1. Which of the following would you rather have if your rate of discount is 20 percent?
a. $300 in one year
b. $350 in two years
c. $420 in three years
d. $1500 in ten years
2. Suppose the rate of discount is 5 percent, 6 percent, 7 percent, or 8 percent. Suppose that you would rather have $425 in one year instead of $400 today. Also, you would rather have $400 today instead of $445 in two years. What is the rate of discount?
a. 5 percent
b. 6 percent
c. 7 percent
d. 8 percent
3. The amount of money you would need to invest today to yield a given future amount is called
a. future value.
b. present value.
c. the rate of discount.
d. the discount factor.
4. Present value is
a. the cost of a bond today, minus the future value of interest payments.
b. the future value of interest payments times the rate of discount.
c. the future value of interest payments times the discount factor.
d. the amount of money you would need to invest today to yield a given future amount.
5. Earning interest on interest that was earned in prior years is called
a. discounting.
b. compounding.
c. present valuing.
d. bonding.
6. In the one-period present-value equation, P = F/(1 + i), the term 1 + i is known as
a. future value.
b. present value.
c. the rate of discount.
d. the discount factor.
7. In the one-period present-value equation, P = F/(1 + i), the discount factor is
a. 1 + i.
b. i.
c. P.
d. F.
8. Discounting is the process of dividing a future value by the ________ to obtain the ________ value.
a. discount factor; past
b. discount factor; present
c. rate of discount; past
d. rate of discount; present
9. In the one-period present-value equation, P = F/(1 + i), the term i is known as
a. future value.
b. present value.
c. the rate of discount.
d. the discount factor.
10. In the one-period present-value equation, P = F/(1 + i), the rate of discount is
a. 1 + i.
b. i.
c. P.
d. F.
11. The present value of a series of payments is
a. inversely related to the future value.
b. directly related to the rate of discount.
c. inversely related to the rate of discount.
d. directly related to the discount factor.
12. A debt security with just one payment is called a
a. coupon bond.
b. fixed-payment security.
c. discount bond.
d. perpetuity.
13. A discount bond is a debt security
a. with just one payment.
b. that pays interest forever and never repays the principal.
c. that makes a regular interest payment until maturity, at which time the face value is repaid (so there is no amortization).
d. that makes the same dollar payment every year, amortizing the principal.
14. Consider a one-year discount bond that pays $1,000 one year from now. If the rate of discount is 7 percent, the present value of the bond is
a. $930.00.
b. $934.58.
c. $993.00.
d. $993.46.
15. Consider a one-year discount bond that pays $1,500 one year from now. If the rate of discount is 4 percent, the present value of the bond is
a. $1,560.00.
b. $1,540.00.
c. $1,440.00.
d. $1,442.31.
16. Consider a one-year discount bond that has a present value of $1,000. If the rate of discount is 7 percent, the future value of the bond (the amount the bond pays in one year) is
a. $930.00.
b. $934.58.
c. $1,000.00.
d. $1,070.00.
17. Consider a one-year discount bond that has a present value of $1,500. If the rate of discount is 4 percent, the future value of the bond (the amount the bond pays in one year) is
a. $1,560.00.
b. $1,540.00.
c. $1,440.00.
d. $1,442.31.
18. The equation that allows us to compare dollar amounts to be received or paid at different dates is the
a. present-value formula.
b. Taylor rule.
c. interest-rate parity equation.
d. yield curve.
19. A debt security that pays interest forever and never repays the principal is
a. a fiduciary obligation.
b. a federal funds loans.
c. a perpetuity.
d. a junk bond.
20. A bond that makes a regular interest payment until maturity, at which time the face value is repaid (so there is no amortization), is called a
a. coupon bond.
b. fixed-payment security.
c. discount bond.
d. perpetuity.
21. A debt security that makes the same dollar payment every year, amortizing the principal, is a
a. coupon bond.
b. fixed-payment security.
c. discount bond.
d. perpetuity.
22. A coupon bond is a debt security
a. with just one payment.
b. that pays interest forever and never repays the principal.
c. that makes a regular interest payment until maturity, at which time the face value is repaid (so there is no amortization).
d. that makes the same dollar payment every year, amortizing the principal.
