1. Indicate whether each of the following 9 statements is true or false.
Statement 1: If a company performs very well, investors in that company’s
... [Show More] bonds are likely to receive a higher coupon payment than the coupon payment indicated by the bond’s coupon rate, face value, and frequency of coupon payments (annual or semi-annual).
Statement 2: If a company performs very poorly, investors in that company’s bonds may receive a lower coupon payment than the coupon payment indicated by the bond’s coupon rate, face value, and frequency of coupon payments (annual or semi-annual).
Statement 3: If Donatello Company is performing very poorly and the firm fails to make promised coupon payments to bondholders, then the bondholders can take legal recourse against the firm.
Statement 4: If Donatello Company is performing very poorly and the firm fails to make promised coupon payments to bondholders, then the bondholders can not take legal recourse against the firm.
Statement 5: On Friday, 10,000 bonds issued by Glorious Vending were bought by a variety of investors for $1,000 per bond. If Glorious Vending received $10 million from the sale of these bonds, then the 10,000 bonds were more likely sold on the primary market than the secondary market.
Statement 6: On Friday, 10,000 bonds issued by Glorious Vending were bought by a variety of investors for $1,000 per bond. If Glorious Vending received $10 million from the sale of these bonds, then the 10,000 bonds were more likely sold on the secondary market than the primary market.
Statement 7: On Friday, 10,000 bonds issued by Glorious Vending were bought by a variety of investors for $1,000 per bond. If Glorious Vending received $0 from the sale of these bonds, then the 10,000 bonds were more likely sold on the primary market than the secondary market.
Statement 8: On Friday, 10,000 bonds issued by Glorious Vending were bought by a variety of investors for $1,000 per bond. If Glorious Vending received $0 from the sale of these bonds, then the 10,000 bonds were more likely sold on the secondary market than the primary market.
Statement 9: Foreign countries, states, cities, counties, corporations, and the U.S. government are all entities that issue bonds. Note that this statement is true if all six entities issue bonds and that this statement is false if one or more of the six entities does not issue bonds.
The following exam questions involve the truthfulness of one or more of the 9 statements
(Spring 2012, test 2, question 7) (Spring 2014, test 2, question 7)
(Fall 2014, test 2, question 7) (Fall 2015, test 2, question 5)
Statement 1 is false
If a firm does well, payments to bondholders do not exceed the coupon payment indicated by the bond’s coupon rate, face value, and frequency of coupon payments (annual or semi-annual). The promised payments are the most that bondholders receive.
Statement 2 is true
If a firm does poorly, payments to bondholders may be less than the coupon payment indicated by the bond’s coupon rate, face value, and frequency of coupon payments (annual or semi-annual). There is a risk (called default risk or credit risk) that all or some of the promised scheduled payments may not be made.
Statement 3 is true
Creditors can take legal recourse to try to secure payment, which may or may not be successful. For example, the bondholders can force the firm into bankruptcy.
Statement 4 is false
Creditors can take legal recourse to try to secure payment, which may or may not be successful. For example, the bondholders can force the firm into bankruptcy.
Statement 5 is true
The primary market is the market for the sale of new securities. The primary bond market involves a bond issuer like a company raising money by selling bonds to investors. The secondary market is the market in which previously issued securities are traded among investors. The secondary bond market involves one investor selling bonds to another investor. A bond issuer like a company gets no money from transactions in the secondary market. In this case, the firm received money, so the bonds were sold on the primary market.
Statement 6 is false
The primary market is the market for the sale of new securities. The primary bond market involves a bond issuer like a company raising money by selling bonds to investors. The secondary market is the market in which previously issued securities are traded among investors. The secondary bond market involves one investor selling bonds to another investor. A bond issuer like a company gets no money from transactions in the secondary market. In this case, the firm received money, so the bonds were sold on the primary market.
Statement 7 is false
The primary market is the market for the sale of new securities. The primary bond market involves a bond issuer like a company raising money by selling bonds to investors. The secondary market is the market in which previously issued securities are traded among investors. The secondary bond market involves one investor selling bonds to another investor. A bond issuer like a company gets no money from transactions in the secondary market. In this case, the firm received no money, so the bonds were sold on the secondary market.
Statement 8 is true
The primary market is the market for the sale of new securities. The primary bond market involves a bond issuer like a company raising money by selling bonds to investors. The secondary market is the market in which previously issued securities are traded among investors. The secondary bond market involves one investor selling bonds to another investor. A bond issuer like a company gets no money from transactions in the secondary market. In this case, the firm received no money, so the bonds were sold on the secondary market.
