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Solutions to Chapter 6

Note: Unless otherwise stated, assume all bonds have $1,000 face (par) value.

1. a. The coupon payments are fixed at $60 per year.

Coupon rate = coupon payment/par value = 60/1000 = 6%, which remains

unchanged.

b. When the market yield increases, the bond price will fall. The cash flows are

discounted at a higher rate.

c. At a lower price, the bond’s yield to maturity will be higher. The higher

yield to maturity on the bond is commensurate with the higher yields

available in the rest of the bond market.

d. Current yield = coupon payment/bond price. As coupon payment remains the

same and the bond price decreases, the current yield increases.

2. When the bond is selling at a discount, $970 in this case, the yield to maturity is

greater than 8%. We know that if the discount rate were 8%, the bond would sell at par.

At a price below par, the YTM must exceed the coupon rate.

Current yield equals coupon payment/bond price, in this case, 80/970. So, current yield

is also greater than 8%.

3. Coupon payment = .08 x 1000 = $80

Current yield = 80/bond price = .07

Therefore, bond price = 80/.07 = $1,142.86

4. Par value is $1000 by assumption.

Coupon rate = $80/$1000 = .08 = 8%

Current yield = $80/$950 = .0842 = 8.42%

Yield to maturity = 9.1185%

[Enter in the calculator: N = 6; PV= -950; FV = 1000; PMT = 80]

5. To sell at par, the coupon rate must equal yield to maturity. Since Circular bonds

yield 9.1185%, this must be the coupon rate.

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6. a. Current yield = annual coupon/price = $80/1,100 = .0727 = 7.27%.

b. On the calculator, enter PV = -1100, FV = 1000, n = 10, PMT = 80

Then compute I/Y (or i) and will get YTM = 6.6023%.

7. When the bond is selling at par, its yield to maturity equals its coupon rate. This

firm’s bonds are selling at a yield to maturity of 9.25%. So the coupon rate on the

new bonds must be 9.25% if they are to sell at par.

8. The current bid yield on the bond was 3.09%. To buy the bond, investors pay the

ask price. The investor would pay 108.21 percent of par value. With $1,000 par

value, this means paying $1,082.1 to buy a bond.

9. Coupon payment = interest = .05 × 1000 = 50

Capital gain = 1100 – 1000 = 100

Rate of return = = = .15 = 15%

10. Tax on interest received = tax rate × interest = .3 × 50 = 15

After-tax interest received = interest – tax = 50 – 15 = 35

Fast way to calculate:

After-tax interest received = (1 – tax rate) × interest = (1 – .3)× 50 = 35

Tax on capital gain = .5 × .3 × 100 = 15

After-tax capital gain = 100 – 15 = 85

Fast way to calculate:

After-tax capital gain = (1 – tax rate) × capital gain = (1 – .5×.3)×100 = 85

After-tax rate of return =

= = .12 = 12%

11. Bond 1

year 1: PMT = 80, FV = 1000, i = 10%, n = 10; Compute PV0 = $877.11

year 2: PMT = 80, FV = l000, i = 10%, n = 9; Compute PV1 = $884.82

Rate of return = = .10 = 10%

Bond 2

year 1: PMT = 120, FV = 1000, i = 10%, n = 10; Compute PV0 = $1122.89

year 2: PMT = 120, FV = l000, i = 10%, n = 9; Compute PV1 =$1115.18

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