23. A fixed-payment security is a debt security
a. with just one payment.
b. that pays interest forever and never repays the principal.
c. that makes a regular interest payment until maturity, at which time the face value is repaid (so there is no amortization).
d. that makes the same dollar payment every year, amortizing the principal.
24. A perpetuity is a debt security
a. with just one payment.
b. that pays interest forever and never repays the principal.
c. that makes a regular interest payment until maturity, at which time the face value is repaid (so there is no amortization).
d. that makes the same dollar payment every year, amortizing the principal.
25. The amount repaid by a coupon bond at maturity is the ________ value.
a. present
b. future
c. face
d. coupon
26. Consider a perpetuity that pays $100 every year. If the rate of discount is 7 percent, the present value of the bond is
a. $107.00.
b. $1,300.00.
c. $1,428.57.
d. $1,700.00.
27. Consider a perpetuity that pays $150 every year. If the rate of discount is 4 percent, the present value of the bond is
a. $210.00.
b. $3,000.00.
c. $3,600.00.
d. $3,750.00.
28. Consider a perpetuity making one payment each year that has a present value of $1,000. If the rate of discount is 7 percent, the annual payment is
a. $70.00.
b. $107.00.
c. $1,428.57.
d. $14,285.71.
29. Consider a perpetuity making one payment each year that has a present value of $1,500. If the rate of discount is 3 percent, the annual payment is
a. $15.00.
b. $45.00.
c. $500.00.
d. $1,500.00.
30. Consider a fixed-payment security that pays $100 at the end of every year for three years. If the rate of discount is 10 percent, the present value of the bond is
a. $24.87.
b. $248.69.
c. $294.10.
d. $1,000.00.
31. Consider a fixed-payment security that pays $100 at the end of every year for ten years. If the rate of discount is 7 percent, the present value of the bond is
a. $142.15.
b. $700.00.
c. $702.36.
d. $1,428.57.
32. Consider a three-year fixed-payment security that has a present value of $1,000. If the rate of discount is 7 percent, the payment made at the end of each year is
a. $70.00.
b. $107.00.
c. $142.86.
d. $381.05.
33. Consider a seven-year fixed-payment security that has a present value of $1,500. If the rate of discount is 2 percent, the payment made at the end of each year is
a. $231.77.
b. $248.69.
c. $300.00.
d. $310.00.
34. Consider a coupon bond that pays $100 every year and repays its principal amount of $1,000 at the end of 10 years. If the rate of discount is 10 percent, the present value of the bond is
a. $909.09.
b. $990.00.
c. $1,000.00.
d. $1,100.00.
35. Consider a coupon bond that pays $105 every year and repays its principal amount of $1,500 at the end of 7 years. If the rate of discount is 7 percent, the present value of the bond is
a. $735.35.
b. $765.00.
c. $1,395.00.
d. $1,500.00.
36. Consider a twelve-year coupon bond that has a present value of $2,000. If the rate of discount is 7 percent, and the payment made at the end of each year is $140, the principal amount to be repaid at the end of twelve years is
a. $1,860.00.
b. $2,000.00.
c. $2,140.00.
d. $2,156.40.
37. Consider a two-year coupon bond that has a present value of $10,000. If the rate of discount is 3 percent, and the payment made at the end of each year is $300, the principal amount to be repaid at the end of two years is
a. $10,000.00.
b. $10,300.00.
c. $33,333.33.
d. $333,333.33.
38. Consider a coupon bond that pays $100 every year and repays its principal amount of $1,000 at the end of ten years. If the rate of discount is 8 percent, the present value of the bond is
a. $671.01.
b. $1,080.00
c. $1,134.20.
d. $1,250.00.
39. Consider a coupon bond that pays $150 every year and repays its principal amount of $1,500 at the end of seven years. If the rate of discount is 7 percent, the present value of the bond is
a. $214.29.
b. $808.39.
c. $1,500.00.
d. $1,742.52.
40. Consider a twelve-year coupon bond that has a present value of $2,000. If the rate of discount is 5 percent, and the payment made at the end of each year is $140, the principal amount to be repaid at the end of twelve years is
a. $1,234.65.
b. $1,363.32.
c. $1,860.00.
d. $2,000.00.
