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 of the following investment options is most valuable? Assume a positive interest rate, and that all options have the same risk.
a. receiving $20,000 today
b. receiving 10 payments of $2,000 per year with the first payment made today
c. receiving $4,000 per year for five years beginning next year
d. receiving $10,000 today and $10,000 next year
e. Without an interest rate there is not enough information to tell.
2. In 3 years you are to receive $5,000. If the interest rate were to suddenly increase, the present value of that future amount to you would:
a. Increase.
b. Decrease.
c. Remain unchanged.
d. Either increase or decrease depending on the interest rate.
e. Cannot be determined without more information.
3. Assuming an interest rate of 0 percent, which of the following cash-inflow streams should you prefer?
|
Answer Choice
|
Year 1 Cash Flow
|
Year 2 Cash Flow
|
Year 3 Cash Flow
|
Year 4 Cash Flow
|
|
a.
|
$400
|
$300
|
$200
|
$100
|
|
b.
|
$100
|
$200
|
$300
|
$400
|
|
c.
|
$250
|
$250
|
$250
|
$250
|
|
d.
|
Any of the above, since the each sum to $1,000
|
4. Assuming an interest rate of 10 percent, which of the following cash-inflow streams should you prefer?
|
Answer Choice
|
Year 1 Cash Flow
|
Year 2 Cash Flow
|
Year 3 Cash Flow
|
Year 4 Cash Flow
|
|
a.
|
$400
|
$300
|
$200
|
$100
|
|
b.
|
$100
|
$200
|
$300
|
$400
|
|
c.
|
$250
|
$250
|
$250
|
$250
|
|
d.
|
Any of the above, since the each sum to $1,000
|
5. 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
6. In a typical loan amortization schedule, the total dollar amount of money paid each period:
a. increases with each payment
b. decreases with each payment
c. remains constant with each payment
7. A security is currently selling for $8,000 and promises to pay $1,000 annually for the next 9 years, and
$1,500 annually in the 3 years thereafter with all payments occurring at the end of each year. If your required rate of return is 7% p.a., should you buy this security?
a. Yes, because the return is greater than 7%
b. No, because the return is less than 7%
c. Yes, because the return is 7%
d. Yes, because the present value at 7% is less than $8,000.
e. There is insufficient information provided to answer this question.
8. A given rate is quoted as 12% APR, but has an effective annual rate (EAR) of 12.55%. What is the frequency of compounding during the year?
a. Annually
b. Semiannually
c. Quarterly
d. Monthly
e. Daily
9. 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.
10. You are considering two perpetuities which are identical in every way except for the when the perpetuity payments will begin. Perpetuity A will begin making annual payments of a fixed amount, with the first payment being made two years from today. Perpetuity B pays the same fixed annual payment, but will make the first payment one year from today. Which of the following statements is most correct?
a. The PV of perpetuity A is greater than the PV of perpetuity B by the amount of the fixed payment.
b. The PV of perpetuity B is greater than the PV of perpetuity A by the amount of the fixed payment.
c. The PV of perpetuity A is equal to the PV of perpetuity B.
d. The PV of perpetuity A is greater than the PV of perpetuity B by the present value of the amount of the fixed payment.
e. The PV of perpetuity B is greater than the PV of perpetuity A by the present value of the amount of the fixed payment.
11. Which one of the following investments provides the highest effective annual rate of return (i.e., which of the following investments represents the largest 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.
12. 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 3.25%, 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. For any problems that require multiple steps, be sure to carry all intermediate step calculations to at least four (4) decimal places to ensure that your final numerical answer is as precise as possible.
When recording your final numerical answers on D2L, 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.
13. A money machine will produce $10,000 exactly 16 years from today. The return on this investment is 10% p.a. The machine is worth $ to you today.
14. Jebron Lames is considering the purchase of a car, which will cost him $125,000. He will borrow the entire purchase price and make monthly payments over the next five years. The first payment is due next month and the interest rate is 3.00%. He will owe $ on the car immediately following the 23rd payment.
15. KQ Technologies plans to borrow money from SunState Bank. KQ agrees to make 15 equal annual payments of $200,000 beginning next year. If the rate on the loan is 8%, then KQ can borrow $ .
16. August Street, Inc. wants to have $3,000,000 in an account exactly 16 years from today. They will make equal quarterly payments of $50,000 beginning next quarter and ending in 16 years. The account earns 8.00% p.a., compounded quarterly. August Street must have $ in its account today.
17. You wish to buy a house today for $350,000. You plan to put 10% down and finance the rest at 5.20%
p.a. for thirty years. You will make equal monthly payments of $ .
18. The effective annual rate of 5.000% compounded monthly is % .
19. An investment will pay $32,000 per year forever beginning 8 years from today. If the relevant rate is 10% compounded monthly, the investment is worth $ today.
20. You just decided to begin saving for retirement. You will make deposits of $1,000 per month into a retirement account that earns 8.00% p.a. The first deposit is made today and the last deposit will be made when you retire exactly 30 years from today. The day you retire you will buy an RV for $240,000. You will begin to make withdrawals from the account the first month after you retire. If you plan to live an addition 25 years, you will be able to withdraw $ . (Note: you make 300 total monthly withdrawals from your retirement account.)
21. Daryl wishes to save money to provide for his retirement. Beginning one year from now, Daryl will begin depositing the same fixed amount each year for the next 30 years into a retirement savings account. Starting one year after making his final deposit, he will withdraw $100,000 annually for each of the following 25 years (i.e. he will make 25 withdrawals in all). Assume that the retirement fund earns 12% annually over both the period that he is depositing money and the period he makes withdrawals. In order for Daryl to have sufficient funds in his account to fund his retirement, how much should he deposit annually (rounded to the nearest dollar)?
22. You have just received an advertisement from Corleone Inc., a “paycheck loan” service. Corleone will charge you a fee of 5% for a two-week loan (i.e. if you borrow $100, you must repay $105 in two weeks’ time). Assuming a 52 week year, what is the Effective Annual Rate (EAR) that Corleone charges (rounded to the nearest whole percent)?
23. Your neighbor offers you an investment opportunity which will pay a single lump sum of $2,000 five years from today. The investment requires a single payment of $1,500 today. What is the annual rate of return on this investment?
24. 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?
25. 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?
26. 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?
27. 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?
28. 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?
29. Suppose you deposit $5,000 into an account earning 4.75 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 triple?
30. What is the future value at the end of year 40 of depositing $15,000 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).
31. If you wanted to fund a scholarship that would pay $17,500 per year forever at GSU, how much would you have to deposit today if you wanted the scholarship to start paying eight (8) years from today? Assume the endowment could earn 7.25% p.a. interest forever.
32. Assume that Randall Ezno was born today and to celebrate his birth, his parents deposited $10,000 into an account in his name. The account pays interest of 3.25 percent p.a., with monthly compounding, and it is expected to continue paying this amount forever. Assume that exactly 1.5 years after the deposit was made, Randall’s parents changed their minds and withdrew $10,000 from the account (all that remained in the account was the interest earned in the first 18 months). How much money will be in Randall’s account on his 65th birthday?
33. 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?
34. 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 $228,700. He paid $50,000 down and financed the balance over 84 months at 5.25% p.a. (Assume that Vito makes all required payments on time).
35. What is the monthly payment on Vito’s loan?
36. What will the balance on Vito’s loan be at the end of the third year (that is, immediately after Vito makes his 36th payment on the loan)?
37. 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)?
38. 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?
39. 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)?
40. You have a $28,000 balance on your credit card. You plan to make monthly payments of $550 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 8.5% p.a., compounded monthly. How many months sooner will you pay off your bill?