Statement 9 is true
Foreign countries, states, cities, counties, corporations, and the U.S. government are all all among the entities that issue bonds.
2. Today, a bond has a coupon rate of 9.64%, par value of $1000, YTM of 9.40%, and semi-annual coupons with the next coupon due in 6 months. One year ago, the bond’s price was $983.42 and the bond had 15 years until maturity. What is the current yield of the bond today?
(Spring 2014, test 2, question 8)
Current yield today = annual coupons / bond value today
Approach:
1) Find the annual coupons
2) Find the value of the bond today
3) Find the current yield today
1) Find the annual coupons
Annual coupons = par × coupon rate
= 1000 × 9.64%
= $96.40
2) Find bond value today
If the bond had 15 years until maturity from 1 year ago, then today it has 14 years until maturity, so
N = 14 years × 2 coupons per year = 28
I% = YTM ÷ # coupons per year = 9.40 ÷ 2 = 4.70
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 9.64% ÷ 2 = 48.20
END mode
Enter 28 4.70 48.20 1000
N I% PV PMT FV
Solve for -1,018.48
Today, the price of the bond is $1,018.48
3) Find current yield today
Current yield today = annual coupons / bond value today
= 96.40 / 1,018.48
= .0947 = 9.47%
3. One year ago, a bond had a coupon rate of 8.80%, par value of $1000, YTM of 9.82%, and semi-annual coupons. Today, the bond’s price is $981 and the bond has 13 years until maturity. What was the current yield of the bond one year ago? The next coupon is due in 6 months.
(Spring 2016, test 2, question 7)
(Fall 2017, final, question 7)
Current yield one year ago = annual coupons / bond value one year ago
Approach:
1) Find the annual coupons
2) Find the value of the bond one year ago
3) Find the current yield one year ago
1) Find the annual coupons
Annual coupons = par × coupon rate
= 1000 × 8.80%
= $88.00
2) Find the value of the bond one year ago
If the bond has 13 years until maturity from today, then one year ago it had 14 years until maturity, so
N = 14 years × 2 coupons per year = 28
I% = YTM ÷ # coupons per year = 9.82 ÷ 2 = 4.91
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 8.80% ÷ 2 = 44.00
END mode
Enter 28 4.91 44.00 1000
N I% PV PMT FV
Solve for -923.27
One year ago, the price of the bond was $923.27
3) Find the current yield one year ago
Current yield one year ago = annual coupons / bond value one year ago
= 88.00 / 923.27
= .0953 = 9.53%
Note: today’s price is irrelevant for this problem
4. Six months ago, a bond had a coupon rate of 22.60%, par value of $1000, YTM of 12.60%, and semi-annual coupons. Today, the bond’s price is $1,495 and the bond has 9 years until maturity. What was the current yield of the bond six months ago? The next coupon is due in 6 months.
(Spring 2013, test 2, question 7)
(Spring 2017, test 2, question 6)
Current yield six months ago = annual coupons / bond value six months ago
Approach:
1) Find the annual coupons
2) Find the value of the bond six months ago
3) Find the current yield six months ago
1) Find the annual coupons
Annual coupons = par × coupon rate
= 1000 × 22.60%
= $226.00
2) Find the value of the bond six months ago
If the bond has 9 years from today until maturity, then six months ago it had 9 years and 6 months until maturity, which is equal to 9.5 years, so
N = 9.5 years × 2 coupons per year = 19
I% = YTM ÷ # coupons per year = 12.60 ÷ 2 = 6.30
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 22.60% ÷ 2 = 113
END mode
Enter 19 6.30 113 1000
N I% PV PMT FV
Solve for -1,545.05
Six months ago, the price of the bond was $1,545.05
3) Find the current yield six months ago
Current yield six months ago = annual coupons / bond value six months ago
= 226.00 / 1,545.05
= .1463 = 14.63%
5. Bond A has a coupon rate of 17.80 percent, a yield-to-maturity of 15.60 percent, and a face value of $1,000; matures in 12 years; and pays coupons annually with the next coupon expected in 1 year. What is (X + Y + Z) if X is the present value of any coupon payments expected to be made in 5 years from today, Y is the present value of any coupon payments expected to be made in 10 years from today, and Z is the present value of any coupon payments expected to be made in 15 years from today?