41. Consider a two-year coupon bond that has a present value of $10,000. If the rate of discount is 3 percent, and the payment made at the end of each year is $250, the principal amount to be repaid at the end of two years is
a. $10,101.50.
b. $10,300.00.
c. $13,333.33.
d. $13,583.33.
42. Interest-rate risk is the risk of a change in the price of a security in the secondary market because of a change in the
a. probability of a default.
b. profitability of the issuer.
c. macroeconomy.
d. market interest rate.
43. According to the theory underlying the present-value formula, would you prefer to receive (a) $75 one year from now, (b) $85 two years from now, or (c) $90 three years from now, if the relevant market interest rate is 10 percent and will remain at 10 percent for the next three years?
a. $75 one year from now
b. $85 two years from now
c. $90 three years from now
d. Indifferent between all three choices (i.e., the present values of all three choices are identical out to seven decimal places).
44. According to the theory underlying the present-value formula, would you prefer to receive (a) $75 one year from now, (b) $85 two years from now, or (c) $90 three years from now, if the relevant market interest rate is 20 percent and will remain at 20 percent for the next three years?
a. $75 one year from now
b. $85 two years from now
c. $90 three years from now
d. Indifferent between all three choices (i.e., the present values of all three choices are identical out to seven decimal places).
45. Your favorite magazine, Fun with Present Value, offers you four different subscription deals for the next four years. It has guaranteed its current and future subscription rates, as shown below. Which will you take, if your rate of discount is 6 percent and you want to get the magazine for four years?
a. A one-year subscription for $24, followed by a one-year renewal each year for $24 each year.
b. A two-year subscription for $45, followed by a two-year renewal for $48.
c. A three-year subscription for $72, followed by a one-year renewal for $24.
d. A four-year subscription for $89.
46. Suppose you take out a car loan of $10,000 for 3 years at an annual interest rate of 8 percent, with payments to be made monthly. The relevant formula is:
.
What will your monthly payments be?
a. $313.36.
b. $323.36.
c. $853.45.
d. $3,880.34.
47. Suppose you take out a home equity loan of $100,000 for 5 years at an annual interest rate of 5 percent, with payments to be made monthly. The relevant formula is:
.
What will your monthly payments be?
a. $1,320.71
b. $1,887.12
c. $1,924.79
d. $5,282.82
48. The average annual return that a security or a portfolio has produced in the past is called past
a. yield.
b. interest.
c. maturity.
d. return.
49. You are considering buying a discount bond that costs $1,000 today and pays you $1,200 in one year. However, there is a 10 percent chance that the company issuing the bond will go bankrupt and not pay you your interest or return your principal. What is the expected return on the bond?
a. 20 percent.
b. 10 percent.
c. 8 percent.
d. ?4 percent.
50. A bond was initially issued on December 31, 2011. It sold for $10,000, had a face value of $10,000 (to be repaid in four years on December 31, 2015), and promised interest payments of $600 at the end of each of the next four years (December 31, 2012, 2013, 2014, and 2015). Aaron bought the bond on December 31, 2011, and owned it for one year, receiving the first interest payment. He sold it to Billy on December 31, 2012, at which time the market interest rate was 7 percent. Billy owned the bond for one year, receiving the second interest payment, and sold it to Corey on December 31, 2013, at which time the market interest rate was still 7 percent. How much was Billy's total return?
a. 0.8 percent
b. 3.4 percent
c. 6.2 percent
d. 7.0 percent
51. According to the Truth-in-Savings Act, the interest rate that banks are required to report when you deposit money in an account, which allows you to compare the returns on different accounts that compound interest with different frequencies, is known as
a. capital-gains yield.
b. annual percentage yield.
c. current yield.
d. total return.
PROBLEM
1. Consider a one-year discount bond that pays $2,000 one year from now. If the rate of discount is 3 percent, calculate the present value of the bond.
2. Consider a one-year discount bond that has a present value of $3,000. If the rate of discount is 5 percent, calculate the future value of the bond (the amount the bond pays in one year).
3. Consider a perpetuity that pays $300 every year. If the rate of discount is 6 percent, calculate the present value of the bond.
