we use the historical costs of existing debt and equity or the current costs as determined in the market? Why?

How is valuation of any financial asset related to future cash flows? Give at least 1 example.

# Time Value of money

Hello, can you please provide the answers and show full calculations and explanations of each of the problems. Thank you.

Assume that you are nearing graduation and that you have applied for a job with a local bank. As part of the Bank’s evaluation process, you have been asked to take an examination that covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions.

a. Draw a time line for:
(1) A \$100 lump sum cash flow at the end of year 2,
(2) An ordinary annuity of \$100 per year for 3 years, and
(3) An uneven cash flow stream of -\$50, \$100, \$75, and \$50 at the end of Years 0 through 3.

b. (1) what is the future value of an initial \$100 after 3 years if it is invested in an account paying 10% annual interest?
(2) What is the present value of \$100 to be received in 3 years if the appropriate interest rate is 10%?

c. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. For example, if a company’s sales are growing at a rate of 20% per year, how long will it take sales to double?

d. If you want an investment to double in 3 years, what interest rate must it earn?

e. What is the difference between an ordinary annuity and an annuity due?
What type of annuity is shown below? How would you change it to the other type of annuity?

0 1 2 3 years

100 100 100

f. (1) what is the future value of a 3-year ordinary annuity of \$100 if the appropriate interest rate is 10%?
(2) What is the present value of the annuity?
(3) What would the future and present values be if the annuity were an annuity due?

g. What is the present value of the following uneven cash flow stream? The appropriate interest rate is 10%, compounded annually.

0 1 2 3 4
0 100 300 300 -50

h. (1) define:
(a) the stated, or quoted, or nominal rate (INOM) and
(b) the periodic rate (IPER).

(2) Will the future value be larger or smaller if we compound an initial amount more often than annually, for example, every 6 months, or semi-annually, holding the stated interest rate constant? Why?

(3) What is the Future value of \$100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding?
(4) What is the effective annual rate (EFF%)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?

i. Will the effective annual rate ever be equal to the nominal (quoted) rate?

j. (1) construct an amortization schedule for a \$1,000, 10% annual rate loan with 3 equal installments.
(2) What is the annual interest expense for the borrower, and the annual interest income for the lender, during year 2?

k. Suppose on January 1 you deposit \$100 in an account that pays a nominal, or quoted, interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account October 1, or after 9 months?

l. (1) What is the value at the end of year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually?

0 1 2 3 years

100 100 100
(2) What is the PV of the same stream?

(3) Is the stream an annuity?

(4) An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: think of annual compounding, when INOM = EFF% = IPER.) What would be wrong with your answer to question 1-(1) and 1-(2) if you used the nominal rate (10%) rather than the periodic rate (I NOM/2 = 10% /2 = 5%)?

m. Suppose someone offered to sell you a note calling for the payment of \$1,000 fifteen months from today. They offer to sell it to you for \$850.00. You have \$850.00 in a bank time deposit that pays a 6.76649% nominal rate with daily compounding , which is a 7% effective annual interest rate, and you plan to leave the money in the bank unless you buy the note. The note is not risky- you are sure it will be paid on schedule. Should you buy the note? Check the decision in three ways: (1) by comparing your future value if you buy the note versus leaving your money in the bank, (2) by comparing the PV of the note with your current bank account, and (3) by comparing the EFF% on the note versus that of the bank account.

# Time Value of Money

Beverly started a paper route on January 1, 1995. Every three months, she deposits \$300 in her bank account, which earns 8 percent annually but is compounded quarterly. On December 31,1998, she used the entire balance in her bank account to invest in a certificate of deposit at 12 percent annually. How much will she have on December 31, 2001?

# Time Value of Money

Your grandfather has offered you a choice of one of the three following alternatives: \$5,000 now; \$1,000 a year for eight years; or \$12,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?

# Time Value of Money

Your girlfriend just won the Florida lottery. She has the choice of \$15,000,000 today or a 20-year annuity of \$1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity?

A. 2.79%
B. 3.10%
C. 3.44%
D. 3.79%
E. 4.17%

# Time Value of Money

What is the present value of the following cash flow stream at an interest rate of 12.0% per year? \$0 at Time 0; \$1,500 at the end of Year 1; \$3,000 at the end of Year 2; \$4,500 at the end of Year 3; and \$6,000 at the end of Year 4.

A. \$9,699.16
B. \$10,209.64
C. \$10,746.99
D. \$11,284.34
E. \$11,848.55

# Time Value of Money

1. At age 25 you invest \$2,000 that earns 6 percent each year. At age 35 you invest \$2,000 that earns 9 percent per year. In which case would you have more money at age 60?

2. You are evaluating the balance sheet for Blue Jays Corporation. From the balance sheet
you find the following balances: Cash and marketable securities = \$200,000, Accounts receivable = \$800,000, Inventory = \$1,000,000, Accrued wages and taxes = \$250,000, Accounts payable = \$400,000, and Notes payable = \$300,000. What are Blue Jay’s Current ratio, Quick ratio, and Cash ratio, respectively?

3. Jack and Jill Corporation’s year-end 2009 balance sheet lists current assets of \$250,000, fixed assets of \$800,000, current liabilities of \$195,000, and long-term debt of \$300,000. What is Jack and Jill’s total stockholders’ equity?

4. Assume that you are saving for your retirement and want to do so using an annuity saving plan that is you will deposit the same amount of funds into your saving account each month. Clearly the length of time you are saving is very important in accumulating your wealth. What other factor(s) also affect your wealth?

6. Suppose that when Apple invests in the resources necessary to create new technology products,
it expects to earn a 20% rate of return. Suppose also that when it invests its cash in bank accounts it earns just 1%. Given this, what rate of return should investors expect if they pay \$200 to acquire one share of Apple?

7. What role do you think market efficiency (or inefficiency) played in the 10 percent fall of JPMorgan’s share price in a single day?

8. Assume that the \$1 billion cost of bringing a new drug to market is spread out evenly over 10 years, and then 10 years remain for Eli Lilly to recover the investment. How much cash would a new drug have to generate in the last 10 years to justify the \$1 billion spent in the first 10 years?

# Time Value of Money

Time Value of Money

Time Value of Money is one of the most important concepts in the financial world. The principles of time value analysis have many applications, ranging from setting up schedules for paying off loans to decisions about whether to acquire new equipment for a company. Time value of money is also called discounted cash flow analysis.

Apply the concept of present value to Under Armour, Inc. Suppose Under Armour, Inc is selling a bond that will pay you \$2,000 in one year from today. Keep in mind that if Under Armour, Inc has financial difficulties in one year you might not get your full \$2,000 back. Given that a dollar one year from now is always worth less than a dollar today, you most certainly would not pay a full \$2,000 for this bond.

If you are highly risk averse or strongly prefer having money today to having money tomorrow, then you would pay significantly less than \$2,000 for this bond. Higher inflation or high interest rates would also lead you to pay less for the bond. Also, the greater the chance of bankruptcy of your company the less you should be willing to pay for the bond.

Given the concepts of the time value of money :

1) How much would you pay for this bond today? Take into consideration your own personal risk preferences, interest rates, inflation, and the probability your company will not be able to pay you back in one year. Note: no need for any math equations for this part. How much you would personally pay for a \$2,000 bond from Under Armour, Inc.

2) Based on your answer to the previous question, what would be your discount rate for this bond? Use the present value formulas.

3) Pick two other companies in the same industry. One should be one that you would pay less for a \$2,000 bond than you would from Under Armour, Inc and another one that you would pay more for a \$2,000 bond from Under Armour, Inc. Would pay more or less for their bonds.

# Time Value of Money

Calculate the future value of the following:

a. \$49,298 if invested for five years at a 7% interest rate

b. \$79,119 if invested for three years at a 4% interest rate

c. \$69,124 if invested for seven years at an 2% interest rate

d. \$39,929 if invested for ten years with a 0.9% interest rate

3) Calculate the present value of the following:

a. \$105,126 to be received three years from now with a 4% Interest rate

b. \$228,231 to be received five years from now with a 5% interest rate

c. \$192,000 to received two years from now with a 12% interest rate

d. \$998,111 to be received eight years from now with a 1% interest rate.