(Fall 2013, test 2, question 7)
(Fall 2014, test 2, question 8)
(Fall 2016, test 2, question 5)
(Fall 2017, test 2, question 4)
Approach:
1) Determine the coupon payments expected in 5, 10, and 15 years
2) Determine the appropriate period length and discount rate
3) Find the present values of any coupon payments expected in 5, 10, and 15 years
4) Add up the present values of any coupon payments expected in 5, 10, and 15 years
1) Determine the coupon payments expected in 5, 10, and 15 years
The expected annual coupon for bond A
= par × coupon rate ÷ # coupons per year
= $1,000 × 17.80% ÷ 1 = $178.00
Since the bond matures in 12 years, a coupon of $178.00 is expected in 5 years and in 10 years, but not in 15 years.
2) Determine the appropriate period length and discount rate
Since coupons are paid annually, the relevant period is a year
Therefore:
- The coupon of $178.00 expected in 5 years, which is in 5 periods
- The coupon of $178.00 expected in 10 years, which is in 10 periods
- There is no coupon expected in 15 years, which is in 15 periods
The relevant discount rate per period for bond A
= YTM ÷ # coupons per year
= 15.60 percent ÷ 1 = 15.60 percent = .1560 per year
3) Find the present values of any coupon payments expected in 5, 10, and 15 years
PV0 = Ct / (1+r)t
X = the present value of the coupon of $178.00 expected in 5 years = $178.00 / 1.15605 = $86.22
Y = the present value of the coupon of $178.00 expected in 10 years = $178.00 / 1.156010 = $41.77
Z = $0, because no coupon is expected in 15 years
4) Add up the present values of any coupon payments expected in 5, 10, and 15 years
X + Y +Z
= $86.22 + $41.77 + $0.00
= $127.99
6. Reg owns investment A and 1 bond B. The total value of his holdings is $2,820. Bond B has a coupon rate of 8.80 percent, par value of $1000, YTM of 9.42 percent, 14 years until maturity, and semi-annual coupons with the next coupon due in 6 months. Investment A is expected to pay annual cash flows to Reg of $312 per year forever with the first annual cash flow expected in 1 year from today. What is the expected return for investment A?
(Spring 2018, test 2, question 5)
Approach to solve
1) Find the price of bond B
2) Find the value of investment A
3) Find the expected return of investment A
1) Find the price of bond B
N = 14 years × 2 coupons per year = 28
I% = YTM ÷ # coupons per year = 9.42 ÷ 2 = 4.71
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 8.80% ÷ 2 = 44.00
END mode
Enter 28 4.71 44.00 1000
N I% PV PMT FV
Solve for -952.32
The price of the bond is $952.32
2) Find the value of investment A
We know that the value of investment A + price of bond B = $2,820
Therefore, the value of investment A = $2,820 – price of bond B
= $2,820 – $952.32
= $1,867.68
3) Find the expected return of investment A
Investment A is a fixed perpetuity
Therefore, the value of the investment is PV = C/r and r = C/PV
C = 312
PV = 1,867.68
r = 312 / 1,867.68 = .1671 = 16.71%
7. Ben owns investment A and 1 bond B. The total value of his holdings is $2,800. Bond B has a coupon rate of 8.80 percent, par value of $1000, YTM of 9.40 percent, 14 years until maturity, and semi-annual coupons with the next coupon due in 6 months. Investment A is expected to pay annual cash flows to Ben of X per year forever with the first annual cash flow expected in 1 year from today. The expected return for investment A is 7.91 percent. What is X, the fixed annual cash flow that will be paid forever by investment A?
Approach to solve
1) Find the price of bond B
2) Find the value of investment A
3) Find the fixed annual cash flow that will be paid forever by investment A
1) Find the price of bond B
N = 14 years × 2 coupons per year = 28
I% = YTM ÷ # coupons per year = 9.40 ÷ 2 = 4.70
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 8.80% ÷ 2 = 44.00
END mode
Enter 28 4.70 44.00 1000
N I% PV PMT FV
Solve for -953.81
The price of the bond is $953.81
2) Find the value of investment A
We know that the value of investment A + price of bond B = $2,800
Therefore, the value of investment A = $2,800 – price of bond B
= $2,800 – $953.81
= $1,846.19
3) Find the fixed annual cash flow that will be paid forever by investment A
Investment A is a fixed perpetuity
Therefore, the value of the investment is PV = C/r and C = PV × r
r = .0791
PV = 1,846.19
C = X = 1,846.19 × .0791 = $146.03
8. Kip owns investment A and 1 bond B. The total value of his holdings is $2,800. Bond B has a coupon rate of 8.64 percent, par value of $1000, YTM of 9.70 percent, 12 years until maturity, and semi-annual coupons with the next coupon due in 6 months. Investment A is expected to produce annual cash flows forever. The next cash flow is expected to be $253 in 1 year, and subsequent annual cash flows are expected to increase by 1.17 percent each year forever. What is the expected return for investment A?