4. Consider a fixed-payment security that pays $250 at the end of every year for eight years. If the rate of discount is 3 percent, calculate the present value of the bond.
5. Consider a coupon bond that pays $150 every year and repays its principal amount of $2,000 at the end of six years. If the rate of discount is 7.5 percent, what is the present value of the bond?
6. Consider a coupon bond that pays $350 every year and repays its principal amount of $5,000 at the end of four years. If the rate of discount is 6 percent, what is the present value of the bond?
7. Answer the questions below.
a. You are negotiating a book deal for your newest novel in which an economist single-handedly saves the world. The publisher offers to pay you an advance of $1 million today plus $500,000 at the end of each of the next three years. What is the present value of these payments, given your rate of discount of 5 percent? Show your work. You may round to the nearest thousand dollars.
b. You counter the publisher's offer with a counteroffer that will pay you $1.5 million today plus $5 per book sold in each of the next three years. You think you will sell 80,000 books each year in that period, but the publisher thinks you will only sell 40,000 books each year. Explain why both you and the publisher like this counteroffer better than the deal in part a. Show your work.
8. Answer the questions below.
a. You buy a government bond that pays interest twice a year. The interest payment is $300 each six months. The bond matures in six years. The face value of the bond is $10,000. The annual market interest rate is 6 percent. What is the present value of the bond? Show your work.
A formula that may be useful to you is:
.
b. After six months go by, you receive the first interest payment of $300. The annual market interest rate has declined to 5 percent and you decide to sell the bond. What is the bond's present value when you sell it? Show your work.
c. What is your total return from owning the bond for six months (expressed at an annual rate, in percentage points, with two decimals)? Show your work.
9. You borrow $30,000 for 10 years to pay tuition and fees. The annual interest rate is 12 percent. What monthly payment would be required to pay off the loan?
10. On September 1, 2012, Al buys a bond for $15,000 that makes coupon payments of $750 after each of the following three years and returns its principal of $15,000 at the end of the three years. In other words, it is a standard coupon bond with a 5 percent annual interest rate making payments once each year.
On September 1, 2013, Al receives his first coupon payment of $750. At that time, the market interest rate on bonds like Al's has risen to 6 percent. Al sells his bond to Biff at that time, for a price equal to the present value of the bond's payments.
a. How much does Biff pay Al for the bond?
b. Calculate Al's current yield, capital-gains yield, and total return for the year.
On September 1, 2014, Biff receives a coupon payment of $750. The market interest rate on bonds like his remains 6 percent. Biff sells his bond to Cass at that time, for a price equal to the present value of the bond's payments.
c. How much does Cass pay Biff for the bond?
d. Calculate Biff's current yield, capital-gains yield, and total return for the year.
On September 1, 2015, Cass receives a coupon payment of $750 and the principal of $15,000. Over the course of the year (between September 1, 2014, and September 1, 2015), the market interest rate on bonds like his rose to 7 percent. But Cass decided to keep the bond.
e. What is Cass's total return for the year?
Explain and show all your work for each part.
11. On February 1, 2013, Janet buys a bond for $10,000 that will make coupon payments of $600 after each of the following two years and returns its principal of $10,000 at the end of the second year. In other words, it is a standard coupon bond with a 6 percent annual interest rate making payments once each year.
On February 1, 2014, Janet receives her first coupon payment of $600. At that time, the market interest rate on bonds like hers has fallen to 4 percent. She sells her bond to Justin at that time, for a price equal to the present value of the bond's payments.
a. How much does Justin pay Janet for the bond?
Both Janet and Justin have tax rates of 30 percent on interest income and 20 percent on capital gains. (Note that if someone has a capital loss, you may assume that he or she can reduce taxes by the amount of the capital loss times the tax rate of 20 percent.)
b. Calculate Janet's after-tax rate of return for the past year (from Feb. 1, 2013, to Feb. 1, 2014).
Justin holds onto the bond from February 1, 2014, to February 1, 2015, so it matures and he receives the second coupon payment and the principal.
c. What is Justin's after-tax rate of return for the year from Feb. 1, 2014, to Feb. 1, 2015?
Explain and show all your work for each part. You may assume, of course, that the market works and does not malfunction.