4) Suppose you are to receive a stream of annual payments (also called an “annuity”) of \$72,394 every year for three years starting this year. The interest rate is 4%. What is the present value of these three payments?

5) Suppose you are to receive a payment of \$189,299 every year for three years. You are depositing these payments in a bank account that pays 2% interest. Given these three payments and this interest rate, how much will be in your bank account in three years?

# Time Value of Money

You have been asked to assist your friends with some personal financial planning. Following their current budget they find they are able to save approximately \$10,000 per year. They expect their investments to grow at a nominal rate of 8% and you expect inflation to remain at approximately 4% per year. Your friends expect to retire in 30 years.

a. How much money will they have available at their retirement date?
b. What will that amount be worth in today’s dollars?

# Time Value of Money

Question 1
Pacific Homecare has three bond issues outstanding. All three bonds pay \$100 in annual interest plus \$1,000 at maturity. Bond S has a maturity of five years, Bond M has a 15-year maturity, and Bond L matures in 30 years.
a. What is the value of these bonds when the required interest rate is 5 percent, 10 percent, and 15 perrcent?
b. Why is the price of Bond L more sensitive to interest rate changes than the price of Bond S?

Question 2
Six years ago, Bradford Community Hospital issued 20-year municipal bonds with a 7 percent annual coupon rate. The bonds were called today for a \$70 call premium-that is, bondholders received \$1,070 for each bond. What is the realized rate of return for those investors who bought the bonds for \$1,000 when they were issued?

# Time Value of Money

1. Hayley makes annual end-of-year payments of \$6,260.96 on a five-year loan with an 8 percent interest rate. The original principal amount was

1. \$25,000.
2. \$30,000.
3. \$31,000.
4. \$20,000.

2.Nico makes annual end-of-year payments of \$5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was

1. \$24,462.
2. \$20,175.
3. \$ 3,092.
4. \$15,000.

3.If a United States Savings bond can be purchased for \$29.50 and has a maturity value at the end of 25 years of \$100, what is the annual rate of return on the bond?

1. 5 percent
2. 6 percent
3. 8 percent
4. 7 percent

4.The present value of a \$25,000 perpetuity at a 14 percent discount rate is

1. \$350,000.
2. \$219,298.
3. \$285,000.
4. \$178,571.

5.Jia borrows \$50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year loan payment is

1. \$10,774.
2. \$15,773.
3. \$14,340.
4. \$12,500.

# Time Value of Money

4-1 If you deposit \$10,000 in a bank that pays 10% interest annually, how much will be in your account after 5 years.

4-2 What is the present value of a security that will pay \$5,000 in 20 years if securities of equal risk pay 7% annually?

4-3 Your parents will retire in 18 years. They currently have \$250,000 and they think they will need \$1 million at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?

4-4 If you deposit money today in an account that pays 6.5% annual interest, how long will it take to double your money?

4-5 You have \$42,180.53 in a brokerage account, and you plan to deposit an additional \$5,000 at the end of every future year until your account totals \$250,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal?

4-6 What is the future value of a 7%, 5-year ordinary annuity that pays \$300 each year? If this were an annuity due, what would its future value be?

4-7 An investment will pay \$100 at the end of each of next 3 years, \$200 at the end of Year 4, \$300 at the end of Year 5, and \$500 at the end of Year 6. If the other investments of equal risk earn 8% annually, what is this investment’s present value? Its future value?

# Time value of money

Gordon Company issued \$1,000,000, 10-year bonds and agreed to make annual sinking fund deposits of \$80,000. The deposits are made at the end of each year into an account paying 5% annual interest. What amount will be in the sinking fund at the end of 10 years?

# Time value of money

My corporation loans money to a subsidiary, in the amount of \$600,000. We accept an 8% note due in 7 yrs. with interest payable semi-annually. After 2 yrs. (and receipt of interest for 2 yrs), we need money, therefore we sell the note to Bank of America, which demands interest on the note of 10% compounded semi-annually. What is the amount we will receive on the sale of the note? (Do not use financial calculator.)

# Time value of money

4. What are the underlying concepts behind time value of money?

# Time Value of Money

What does that term “time value of money” mean and how does it relate to the calculation of interest, present values of annuities, and payments to amortize a loan?

# Time Value of Money

1. Your wealthy aunt has just established a trust fund for you that will accumulate to a total of \$1000, 000 in 12 years. Interest on the trust fund is compounded annually at an 8 percent interest rate. How much is in the trust fund today?

2. On Jan. 1, you will purchase a new car. The car dealer will allow you to make increasing annual Dec. 31 payments over the following four years. The amounts of these payments are \$4,000; \$4,500; \$5,000; \$6,000. On Jan 1, your mother will lend you just enough money to enable you to meet these payments. Interest rates are expected to be 8 percent for the next five years. Assuming that you can earn annual compounding interest by depositing the loan from your mother in a bank, what is the minimum amount your mother must loan you to enable you to meet the car payments?

3. In a settlement of a claim for your recently wrecked car, your insurance company will pay you either a lump sum today or three annual payments of \$3,100 starting one year from now. Interest rates are expected to be 6 percent for the next five years. What is the least amount of money that you should be willing to accept today?

4. What is the present value of \$3,000 a year to be received in years 3 through 11, assuming a 12 percent discount rate?

# Time value of money

You want to purchase a boat that costs \$40,000. you want to finance as much of the purchase as possible with a 5-year bank loan at 12% compounded monthly, but you can only afford loan payments of \$750 per month. how much will you need as a down payment to buy the boat?

# Time Value of Money

Minnesota Metal Forming Company has just invested \$500,000 of fixed capital in a manufacturing process, which is estimated to generate an after-tax annual cash flow of \$200,000 in each of the next 5 years. At the end of year 5, no further market for the product and no salvage value for the manufacturing process is expected. If a manufacturing problem delays plant start-up for 1 year (leaving only 4 years of process life), what additional after-tax cash flow will be needed to maintain the same internal rate of return as would be experienced if no delay occurred?

# Time Value of Money

You are saving for the college education of your two children. One child will enter college in 5 years, while the other child will enter college in 7 years. College costs are currently \$10,000 per year and are expected to grow at a rate of 5 percent per year. All college costs are paid at the beginning of the year. You assume that each child will be in college for four years.

You currently have \$50,000 in your educational fund. Your plan is to contribute a fixed amount to the fund over each of the next 5 years. Your first contribution will come at the end of this year, and your final contribution will come at the date at which make the first tuition payment for your oldest child. You expect to invest your contributions into various investments which are expected to earn 8 percent per year. How much should you contribute each year in order to meet the expected cost of your children’s education?

(b) If you wanted to be safe and assume that your investments would earn 5 percent per year, how much should you contribute each year. SUGGESTION: START WITH A TIME LINE.

# Time Value of Money

A) Joe won a lottery jackpot that will pay him \$12,000 each year for the next ten years. If the market interest rates are currently 12%, how much does the lottery have to invest today to pay out this prize to Joe over the next ten years?

b) Mary just deposited \$33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in the account at the end of the seventh year?

c) Mary and Joe would like to save up \$10,000 by the end of three years from now to buy new furniture for their home. They currently have \$2500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 8% interest, how much should the year end payments be?

# Time value of money

The Acme Company must solve a series of five problems that require you to apply the concept of “time value of money,” or TVM. The five problems are listed below. Solving them will require the use of Microsoft Excel. Before you begin your work, each student is to select a unique nine-digit random number that contains no zeros, no “patterns,” and should use most of the digits between one and nine. This value will be referred to as the student unique number (SUN). Further, digits within the SUN are read from left to right. For example, if the SUN = 123456789, the first digit = 1, the second digit = 2, etc. Please note that the interest rate used in all questions represents an annual rate and all dollar figures are in whole dollars (not dollars and cents).

1. Acme plans to construct a new manufacturing facility in 14 years. If Acme estimates that today’s cost of the new plant is SUN dollars (use all 9 digits) and annual inflation is A% (A = the first digit of SUN), how much will the manufacturing plant cost in 14 years?

2. Acme has decided to establish a sinking fund for its outstanding preferred stock issue. SUN (use all 9 digits) represents the amount of the issue that will be retired in 26 years. At the beginning of each of these 26 years, Acme will deposit an equal amount into an account that earns B% (B = the second digit of SUN). What is the value of this periodic deposit?

