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FI 3300 - CORPORATION FINANCE Take-Home Problem Set Three (THPS-3)

Spring 2016

Directions: This problem set covers chapters 6 and 7 in the textbook. Determine or compute an answer for

each question/problem. After you have computed an answer for every question, enter your answers online

via the “quiz” function entitled “THPS-3 ANSWER SUBMISSION FORM.” See the course calendar for

when the answer submission form will open and close. I will post a detailed solution key to the problem set

right after the Answer Submission Form closes. See the course calendar for the day(s) on which I will

answer questions about these problems in the chat room.

This is a take-home, open book, open notes financial statement analysis problem set. Work on this

Assignment is to be yours alone - any discussion of either the questions on the assignment or your

answers with anyone other than your instructor will be considered as cheating and, thus, as a

violation of the GSU honor code.

All questions are equally weighted.

_______________________________________________

PART I: MULTIPLE CHOICE – Choose the letter of the most correct answer for each question. Record

only one answer per question.

1. Which following statement is true, assuming an interest rate of greater than 0%:

a. The present value of a dollar to be received one year from today is ALWAYS worth less than one dollar.

b. The present value of a dollar to be received one year from today is ALWAYS worth more than one dollar.

c. The present value of a dollar to be received one year from today is ALWAYS equal to one dollar. d. None of the answers listed above is correct (in particular, the word ALWAYS in the answers

negates any one of them from being strictly correct).

e. All of the answers listed above (even answer d) are incorrect.

2. Which one of the following investments provides the highest effective annual rate of return (i.e., which of the following investments is the WORST (i.e., the smallest EAR), assuming an investor wants to

avoid earning the lowest return over an investing horizon of 10 years)?

a. An investment which has a 3.0 percent nominal rate with annual compounding. b. An investment which has a 2.98 percent nominal rate with semi-annual compounding. c. An investment which has a 2.965 percent nominal rate with quarterly compounding. d. An investment which has a 2.9575 percent nominal rate with monthly compounding. e. An investment which has a 2.955 percent nominal rate and daily (365) compounding.

3. For a given nominal interest rate greater than 0%, if the number of compounding periods per year increases (for example, from quarterly to daily), the present value of $1000 to be received exactly 10

years from today will:

a. increase. b. decrease. c. remain unchanged. d. either increase or decrease, depending on the nominal interest rate.

4. Harrison, Inc. is considering two investment opportunities. Each investment costs $7,000 (i.e., year 0 cash flow associated with each opportunity is -$7,000) and will provide the same total future cash

inflows. The schedule of estimated cash receipts for each investment follows (assume cash is received

at year-end):

Which investment should Harrison choose assuming all other variables for the two investments are the

same (specifically, the appropriate discount rate for both investments is 4% p.a.)?

a. Harrison should be indifferent between the two investments since they provide the same total cash inflows.

b. Harrison should choose Investment I because of the time value of money. c. Harrison should be indifferent between the two investments since the initial cash outflow is the

same.

d. Harrison should choose Investment II because it generates larger cash inflows at the end of the investment's useful life.

e. None of the answers listed above are correct.

5. Which of the following will increase the present value of the mixed cash flows for years 1 through 5 of $1,000; $4,000; $9,000; $5,000; and $2,000 respectively given a 10% discount rate? (Choose all that

apply - this is an all or nothing problem; if you choose an option that is wrong or do not choose an

option that is correct, your entire answer will be marked wrong).

a. Decrease the discount rate by 2%. b. Switch cash flows for years 1 and 5 so that year 1 is $2,000 and year 5 is $1,000. c. Switch cash flows for years 2 and 4 so that year 2 is $5,000 and year 4 is $4,000. d. Switch cash flows for years 2 and 5 so that year 2 is $2,000 and year 5 is $4,000. e. Switch cash flows for years 3 and 1 so that year 1 is $9,000 and year 3 is $1,000.

6. Which of the following banks is offering the BEST rate (assuming that you plan to deposit $10,000 in the account today and leave the money in the account for 25 years)?