(Fall 2016, test 2, question 6)
Approach to solve
1) Find the price of bond B
2) Find the value of investment A
3) Find the expected return of investment A
1) Find the price of bond B
N = 12 years × 2 coupons per year = 24
I% = YTM ÷ # coupons per year = 9.70 ÷ 2 = 4.85
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 8.64% ÷ 2 = 43.20
END mode
Enter 24 4.85 43.20 1000
N I% PV PMT FV
Solve for -925.79
The price of the bond is $925.79
2) Find the value of investment A
We know that the value of investment A + price of bond B = $2,800
Therefore, the value of investment A = $2,800 – price of bond B
= $2,800 – $925.79
= $1,874.21
3) Find the expected return of investment A
Investment A is a growing perpetuity
Therefore, the value of the investment is PV = C1/(r – g) and r = (C1/PV) + g
C1 = 253
PV = 1,874.21
g = .0117
r = (253 / 1,874.21) + .0117 = .1350 + .0117 = .1467 = 14.67%
9. Red owns investment A and 1 bond B. The total value of his holdings is $3,150. Bond B has a coupon rate of 16.86 percent, par value of $1000, YTM of 8.72 percent, 9 years until maturity, and semi-annual coupons with the next coupon due in 6 months. Investment A is expected to produce cash flows forever. The next cash flow is expected to be X in 1 year, and subsequent annual cash flows are expected to increase by 1.19 percent each year forever. The expected return for investment A is 14.37 percent. What is X, the annual cash flow that will be paid in 1 year from now by investment A?
Approach to solve
1) Find the price of bond B
2) Find the value of investment A
3) Find the annual cash flow that will be paid in 1 year from today by investment A
1) Find the price of bond B
N = 9 years × 2 coupons per year = 18
I% = YTM ÷ # coupons per year = 8.72 ÷ 2 = 4.36
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 16.86% ÷ 2 = 84.30
END mode
Enter 18 4.36 84.30 1000
N I% PV PMT FV
Solve for -1,500.48
The price of the bond is $1,500.48
2) Find the value of investment A
We know that the value of investment A + price of bond B = $3,150
Therefore, the value of investment A = $3,150 – price of bond B
= $3,150 – $1,500.48
= $1,649.52
3) Find the annual cash flow that will be paid in 1 year from today by investment A
Investment A is a growing perpetuity
Therefore, the value of the investment is PV = C1/(r – g) and C1 = PV × (r – g)
PV = 1,649.52
r = .1437
g = .0119
C1 = X = PV × (r – g) = 1,649.52 × (.1437 – .0119) = 1,649.52 × (.1318) = $217.41
10. Don owns investment A and 1 bond B. The total value of his holdings is $3,250. Bond B has a coupon rate of 12.44 percent, par value of $1000, YTM of 11.56 percent, 23 years until maturity, and semi-annual coupons with the next coupon due in 6 months. Investment A is expected to produce cash flows forever. The next cash flow is expected to be $179 in 1 year, and subsequent annual cash flows are expected to increase by g each year forever. The expected return for investment A is 15.27 percent. What is g, the annual growth rate for the annual cash flows paid by investment A?
Approach to solve
1) Find the price of bond B
2) Find the value of investment A
3) Find the annual growth rate for the annual cash flows paid by investment A
1) Find the price of bond B
N = 23 years × 2 coupons per year = 46
I% = YTM ÷ # coupons per year = 11.56 ÷ 2 = 5.78
FV = par = 1,000
PMT = par × coupon rate ÷ # coupons per year = 1000 × 12.44% ÷ 2 = 62.20
END mode
Enter 46 5.78 62.20 1000
N I% PV PMT FV
Solve for -1,070.38
The price of the bond is $1,070.38
2) Find the value of investment A
We know that the value of investment A + price of bond B = $3,250
Therefore, the value of investment A = $3,250 – price of bond B
= $3,250 – $1,070.38
= $2,179.62
3) Find the annual growth rate for the annual cash flows paid by investment A
Investment A is a growing perpetuity
Therefore, the value of the investment is PV = C1/(r – g) and g = r – (C1/PV)
C1 = 179
PV = 2,179.62
r = .1527
g = r – (C1/PV) = .1527 – (179 / 2,179.62) = .1527 – .0821 = .0706 = 7.06% [Show Less]