3. One of Acme’s new projects will generate the following cash flows at the end of each of the stated years: year 1 = SUN digits 1-3; year 3 = SUN digits 4-6; year 5 = SUN digits 7-9. If these cash flows are discounted at 12%, what is the sum of their present values?

4. Acme is assessing its employee pension fund. At the end of each of the next 23 years Acme will have to pay its retirees (use the first 4 digits of your SUN). If the fund is estimated to earn D% (D = the fourth digit of SUN), how much does Acme need to have set aside today to ensure that it can meet its future obligations? (At the end of the 23th year, the balance should be drawn down to zero.)

5. As part of a new labor contract, Acme has agreed to make a one-time contribution of \$1,000,000 to the construction of a new physical fitness facility for its employees. It is estimated that in E years (E = 10 + the fifth digit of SUN) the total cost of the new gym will be \$1,850,000. What annual percentage interest rate must the initial contribution earn to attain the required amount in E years? (Note: your answer should be accurate to two decimal places – e.g., 5.79%.)

Prepare for Acme’s CFO an analysis that contains solutions for all five problems. Be sure to clearly present and label all values and variables, provide Excel TVM formulas, and conclude each question with a brief interpretation of your results. Your entire submission must be contained within an Excel document. (Note: You must use Excel TVM functions to complete this assignment; using a hand calculator or website and plugging values into a template is not acceptable.)

# Time Value of Money

Identify and describe at least one financial application of Time Value of Money employed by each of the following businesses:

Commercial banks

Credit card financial service companies

Insurance companies

State governments – lotteries

Retirement plan financial service providers

# Time Value of Money

1. Over the past several years, Helen Chang has been able to save regularly. As a result, today she has \$14,188 in savings and investments. She wants to establish her own business in 5 years and fells she will need \$50,000 to do so.

a. If Helen can earn 12% on her money, how much will her \$14,188 be worth in about 5 years? Will Helen have the \$50,000 she needs? If not, how much more will she need?

b. Given your answer to part a, how much will Helen have to save each year over the next 5 years to accumulate the additional money, assuming she can earn interest at a rate of 12%?

c. If Helen can afford to save only \$2000 a year, given your answer to part a, will she have the \$50,000 she needs to start her own business in 5 years?

# Time Value of Money

1. Clarence Weatherspoon, a super salesman contemplating retirement on his 55 birthday, decides to create a fund on an 8% basis that will enable him to withdraw \$20,000 per year on June 30th, beginning in 2014 and continuing through 2017.
To Develop this fund, Clarence intends to make equal contributions on June 30th of each of the years 2010-2013.
a. How much must the balance of the fund equal on June 30, 2013, in order for Clarence Weatherspoon to satisfy his objective.

b. What are each of Clarence’s contributions to the fund?

2. Lance Armstrong Inc. manufactures cycling equipment. Recently the vice president of operations of the company has requested construction of a new plant to meet the increasing demand for the company’s bikes.

After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing \$2,000,000 of 11% term corporate bonds on March 1, 2007, due on March 1, 2022, with the interest payable each March 1 and September 1.

At the time of issuance, the market interest rate for similar financial instruments is 10%.

a. as the controller of the company determine the selling price of the bonds.

3. Andrew Bogut just received a signing bonus of \$1,000,000. His plan is to invest this payment in a fund that will earn 8%, compounded annually.

a. If Bogut plans to establish the AB Foundation once the fund grows to \$1,999,000, how many years until he can establish the foundation?

b. Instead of investing the entire \$1,000,000, Bogut invests \$300,000 today and plans to make 9 equal annual investments into the fund beginning one year from today. What amount should the payments be if Bogut plans ot establish the \$1,999,000 foundation at the end of 9 years?

4. Assume that Sonic Foundry Corporation has contractual debt outstanding. Sonic has available two means of settlement: it can either make immediate payment of \$2,600,000, or it can make \$300,000 payments beginning now and be made on the first day of each of the 15 years.

a. What payment method would you recommend?

# Time value of money

The Acme Company must solve a series of five problems that require you to apply the concept of “time value of money,” or TVM. The five problems are listed below solving them will require the use of Microsoft Excel. Before you begin you work, each student is to select a unique nine-digit random number that contains no zeros, no “patterns,” and should yes most of the digits between on and nine. This value will be referred to as the student unique number (SUN). Further, digits within the SUN are read from left to right. For example, if the SUN=123456789, the first digit=1, the second digit=2, etc. Please note that the interest rate used in all questions represents an annual rate and all dollar figures are in whole dollars (not dollars and cents).

# Time value of money

Your brother is 55 years old now and his current savings declined to \$500000 and he does not feel this is sufficient ,so he works for another 10 years to retire at age 65.He expects to live for another 20 years after he retires he wants to have \$100000 to live on each of the 20 years ,the first payment occuring at the time of retirement at 65 years. He will the recieve an additional payment each year for more 19 years . His account will pay 5% annually.

1. How much he should accumulated into his account on the date of retirement 65 to be able to make payments ?

2.How much must he put aside each of next 10 years to achieve this if the payments are made at the end of year starting on his 56 th birthday and his \$500000 is still safe.

3.Assume that yours brother is only 45 and he has 20 years to make payments before retiring .how much would he have had to put aside each of the 20 years to achieve his retirement goal?The payments are made at the end of the year starting on 46 th birthday.

# Time Value of Money

Use nominal rate 4.8% compounded monthly:

(1) James and Jane retire with \$500,000 in their retirement account. If they want that to last for 25 years, how much can they take out each month.

(2) Nick and Nora are 30 and intend to retire at age 65; they are just starting a retirement plan. How much must they deposit each month so that after retirement, they can draw out \$3,500 each month for 20 years?

(3) Mick and Moira are 30 and intend to retire at age 65; they are just starting a retirement plan. How much must they deposit each month so that after retirement, they can take out \$30,000 for a wild vacation and then draw out \$3,500 each month for 20 years?

# Time value of money

See attached file for full problem description. I also attached the relevant lecture slide.

# Time Value of Money

Q1: You are saving for retirement. To live comfortably, you decide you will need to save \$2 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 5%, how much must you set aside each year to make sure that you will have \$2 million in the account on your 65th birthday?

Q2: You realize that the plan above has a flaw. Because your income will increase over your lifetime, it would be more realistic to save less now and more later. Instead of putting the same amount aside each year, you decide to let the amount that you set aside grow by 7% per year. Under this plan, how much will you put into the account today? (Recall that you are planning to make the first contribution to the account today.)

# Time Value of Money

The Time Value of Money

You have been asked by the local elementary school to come and explain the concept of the time value of money.

a) Discuss this topic as you might explain it to an 8-year old child. What would you say?

b) What demonstration will you perform to help them understand the topic?
Submit thoughtful, substantial, and appropriate responses early in the week to allow time for your peers to read and review them.

c) Is the explanation of the concept and demonstration effective and appropriate for an 8-year old child? Support your comments with valid reasons.

# Time Value of Money

1. John Smith has received a \$1,000,000 gift from his grandmother. Below are two alternatives for investment. Calculate the current value of each. Which investment should John choose and why?

A. Invest in a one year government security yielding 5%.
B. Invest in real estate with some risk. John has found a piece of property for \$1,000,000 that is forecasted to be worth \$1,100,000 after one year.

2. Tom Jones is 65 years of age and has a life expectancy of 12 more years. He wishes to invest \$20,000 in an annuity that will make a level payment at the end of each year until his death. If the interest rate is 8%, what income can Mr. Jones expect to receive each year?

3. Evaluate the three investment opportunities for bonus of \$1,000 you just received. Find the values at 1 year, 5 years, and 20 years. Indicate which opportunity is the best for each of time periods.

A. An account paying 12% interest compounded annually.
B. An account paying 11% interest compounded semi-annually.
C. An investment that will pay you 14% annual interest only at the end of the investment period. of 1 year, 5 years, or 20 years.

# Time Value of money

Suppose the risk-free interest rate is 4%.

a. Having \$200 today is equivalent to having what amount in one year?
b. Having \$200 in one year is equivalent to having what amount today?
c. Which would you prefer, \$200 today or \$200 in one year? Does your answer depend on when you need the money? Why or why not?