Bank Nominal Rate Number of Compounding Periods Per Year

A 16.000% 2

B 15.700% 4

C 15.500% 12

D 15.350% 365

E 15.250% Continuous

a. Bank A which offers a rate of 16.000% with semi-annual compounding. b. Bank B which offers a rate of 15.700% with quarterly compounding. c. Bank C which offers a rate of 15.500% with monthly compounding. d. Bank D which offers a rate of 15.350% with daily compounding. e. Bank E which offers a rate of 15.250% with continuous compounding.

Year Investment I Investment II

1 $4,000 $1,000

2 $2,500 $2,000

3 $2,000 $3,000

4 $1,500 $4,000

Total Cash Flow $10,000 $10,000

7. In 3 years you are to receive $5,000. If the current interest rate (which is 3.284%) were to suddenly decrease, the present value of this future amount to you would

a. decrease. b. increase. c. remain unchanged. d. cannot be determined without more information.

8. In a typical loan amortization schedule, the dollar amount of interest paid each period ____________.

a. increases with each payment b. decreases with each payment c. remains constant with each payment

9. The concept of compound interest refers to:

a. earning interest on the original investment. b. payment of interest on previously earned interest. c. investing for a multi-year period of time. d. determining the APR of the investment.

10. Suppose that you can subscribe to a magazine using either a one-year rate of $27, a two-year rate of $52, a three-year rate of $65, or a four-year rate of $100. If want to receive this magazine for four years

and if your opportunity cost of funds is 8%, which rate offers the lowest cost?

a. A four-year subscription costing $100 and paid immediately. b. Four one-year subscriptions, of $27 each, paid at the beginning of each year. c. A two-year subscription paid immediately, costing $52, followed by another two-year subscription

costing $52 and paid at the beginning of the third year.

d. A one-year subscription paid immediately, costing $27, followed by a three-year subscription costing $65 and paid at the beginning of the second year.

e. There is not enough information provided to answer this question.

Part II: PROBLEMS – Compute a final numerical answer for each of the following problems. You should

work out your solutions on loose leaf paper, however, I may or may not collect your worked out solutions.

To be safe, however, I suggest that you write out a solution for every problem and be ready to turn it in if

asked. Round all dollar answers to 2 decimal places, round time (years or months) answers to one (1)

decimal place and record interest rates as percent values rounded to one (1) decimal place. However, be

sure to NOT input a dollar sign, commas, or percent sign on D2L. For example, record $3,284.33965 as

3284.34, record 37.285432 years as 37.3 and record .064358 = 6.4358% as 6.4.

11. What will be the approximate population of the United States, if its current population of 316 million grows at a compound rate of 2.1% annually for 25 years?

12. Assume that a gallon of milk costs $2.99 today. If the average annual inflation rate over the past 30 years was 2.75% p.a., what did a gallon of milk cost 30 years ago?

13. What is the future value on the day of the last deposit of 25 annual deposits of $750 per year (first deposit to be made today) given an interest rate of 5.5% p.a.?

14. Assume that I deposit $750 into an account exactly 10 years from today. How much will be in my account at the end of year 50, assuming that my account pays interest of 4.5% p.a.?

15. What is the future value at the end of year 15 of $10,000 deposited today into an account that pays interest of 4.5% p.a., but with monthly compounding?

16. Walt is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $12,500; year 2, $10,000; year 3, $7,500; year 4, $5,000; year 5, $2,500; year

6, $0; and year 7, $12,500. Walt believes that he should earn an annual rate of 8 percent on this

investment. How much should he pay for this investment?

17. Assume that Claudia started a paper route on January 1, 1970. Since that day, at the end of every three (3) months (first deposit made on April 1, 1970), she deposited $500.00 into a savings account, which

paid her interest of 4 percent annually but with quarterly compounding. On January 1, 1980, she took

the balance in her savings account and transferred it to an account that paid 11.5% p.a. Assuming that

Claudia did not deposit any additional money into the account after the transfer, how much did she

have in her account on January 1, 2014?

18. On the day that his first child was born, Ezio Auditore de Firenze deposited $3,000 into an investment account. The only purpose for the account was to pay for his son’s first year of college tuition. Assume

that his son, Flavia, started college on his 18th birthday and his first year tuition payment had to be made

that day. The amount needed on that day was $26,000. If that was indeed the amount of money in the

account on Flavia’s 18th birthday, what annual rate of return did Ezio earn on his investment account?