# Time Value of Money

You want to buy your dream car, but you are \$5,000 short. If you could invest your entire savings of \$2,350 at an annual interest of 12%, how long would you have to wait until you have accumulated enough money to buy the car?

# Time value of money

In a Word document, please explain the following questions below. Very importantly – show all your work showing all of your steps and demonstrate a good understanding of the time value of money so I’ll know what you’re talking about.
1. In two to three paragraphs, explain why the concept of present value is so important for corporate finance and is often the very first topic taught in any finance class.
2. Calculate the future value of the following:
a. \$600 if invested for five years at a 3% interest rate
b. \$400 if invested for three years at a 5% interest rate
c. \$1100 if invested for seven years at an 11% interest rate
d. \$900 if invested for ten years with a 0% interest rate
3. Calculate the present value of the following:
a. \$2200 to be received three years from now with a 5% discount rate
b. \$950 to be received five years from now with a 11% interest rate
c. \$2150 to received two years from now with a 24% interest rate
d. \$145,000 to be received eight years from now with a 7% interest rate.
4. Suppose you are to receive a stream of annual payments (also called an “annuity”) of \$9000 every year for three years starting this year. The discount rate is 6%. What is the present value of these three payments?
5. Suppose you are to receive a payment of \$5000 every year for three years. You are depositing these payments in a bank account that pays 2% interest. Given these three payments and this interest rate, how much will be in your bank account in three years?

# Time Value of Money

I have to answer the questions below.

What is the difference between present values and future values?

How would you use present and future value techniques in preparing a financial plan for retirement?

How would various required rates of return affect your decision?

# Time Value of Money

Joe won a lottery jackpot that will pay him \$12,000 each year for the next ten years. If the market interest rates are currently 12%, how much does the lottery have to invest today to pay out this prize to Joe over the next ten years?

b) Mary just deposited \$33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in the account at the end of the seventh year?

c) Mary and Joe would like to save up \$10,000 by the end of three years from now to buy new furniture for their home. They currently have \$2500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 8% interest, how much should the year end payments be?

Show work.

# Time Value of Money

1) Joe won a lottery jackpot that will pay him \$12,000 each year for the next ten years. If the market interest rates are currently 12%, exactly how much should the lottery invest today, assuming end of year payments, so there will be nothing left in the account after the final payment is made?

2) Mary just deposited \$33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in the account at the end of the seventh year?

3) Mary and Joe would like to save up \$10,000 by the end of three years from now to buy new furniture for their home. They currently have \$2500 in a savings account set aside for the furniture. They would like to make equal year end deposits to this savings account to pay for the furniture when they purchase it three years from now. Assuming that this account pays 8% interest, how much should the year end payments be?

Show all work for each assignment and explain each step carefully.

# Time Value of Money

IRA Investments develops retirement programs for individuals. You are 30 years old and plan to retire on your 60th birthday. You want to establish a plan with IRA that will require a series of equal, annual, end-of-year deposits into the retirement account. The first deposit will be made 1 year from today on your 31st birthday. The final payment on the account will be made on your 60th birthday. The retirement plan will allow you to withdraw \$120,000 per year for 15 years, with the first withdrawal on your 61st birthday. Also at the end of the 15th year, you wish to withdraw an additional \$250,000. The retirement account promises to earn 12 percent annually.

What periodic payment must be made into the account to achieve your retirement objective?

# Time value of money

Keith Stone has 10-year old daughter, Kate, who will be entering college in 8 years. Keith estimate college costs to be \$16,000 \$17,000, \$18,000 and \$19,000 payable at the beginning of each of Kate’s four years in college. He has \$2,000 in his account and intends to leave it there for the next 8 years.

How much more must Keith save each year (assume end of the year payments) for each of the next 8 years to have enough savings to pay for his daughter? Assume Keith can earn 9% on his savings.

# Time Value of Money

1. You want to put some money away for your child’s college education. College will cost \$65,000 in 18 years. You can earn 8% compounded annually. How much do you need to invest?

2. In order to help you through college, your parents just deposited \$25,000 into a bank account paying 8% interest. Starting next year, you plan to withdraw equal amounts for the account at the end of each of the next four years. What is the most you can withdraw annually?

3. What is the market value of a bond that will pay a total of forty semiannual coupons of \$50 each over the remainder of its life? Assume the bond has a \$1,000 face value and an 8% yield to maturity (YTM).

4. What would you pay for a bond that pays an annual coupon of \$35, has a face value of \$1,000, matures in 7 years, and has a yield to maturity (YTM) of 8%?

5. What would you pay for a share of ABC Corporation stock today if the next dividend will be \$2 per share, your required return on equity investments is 12%, and the stock is expected to be worth \$110 one year from now?

# Time value of money

I need to discuss the answers in class. Just wanted to double check my answers to be sure.

1. Polly Graham will receive \$12,000 a year for the next 15 years as a result of her patent. If a 9 percent rate is applied, should she be willing to sell out her future rights now for \$100,000?

2. The Clearinghouse Sweepstakes has just informed you that you have won \$1 million. The amount is to be paid out at the rate of \$20,000 a year for the next 50 years. With a discount rate of 10 percent, what is the present value of your winnings?

3. Juan Garza invested \$20,000 10 years ago at 12 percent, compounded quarterly. How much has he accumulated?

4. Exodus Limousine Company has \$1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 50 years. Compute the current price of the bonds if the percent yield to maturity is:

a. 5 percent.
b. 15 percent.

5. Venus Sportswear Corporation has preferred stock outstanding that pays an annual dividend of \$12. It has a price of \$110. What is the required rate of return (yield) on the preferred stock?

6. Static Electric Co. currently pays a \$2.10 annual cash dividend (D0). It plans to maintain the dividend at this level for the foreseeable future as no future growth is anticipated. If the required rate of return by common stockholders (Ke) is 12 percent, what is the price of the common stock?

7. Sullivan Cement Company can issue debt yielding 13 percent. The company is paying a 36 percent rate. What is the aftertax cost of debt?

8. You buy a new piece of equipment for \$16,980, and you receive a cash inflow of \$3,000 per year for 12 years. What is the internal rate of return?

# Time value of money

1. How long will it take double if invested at 12% compounded monthly?

2. Colortime Rent To Own sells a compact disk stereo for \$3,000. You pay one third down and amortize the rest with equal payments over a 2 year period. If you are charged 1.5% interest per month on the unpaid balance.
a) What is your monthly payment?
b) How much interest will you pay over the 2 years?

3.Two years ago you borrow \$10,000 at 12% interest compounded monthly which was to be amortized over 5 years. Now you have acquired some additional funds and decide that you want to pay off this loan. What is the unpaid balance after making equal monthly payments for 2 years?

a) Find the monthly payment
b) Find the present market value of \$222.44 a month 5 year annuity (3 years left)

4.Starting on his 21st birthday, and continuing on every birthday up to and including his 65th, if the account earns:
a) 7% compounded annually
b) 11% compounded annually

5.A company established a sinking fund for plant retooling in 6 years at an estimated cost of \$850,000.
a)How many should be invested semiannually into an account paying 8.76% compounded semiannually?
b)How much interest will you earn in the 6 years?

# Time value of money

1.A salesperson tells you that you can buy the car you are looking at for \$3000 down and \$200 a month for 48 months. If interest is 14% compounded monthly:

a)What is the selling price car?

b)How much interest will you pay during the 48 months?

2.A man deposits \$2000 in an IRA on his 21st birthday and on each subsequent birthday up to and including his 29th birthday (9 deposits in all). The account earns 8% compounded annually.

a)If he leaves the money in the account without making any more deposits, how much will he have on his 65th birthday, assuming the account continues to earn the rate of interest?

b)(same man as in question part a) How much would be in the account on his 65th birthday, assuming the account continues to earn the same rate of interest?

3. A loan company will loan up to 60% of the equity in a home. A family purchase their home 8 years ago for \$83,000. The home was financed by paying 20% down and signing a 30 year mortgage at 11.25% for the balance. Equal monthly payments were made to amortize the loan over the 30 year period. The market value of the house is now \$95,000. After making 96th payment, the family applied to the loan company for the maximum loan. How much will they receive?

# Time value of Money

Identify at least one financial application of TVM employed by each of the following businesses:

Commercial banks

Credit card financial service companies

Insurance companies

State governments – lotteries

Retirement plan financial service providers

# Time value of money

Find the present value and the amount of interest earned. Use the present value of a dollar table.
Round to the nearest cent as needed.
Amount needed \$11,200
Time (years) 10
Interest 4%
Compounded semiannually
Present value \$ ____________________
Interest earned \$ ____________________

Amount needed \$18,640
Time (years) 7
Interest 6%
Compounded quarterly
Present value \$ ________________
Interest earned \$ ________________

Amount needed \$18,948
Time (years) 12
Interest 6%
Compounded quarterly
Present value \$ ______________
Interest earned \$ ______________

In 6 years, Mrs. Folkers may pay off a note with a face value of \$14,000, and interest of 10% per year, compounded semiannually. Find the future value of the note. Then find the amount that the holder of the note should accept as a complete payment today if money can be invested at 8% per year, compounded quarterly. Round to the nearest cent.
What is the maturity value of the note? \$ ___________________
How much money should the holder of the note accept as complete payment today? \$ _____

Find the present value and the amount of interest earned.
Amount needed \$12,700
Time (years) 6
Interest 8%
Compounded annually
Present value \$ _____________
Interest earned \$ _____________

A company recently expanded their assemble operations at a cost of \$490,000. Management expects that the investment will grow at a rate of 14% per year compounded annually for the next 5 years. Find the future value of the investment. Then find the present value of that amount at a rate of 8% per year compounded annually.
What is the future value of the investment? \$ ____________________
What is the present value of that future value? \$ __________________

Mr. Jordan wants all of his grandchildren to go to college and decides to help financially. How much must he give to each child a birth if they are to have \$16,917 at entering college 18 years later, assuming 5% interest compounded annually?
How much should he give each child at birth? \$ ______________

# Time Value of Money..

THANKS

I NEED HELP WITH THE ANNUITY PAYMENT (HIGHLIGHTED IN YELLOW) WHICH HAS TO BE POSITIVE AND NOT NEGATIVE.

Directly below these instructions is a blank table to compute PV factors.
Using cell formulas or functions, calculate the PV for the years and interest rates
given. Remember, only use cell formulas and reference the years and interest
rates that are on the borders of the table. Following the tables are TVM problems that
require that you calculate PV, FV, periods, or the interest rate. The answer cell is the
yellow shaded cell. Place your solution in the yellow cell provided below each problem.
Remember use cell formulas throughout. Also, you may use Excel =functions.
The =PV =FV =NPV =IRR =RATE may be helpful. Never hardcode numbers in the
cell formulas. For example, do not put the interest rate or periods in the cell formula,
only reference the proper cell on the border of the table.

Do not add or delete columns or rows, the cell references must be the same as my original.

# Time Value of Money

On a contract, you have a choice of receiving \$25,000 six years from now or \$50,000 twelve years hence. What is the implied discount rate that equates these two amounts?

# Time Value of Money

1. Alexis Mantle recently won a lottery and has the option of receiving one of the following three prizes: (1) \$64,000 cash immediately, (2) \$20,000 cash immediately and six-period annuity of \$8,000 beginning one year from today, or (3) a six-period annuity of \$13,000 beginning one year from today. Assuming an interest rate of 6%, which option should Alex choose?

2. The Maris Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2015. Maris will make annual deposits of \$100,000 into a special bank account at the end of each of 10 years beginning December 31, 2006. Assuming the bank account pays 8% interest compounded semiannually, what will be the fund balance after the last payment is made on December 31, 2015?

3. Don Larsen purchased a new automobile for \$20,000. Don made a cash down payment of \$5,000 and agreed to pay the remaining balance in 30 monthly installments, beginning one month from the date of purchase. Financing is available at a 24% annual interest rate. Calculate the amount of the required monthly payment.

4. Mays Warehouse borrowed \$100,000 from a bank and signed a note requiring 20 annual payments of \$13,388 beginning one year from the date of the agreement. Determine the interest rate implicit in this agreement.

5. On September 30, 2006, the Roberto Clemente Corporation issued 8% stated rate bonds with a face amount of \$300 million. The bonds mature on September 30, 2006 (20 years). The market rate of interest for similar bonds was 10%. Interest is paid semiannually on March 31 and September 30. Determine the price of the bonds on September 30, 2006.

6. On June 30, 2006, the Campanella Company purchased equipment from Alston Corp. Campanella agreed to pay Alston \$10,000 on the purchase date and the balance in five annual installments of \$8,000 on each June 30 beginning June 30, 2007. Assuming that an interest rate of 10% property reflects the time value of money in this situation, at what amount should Campanella value the equipment?

7. Reese needs to accumulate sufficient funds to pay a \$400,000 debt that comes due on December 31, 2011. The company will accumulate the funds by making 5 equal annual deposits to an account paying 6% interest compounded annually. Determine the required annual deposit if the first deposit is made today, December 31, 2006.

8. On January 1, 2006 Sal Maglio leased on office building. Terms of the lease require Maglio to make 20 annual lease payments of \$120,000 beginning on January 1, 2006. A 10% interest rate is implicit in the lease agreement. At what amount should Maglio record the lease liability on January 1, 2006, before any lease payment is made?

9. Para Salin and her friends are planning a trip to Europe in a little over 3 years. In order to accumulate enough money for the trip, Para opens a savings account. Assuming an interest rate of 4%, compounded quarterly, how much will she accumulate in 3 years by depositing \$500 at the end of each of the next 12 quarters, beginning three months from now.

10. John Smith is 55 years old and has been asked to accept early retirement from his company. The company has offered John three alternative compensation packages. Which alternative should John choose assuming he is able to invest funds at a 7% rate?

a) \$180,000 cash to be paid immediately.
b) A 20-year annuity of \$16,000 beginning immediately.
c) A 10-year annuity of \$50,000 beginning at age 65

Thank you so much for taking the time to review my post.

# Time value of money

Sharon Smith will receive \$1 million in 50 years. The discount rate is 14. As an alternative, she can receive \$2,000 today. Which should she choose?
\$1 million dollars in 50 years
\$2,000 today
she should be indifferent

# Time Value of Money

Time Value of Money?An Application

If you have \$10 today, you can invest that \$10 and earn interest. If, for example, you earn 5% interest, you will earn \$0.50 interest and have a total of \$10.50 at the end of one year. If you invest the \$10.50 for another year, you will earn \$0.53 interest and have a total of \$11.03 at the end of the second year. In year two, you earned \$0.50 interest on your initial \$10 and \$0.03 interest on the \$0.50 interest earned in year one. Earning interest on interest is called compound interest. The longer you leave your money invested, the greater the compounding effect becomes.

Oftentimes, people project how fast their money will grow and get the idea that they will become so much wealthier sometime in the future. What they often forget is that while their money is growing, the prices of everything they buy are increasing. To really get ahead, your money must grow at a faster pace than the prices of the products you buy.

You would like to take a cruise in six years. The cruise currently costs \$4,250. You expect the price to increase by 4% annually. You can earn 5% on your savings. How much do you need to save at the end of each month so you will be able to afford your cruise in six years?

You invest \$250 in your savings account at the end of each year and earn an average of 6% per year in interest. How much will you have in your savings account at the end of forty years?

You want to have \$40,000 to buy a new boat in six years. How much do you have to save at the end of each year to reach this goal if you earn 5% a year on your savings?

# Time Value of Money

1. A bond is selling for 95% of par and has an annual coupon rate of 6% and will mature in five years. There are semi-annual coupon payments. Calculate the yield-to-maturity.

2. How much money will William have in five years if he places \$2500 into a CD earning an annual interest rate of 7.5% compounded annually?

3. An ordinary annuity has equal periodic cash flows at the_____ of the period and an annuity due has equal periodic cash flows at the_________ of the period.

4. Your firm is planning to invest \$350,000 per year in equal annual end-of-the-year cash flows to fund a capital improvement fund. If the investments are expected to earn 10% per year, how much will the account be worth in 7 years?

5. Your parents put equal annual beginning-of-the-year deposits of \$1,200 into an account earning 8% per year from the day you were born until your 18th birthday (a total of 19 deposits). How much money is in that account today?