19. Desmond Miles has $1,500 that he will use as a down payment on a car. Assuming that he can afford a payment of $225 per month, how much can Desmond spend on a car (that is, what is the total cost of

the car that Desmond can purchase) if the interest rate is 5.75% and if he will finance his purchase with

a 5 year, monthly payment loan?

20. Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly. How many years (rounded to one decimal place – for example, 32.1843 year = 32.2) will it take for your

account to be worth $8,500?

21. Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly and you also make monthly contributions of $50 (first monthly contribution made one month after the initial

deposit is made). How many years (rounded to one decimal place – for example, 32.1843 year = 32.2)

will it take for the account to grow to $7,500 in this case?

22. Assume that I am trying to borrow money from you to finance my business. Assume that I promise to repay you in three installments, one payment of $5,000 to be made exactly 2 years from today, a second

payment of $10,000 to be made exactly 5 years from today, and a final payment of $15,000 to be made

8 years from today. If your opportunity cost of funds is 7.5% p.a., (that is, use an interest rate of 7.5%

for this question), how much should be willing to lend me today?

23. What is the future value at the end of year 25 of depositing $5,000 today, $3,500 at the end of years 1, 2 and 3, $5,000 at the end of years 4, 5, 6 and 7 and $4,250 at the end of years 8, 9, 10, 11 and 12 into

an account that pays 9.5% p.a.? (No deposits will be made into the account after year 12).

24. If you wanted to fund a scholarship that would pay $12,500 per year forever at GSU, how much would you have to deposit today if you wanted the scholarship to start paying five (5) years from today?

Assume the endowment could earn 6.25% p.a. interest forever.

25. You currently owe $20,000 on a car loan at 8.25 percent interest. If you make monthly payments of $596.59 per month, how long (i.e., number of months rounded to one decimal place) will it take you to

fully repay the loan?

26. It is now January 1. You plan to make 5 deposits of $300 each, one every 6 months, with the first payment being made exactly six months from today. If the bank pays a nominal interest rate of 12%

but uses semiannual compounding, how much will be in your account exactly 12 years from today?

27. You must make a payment of $3,800 exactly 8 years from today. To prepare for this payment, you will make 5 equal deposits into an account that pays a nominal interest rate of 7.6% p.a., with quarterly

compounding. If your first deposit is made today (and then you make four additional deposits in each

of the next four quarters – that is, a deposit 3 months from today, another 6 months from today and so

on), what must each of the 5 payments be for you to exactly achieve your goal?

USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREE QUESTIONS

Vito Scaletta just bought his dream car, 2014 Aston Martin DB9 that cost $208,700. He paid $35,000 down

and financed the balance over 84 months at 6.25% p.a. (Assume that Vito makes all required payments on

time).

28. What is the monthly payment on Vito’s loan?

29. What will the balance on Vito’s loan be at the end of the fourth year (that is, immediately after Vito makes his 48th payment on the loan)?

30. What is the total amount of interest that Vito will pay over the entire term of the loan (that is, the total amount of interest that is paid on payments 1 through 84)?

31. Today is your 30th birthday and you have a dream of retiring on your 65th birthday. You want to put aside however much is necessary on your 31st through 65th birthdays (35 annual payments) to have

enough to retire. You've estimated that you will live until you are 90 and you want the first withdrawal

to occur on your 66th birthday, with the last payment occurring on your 90th birthday. You think that

you will need $150,000 per year to spend during retirement. You estimate constant interest rates of

11.25%. Assuming that you currently have $7,500 deposited in your retirement account, how much

must you put aside each year in order to have sufficient money to retire at age 65?

32. John Keene recently invested $5,000 in a project that is promising to return 6.5 percent per year. The cash flows are expected to be as follows:

End of Cash

Year Flow 1 $1000

2 950

3 875

4 ???

5 850

Note that the 4th year cash flow is unknown. Assuming the present value of this cash flow stream is

$5,000 (that is, CF0 = -5000), what is the missing cash flow value (that is, what is the cash flow at the

end of the 4th year)?

33. You have a $25,000 balance on your credit card. You plan to make monthly payments of $450 until the balance is paid off. The interest rate on your credit card is 17.5% p.a., compounded monthly. A letter

in the mail informs you that you are approved for a new credit card and balance transfers are subject to

a 9.5% p.a., compounded monthly. How many months sooner will you pay off your bill?