6. Tucker Binson put \$5,000 into a three-year CD paying 7% interest compounded quarterly. How much interest will he have earned when the CD matures?

# Time Value of Money

Michael is planning for his son’s college education to begin ten years from today. He estimates the yearly tuition, books, and living expenses to be \$10,000 per year for a four-year degree. How much must Michael deposit today, at an interest rate of 12 percent, for his son to be able to withdraw \$10,000 per year for four years of college?

# Time value of money

Find the following values, using equations. Disregard rounding the differences.

A) an initial \$500 compounded for 1 yr at 6%
B) an initial \$500 compounded for 2 yrs at 6%
C) The present value of \$500 due in 1 yr at a discount rate of 6%
D) The present value of \$500 due in 2 years at a discounted rate of 6%
E) An initial \$500 compounded for 10 years at 6%
F) An initial \$500 compounded for 10 years at 12%
G) The present value of \$500 due in 10 years at a 6% discounted rate.
H) The present value of \$1552.90 due in 10 years at a 12% discount rate and at a 6\$ rate. Give a verbal definition of the term present value and illustrate it using a time line with data from E-H. Explain why present values are dependent upon interest rates.

# Time value of money

Please assist with the following homework:
1.Calculate the future value of the following
a, \$500 invested for 5 yrs at a 5 % interest rate
b. \$700 invested for 3 years at a 2 % interest rate
c. \$1200 if invested for 7 years at an 11 % interest rate
d. \$400 if invested for 10 years with an 0 % interest rate
CALCULATE THE PRESENT VALUE OF THE FOLLOWING
a. \$2400 to be received 3 years from now with a 4% discount rate
b. \$900 to be received 5 years from now with a 10% interest rate
c. \$1100 to be received 2 years from now with a 24% interest rate
d. \$45,000 to be received 8 years from now with a 7 % interest rate
e. Suppose you to are receive a stream of annual payments(also called annuity) of \$7000 every year for 3 years starting this year. The discount rate is 6 % .What is the present value of these payments
f. Suppose you are to receive a payment of \$4000 every year for 3 years.You are depositing these payments in a bank account that pays 3 % interest.Given these 3 payments and this interest rate, how much will be in your account in 3 years.

# Time value of money

Present Values. Compute the present value of a \$100 cash flow for the following combinations of discount rates and times:

r = 8 percent. t = 10 years.
r = 8 percent. t = 20 years.
r = 4 percent. t = 10 years.
r = 4 percent. t = 20 years

Future Values. Compute the future value of a \$100 cash flow for the same combinations of rates and times a in problem 1

Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values:
Present Value Years Future Value
\$400 11 \$684
\$183 4 \$249
\$300 7 \$300

# Time Value of Money

You are considering a project with the following cash flows:
Year Cash flow
1 5600
2 9000
3 2000

5. What is the present value of these cash flows, given an 11% discount rate?
\$8,695.61
\$8,700.89
\$13,732.41
\$13,812.03
\$19,928.16

6. What is the future value of the following cash flows at the end of year 3 if the interest rate is 7.25%? The cash flows occur at the end of each year.

Year Cash flow
1 6800
2 2100
3 0

\$8,758.04
\$8,806.39
\$10,073.99
\$10,314.00
\$10,804.36

# Time value of money

Finance Ch5 Q’s

Answer these questions using Excel functions where applicable.
Show formulas and how the answer was obtained.
On the first question the instructor wants us to use our present age to nearest month. I am 22 years and 2 months.

1. Assume you drink one coffee per day, 5 days a week. Assume coffee is \$4.00. That makes it \$20 per week and \$80 per month. Assume you can invest \$80 per month in the stock market and assume you can earn 1% per month on your stock investment.

a. At your retirement, when you are 65 years old, how much will be the total amount of money if you switch from coffee drinking to investing in the stock market?

b. Assume that when you get to 65, you switch your funds from stock market investment to bond market investment. Assume you can earn 7% on your bond investment. You decide to withdraw a constant amount each year for the next 20 years when get to retirement age. How much will be your annual withdrawal from age 66 to 85 (nothing left at 85) if you switch your coffee drinking to stock and bond investments?

2. You want to buy a new car for \$48,000. The contract is in the form of 60 month annuity due at 7.45% APR. What will be your monthly payment?

3. You borrow \$10,000 from your bank that charges you 15% per year compounded monthly for the first 6 months, increasing thereafter to 18% compounded monthly. How much interest do you owe at the end of the first year?

4. How long does it take for a sum of \$89,000 to grow to \$175,000 if 1) simple interest of 5% and 2) interest rate is 5% compounded monthly?

5. You have an investment that will pay you 1.05% per month. How much will you have per dollar invested in one year? In two years?

6. To finance the purchase of a warehouse, you have arranged for a 30-year mortgage loan for 80% of \$2,500,000 purchase price. The monthly payment on the loan will be \$13,400. What is the APR on this loan? The EAR?

7. You want to buy a sports car for \$61,000. The contract is in the form of a 60-month annuity due at an 8.15% APR. What will be your monthly payment?

8. Mary is going to receive a 30-year annuity of \$8,000. Nancy is going to receive perpetuity of \$8,000. If the appropriate interest rate is 9%, how much more is Nancy’s cash flow worth?

# Time value of money

I need some guidance to be able to complete my assignment. i don’t have my accounting books with me. My SUN number is 457123896. I will appreciate any help that you can provide.

The Acme Company must solve a series of five problems that require you to apply the concept of “time value of money,” or TVM. The five problems are listed below. Solving them will require the use of Microsoft Excel. Before you begin your work, each student is to select a unique nine-digit random number that contains no zeros, no “patterns,” and should use most of the digits between one and nine. This value will be referred to as the student unique number (SUN). Further, digits within the SUN are read from left to right. For example, if the SUN = 123456789, the first digit = 1, the second digit = 2, etc. Please note that the interest rate used in all questions represents an annual rate and all dollar figures are in whole dollars (not dollars and cents).

1. Acme plans to construct a new manufacturing facility in 14 years. If Acme estimates that today’s cost of the new plant is SUN dollars (use all 9 digits) and annual inflation is A% (A = the first digit of SUN), how much will the manufacturing plant cost in 14 years?

2. Acme has decided to establish a sinking fund for its outstanding preferred stock issue. SUN (use all 9 digits) represents the amount of the issue that will be retired in 26 years. At the beginning of each of these 26 years, Acme will deposit an equal amount into an account that earns B% (B = the second digit of SUN). What is the value of this periodic deposit?

3. One of Acme’s new projects will generate the following cash flows at the end of each of the stated years: year 1 = SUN digits 1-3; year 3 = SUN digits 4-6; year 5 = SUN digits 7-9. If these cash flows are discounted at 12%, what is the sum of their present values?

4. Acme is assessing its employee pension fund. At the end of each of the next 23 years Acme will have to pay its retirees (use the first 4 digits of your SUN). If the fund is estimated to earn D% (D = the fourth digit of SUN), how much does Acme need to have set aside today to ensure that it can meet its future obligations? (At the end of the 23th year, the balance should be drawn down to zero.)

5. As part of a new labor contract, Acme has agreed to make a one-time contribution of \$1,000,000 to the construction of a new physical fitness facility for its employees. It is estimated that in E years (E = 10 + the fifth digit of SUN) the total cost of the new gym will be \$1,850,000. What annual percentage interest rate must the initial contribution earn to attain the required amount in E years? (Note: your answer should be accurate to two decimal places – e.g., 5.79%.)

Prepare for Acme’s CFO an analysis that contains solutions for all five problems. Be sure to clearly present and label all values and variables, provide Excel TVM formulas, and conclude each question with a brief interpretation of your results. Your entire submission must be contained within an Excel document. (Note: You must use Excel TVM functions to complete this assignment; using a hand calculator or website and plugging values into a template is not acceptable.)

Objective: Propose realistic managerial options on capital structure for the multinational firm.
Discuss the opportunities provided by technology for businesses.

# Time Value of Money

1) Calculating Annuity Present Value. An investment offers \$6,000 per year for 15 years, with the first payment occurring 1 year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

2) Calculating Annuity Future Values If you deposit \$2,000 at the end of each of the next 20 years into an account paying 7.5 percent interest, how much money will you have in the account in 20 years? How much will you have if you make deposits for 40 years?

3) EAR versus APR. Ricky Ripov’s Pawn Shop charges an interest rate of 20 percent per month on loans to its customers. Like all lenders, Ricky must report an APR to consumers. What rate should the shop report? What is the effective annual rate?

4) Calculating Loan Payments. You want to buy a new sports coupe for \$52,350, and the finance office at the dealership has quoted you an 8.6 percent APR loan for 60 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?

5) Calculating Annuity Future Values. You are to make monthly deposits of \$200 into a retirement account that pays 11 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years?

# Time Value of Money

1) You are considering buying an expensive Fancycar MSRP \$99,000. The dealer has offered you 2 alternatives for purchasing the car:
a. You buy the car for \$90,000 I cash and get a \$9,000 discount
b. You can buy the car for \$99,000 with a down payment of \$39,000. The balance is a zero interest loan to be paid back in 36 equal installments.
Alternatively, your bank is willing to give you a car loan at an annual rate of 10%. Decide how to finance the car: bank loan, zero percent interest loan with the dealer or cash payment.

2) Michael is considering his consumption habits, trying to figure out how to save money. He realizes that he could save \$2 every day by ordering regular coffee instead of a lattee at the coffee store. Because he buys coffee every work day, this works out to \$10 per week, which amounts to a savings of \$520 per year.
a. If Michael is 25 today and retires at age 65, how much will he have accumulated from savings on coffee versus latte? Assume that the interest rate is 4% and that the \$520 savings occur at the end of each year.

# Time value of money

1. Housing rates have rapidly increased, and you have decided to save to buy your first house. You expect to save \$1500 per month at the end of each month for the next 3 years, investing these funds in a mutual fund you expect to earn 6.5% interest, compounded monthly. At the end of three years of savings, you will buy the house with your savings, and use the \$1500 per month as your mortgage payments. If interest rates on mortgages are 7% compounded monthly in three years, and you will take a 30-year mortgage, paying at the beginning of each month.
a. How much of a mortgage can you obtain given the above information?
b. How much of a down payment will you have saved to buy your house in 3 years?
c. What is the total value of the house you will be able to purchase given this information?
2. A friend of yours just won the lottery. She has been given the choice of \$5,000,000 today, or \$700,000 per year for the next 10 years, at the beginning of each year.. If she received the \$5 million immediately, she would invest in a balanced asset fund she expects to earn 8%, compounded annually. Which option should she take?
3. You are saving for retirement with a \$4,000 investment in a traditional IRA at the end of each year, and are investing the funds into a mutual fund you expect to earn 7.75% interest, compounded quarterly.
a. How much will you have saved towards retirements in 35 years if you make your investment on Jan. 1 each year?
b. How much will you have saved towards retirement in 35 years if you make your investment on December 31 each year?
4. You have decided to start investing in the stock market, and buy a small cap mutual fund with a price of \$31. The fund’s value has been growing at 14% per year.
a. How many years will it take the fund’s price to triple in price at this growth rate?
b. If you hold the fund for 6 years, then sell it at \$72, compute the growth rate for each year.
5. You have a credit card offer. It carries an 18% interest rate, compounds monthly, and you will transfer \$2,000 to the card. If you pay the minimum payment of 2% of the balance, or \$40 at the end of each month, how many years will it be before you pay off the balance completely? To solve this algebraically, you have to manipulate the equation to isolate the unknown variable, then use natural logs to solve.

# Time value of money

Johnny has a technology that will be available in the near term. He anticipates his first annual cash flow from the technology to be \$215,000, received two years from today. Subsequent annual cash flows will grow at 4% in perpetuity. What is the present value of the technology if the discount rate is 10%?

What is the relationship between the value of an annuity and the level of interest rates? Suppose you just bought a 12 year annuity of \$7,500 per year at the current interest rate of 10% per year. What happens to the value of your investment if interest rates suddenly drop to 5%? What if interest rates suddenly rise to 15%?

use formula or calculator, not excel

# TIME VALUE OF MONEY

This week we learn how to calculate the time value of money and why it is an important equation. It is fairly certain that this equation will become relevant in our lives. Drawing on your personal experience and/or future expectations, come up with an example where the time value of money would be important to you. Develop the values, draft the scenario and work out the equation in your answer. How would your answer change if interest rates skyrocketed 3 years from now?

# Time Value of Money

The Acme Company must solve a series of five problems that require you to apply the concept of “time value of money,” or TVM. The five problems are listed below. Solving them will require the use of Microsoft Excel. Before you begin your work, each student is to select a unique nine-digit random number that contains no zeros, no “patterns,” and should use most of the digits between one and nine. This value will be referred to as the student unique number (SUN). Further, digits within the SUN are read from left to right. For example, if the SUN = 123456789, the first digit = 1, the second digit = 2, etc. Please note that the interest rate used in all questions represents an annual rate and all dollar figures are in whole dollars (not dollars and cents).

5. As part of a new labor contract, Acme has agreed to make a one-time contribution of \$1,000,000 to the construction of a new physical fitness facility for its employees. It is estimated that in E years (E = 10 + the fifth digit of SUN) the total cost of the new gym will be \$1,850,000. What annual percentage interest rate must the initial contribution earn to attain the required amount in E years? (Note: your answer should be accurate to two decimal places – e.g., 5.79%.)

# Time Value of Money

1) Will annual payments of \$4800 be sufficient to repay a loan of \$40,000 in 20 years of an interest rate of
10% compounded annually?
10% compounded continuously?
12% compounded quarterly?

2) Maintenance costs for a new piece of mining equipment are expected to be \$20,000 in the first year, rising by \$1,000 per year thereafter. The machine has an expected life of 8 years and interest is 10% annually. To evaluate bids from outside firms for a maintenance contract you need to know the present value of these costs. What is this value?
In question 8 if the maintenance costs rose by 6% per year instead of the fixed amount what is the present value of the maintenance costs?

# Time value of money

What will \$1,130 amount to in 5 years at 5% interest?
What is the present value of \$10,000 due in 11 years time at 5% compound interest?
The power cost of running a pump is \$1,900 per year; determine the present value of this expenditure over 15 years at 6% interest.
A machine is purchased for \$50,000 and costs \$30,000 per year in electrical and maintenance costs. The estimated life is 15 years and interest is at 6% compound. What is the total annual cost of this machine?
A bank offers an annual interest rate of 10% compounded continuously for savings in excess of \$1000 or more deposited for over 2 years. If \$1642 is deposited on the first of January 1999 how much would this amount to in July 2001?
If income from the sales of an item occurs continuously at the rate of \$17,000 per year and is immediately deposited into an account that yields 12% per year, compounded continuously, how much would accumulate at the end of 3 years?

# Time value of Money

Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling securities that call for 4 payments, \$50 at the end of each of the next 3 years, plus a payment of \$1,050 at the
end of Year 4. Your friend says she can get you some of these securities at a cost of \$900 each. Your money is now invested in a bank that pays an 8% nominal (quoted) interest rate but with quarterly compounding.

You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?

# Time Value of Money

A friend plans to buy a big-screen TV/entertainment system and can afford to set aside \$1,320 toward the purchase today. If your friend can earn 5.0%, how much can your friend spend in four years on the purchase? Round off to the nearest \$1.

a. \$1,444
b. \$1,604
c. \$1,764
d. \$1,283.

# Time Value of Money

Babe Ruth Jr. has agreed to play for the Cleveland Indians for \$3 million per year the next ten years. What table would you use to calculate the value of this contract in today’s dollars? A)Present value of an annuity, B)Present value of a single amount, C)Future value of an annuity, D)None of the above

# Time Value of Money

Old Alfred Road, who is well-known to drivers on the Maine Turnpike, has reached his seventieth birthday and is ready to retire. Mr. Road has no formal training in finance but has saved his money and invested carefully.

Mr. Road owns his home?the mortgage is paid off?and does not want to move. He is a widower, and he wants to bequeath the house and any remaining assets to his daughter. He has accumulated savings of \$180,000, conservatively invested.

The investments are yielding 9 percent interest. Mr. Road also has \$12,000 in a savings account at 5 percent interest. He wants to keep the savings account intact for unexpected expenses or emergencies.

Mr. Road’s basic living expenses now average about \$1,500 per month, and he plans to spend \$500 per month on travel and hobbies. To maintain this planned standard of living, he will have to rely on his investment portfolio. The interest from the portfolio is \$16,200 per year (9 percent of \$180,000), or \$1,350 per
month.

Mr. Road will also receive \$750 per month in social security payments for the rest of his life. These payments are indexed for inflation. That is, they will be automatically increased in proportion to changes in the consumer price index.
Mr. Road’s main concern is with inflation. The inflation rate has been below 3 percent recently, but a 3 percent rate is unusually low by historical standards. His social security payments will increase with inflation, but the interest on his investment portfolio will not.

What advice do you have for Mr. Road? Can he safely spend all the interest from his investment portfolio? How much could he withdraw at year-end from that portfolio if he wants to keep its real value intact?

Suppose Mr. Road will live for 20 more years and is willing to use up all of his investment portfolio over that period. He also wants his monthly spending to increase along with inflation over that period. In other words, he wants his monthly spending to stay the same in real terms. How much can he afford to spend per month?

Assume that the investment portfolio continues to yield a 9 percent rate of return and that the inflation rate will be 4 percent

# Time Value of Money

If you invest \$100,000 today at 12% per year over the next 15 years, what is the most you can spend in equal amounts out of the fund each year over that time.

# Time Value of Money

1) Dr. Oats, a nutrition professor, invests \$80,000 in a piece of land that is expected to increase in value by 14 percent per year for the next five years. She will then take the the proceeds and provide herself with a 10- year annuity. Assuming a 14% interest rate for the annuity how much will this be?

2) I have a contract in which I will receive the following payments for the next five years: \$3000, \$4000, \$5000, \$6000, and \$7000. Then I will receive an annuity of \$9000 a year from the end of the sixth through the end of the 15th year. The discount rate is 13%. If I am offered \$40,000 to cancel the contract should I ?

# Time Value of Money

1. Bozeman’s Best Inc. is establishing a pension plan for its sole employee. He will receive credit for 12 years of prior service and is expected to work 18 years until retirement. After retirement, he is expected to collect annual pension payments for 17 years. His current salary is \$75,000 with estimated future pay increases to average 5% per year. What will be the initial amount of projected benefit obligation (i.e., prior service cost) at the inception of the plan if the benefit formula is final year’s annual salary times years of service times 2%? You may assume ordinary annuities and end-of-year annual payments upon retirement and 8% per annum discount rate.

2. Using the facts above (but not related to the answer to #1), assume that the Bozeman’s Best pension plan must have \$869,000 in plan assets at the date the employee retires. If the company wants to make 18 equal annual payments at the end of each year of service to fund the plan, what is the amount of the annual contribution? Assume that the plan assets are expected to earn a 10% return.

# Time Value of Money

1.) John Longwaite will receive \$100,000 in 50 years. His friends are very jealous of him. If the funds are discounted back at a rate of 14 percent, what is the present value of his future “pot of gold”?

2.) Al Lopez invests \$2,000 in a mint condition Nolan Ryan baseball card. He expects the card to increase in value by 20 percent a years for the next five years. After that, he anticipates a 15 percent annual increase for the next three years. What is the projected value of the card after eight years?

3.) You wish to retire in 20 years, at which time you want to have accumulated enough money to receive an annuity of \$12,000 for 25 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money.

What annual contributions to the retirement fund will allow you to receive the \$12,000 annuity?

# Time value of money

4.6) For an interest rate of 12% per year compounded every 2 months, determine the nominal interest rate per (a) 4 months, (b) 6 months, (c) 2 years.

4.11) What nominal interest rate per year is equivalent to an effective 16% per year, compounded semiannually?

# Time Value of Money

Juan Garza invested \$20,000 10 years ago at 12 percent, compounded quarterly. How much has he accumulated?

What is the future value of a 10-year annuity of \$4,000 per period where payments come at the beginning of each period? The interest rate is 12 percent.

You need \$28,974 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.
a. What single payment could be made at the beginning of the first year to achieve this objective?
b. What amount could you pay at the end of each year annually for 10 years to achieve this same objective?

On January 1, 2002, Mike Irwin, Jr., bought 100 shares of stock at \$14 per share. On December 31, 2004, he sold the stock for \$21 per share. What is his annual rate of return? Interpolate to find the exact answer.

Bridget Jones has a contract in which she will receive the following payments for the next five years: \$1,000, \$2,000, \$3,000, \$4,000, and \$5,000. She will then receive an annuity of \$8,500 a year from the end of the 6th through the end of the 15th year. The appropriate discount rate is 14 percent. If she is offered \$30,000 to cancel the contract, should she do it?

# Time Value of Money

Can you help me get started with this assignment?

1. In two to three paragraphs, explain why the concept of present value is so important for corporate finance and is often the very first topic taught in any finance class. Do not focus your answer on explaining what present is, instead focus on some specific reasons why you think it is important and why it is taught first in corporate finance classes before other topics are introduced.

2. Calculate the future value of the following (show all work):

a. \$200 if invested for five years at a 4% interest rate

b. \$500 if invested for three years at a 7% interest rate

c. \$7500 if invested for seven years at an 3% interest rate

d. \$2000 if invested for ten years with a 0.6% interest rate

3. Calculate the present value of the following (show all work):

a. \$6500 to be received three years from now with a 2% Interest rate

b. \$4500 to be received five years from now with a 5% interest rate

c. \$8000 to received two years from now with a 11% interest rate

d. \$480,000 to be received eight years from now with a 9% interest rate.

4. Suppose you are to receive a stream of annual payments (also called an “annuity”) of \$5000 every year for three years starting this year. The interest rate is 5%. What is the present value of these three payments? (show all work)

5. Suppose you are to receive a payment of \$7000 every year for three years. You are depositing these payments in a bank account that pays 2% interest. Given these three payments and this interest rate, how much will be in your bank account in three years? (show all work)

# Time value of Money

What is the present value of the following future amounts?

a. \$800 to be received 10 years from now discounted back to the present at 10 percent
b. \$300 to be received 5 years from now discounted back to the present at 5 percent
c. \$1,000 to be received 8 years from now discounted back to the present at 3 percent
d. \$1,000 to be received 8 years from now discounted back to the present at 20 percent

# Time value of money

What is the accumulated sum of each of the following streams of payments?

a. \$500 a year for 10 years compounded annually at 5 percent
b. \$100 a year for 5 years compounded annually at 10 percent
c. \$35 a year for 7 years compounded annually at 7 percent
d. \$25 a year for 3 years compounded annually at 2 percent

# Time Value of Money

What is the present value of:
a. \$9,000 in 7 years at 8 percent?
b. \$20,000 in 5 years at 10 percent?
c. \$10,000 in 25 years at 6 percent?
d. \$1,000 in 50 years at 16 percent?

How much would you have to invest today to receive:
a. \$15,000 in 8 years at 10 percent?
b. \$20,000 in 12 years at 13 percent?
c. \$6,000 each year for 10 years at 9 percent?
d. \$50,000 each year for 50 years at 7 percent?

Your rich godfather has offered you a choice of one of the three following
alternatives: \$10,000 now; \$2,000 a year for eight years; or \$24,000 at the end
of eight years. Assuming you could earn 11 percent annually, which alternative
should you choose? If you could earn 12 percent annually, would you still
choose the same alternative?

You need \$28,974 at the end of 10 years, and your only investment outlet is
an 8 percent long-term certificate of deposit (compounded annually). With the
certificate of deposit, you make an initial investment at the beginning of the
first year.
a. What single payment could be made at the beginning of the first year to
achieve this objective?
b. What amount could you pay at the end of each year annually for 10 years to
achieve this same objective?

# Time value of money

Your uncle has \$300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw \$35,000 at the beginning of each year, beginning immediately. He also wants to have \$25,000 left to give you he ceases to withdraw funds from the account.

For how many years can he make the \$35,000 withdraws and still have \$25,000 left in the end?

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# Time value of money

1. What is the present value of a security that will pay \$5,000 in 20 years if securities of equal risk pay 7% annually?

2. You have \$42,180.53 in a brokerage account, and you plan to deposit an additional \$5,000 at the end of every future year until your account totals \$250,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal?

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