Assume you have a 1-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 6.2% coupon rate and pays the $62 coupon once per year. The third has a 7.2% coupon rate and pays the $72 coupon once per year. a. If all three bonds are now priced to yield 7% to maturity, what are their prices?
b. If you expect their yields to maturity to be 7% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each?
c. If you expect their yields to maturity to be 6% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each?

a. If all three bonds are now priced to yield 7% to maturity, what are their prices?

zero coupon bond = $1,000 / (1 + 7%)¹⁰ = $508.35

6.2% coupon bond:

PV of face value = $1,000 / (1 + 7%)¹⁰ = $508.35

PV of coupon payments = $62 x 7.0236 (PV annuity factor, 7%, 10 periods) = $435.46

market price = $943.81

7.2% coupon bond:

PV of face value = $1,000 / (1 + 7%)¹⁰ = $508.35

PV of coupon payments = $72 x 7.0236 (PV annuity factor, 7%, 10 periods) = $505.70

market price = $1,014.05

b. If you expect their yields to maturity to be 7% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each?

zero coupon bond = $1,000 / (1 + 7%)⁹ = $543.93

before tax holding period return = ($543.93 - $508.35) / $508.35 = 7%

after tax HPR = 7% x 0.8 = 5.6%

6.2% coupon bond:

PV of face value = $1,000 / (1 + 7%)⁹ = $543.93

PV of coupon payments = $62 x 6.5152 (PV annuity factor, 7%, 10 periods) = $403.94

market price = $947.87

before tax holding period return = ($947.87 - $943.81 + $62) / $943.81 = 7%

after tax HPR:

($4.06 x 0.8) / $943.81 = 0.34%

($62 x 0.7) / $943.81 = 4.60%

total = 4.94%

7.2% coupon bond:

PV of face value = $1,000 / (1 + 7%)⁹ = $543.93

PV of coupon payments = $72 x 6.5152 (PV annuity factor, 7%, 10 periods) = $469.09

market price = $1,013.02

before tax holding period return = ($1,013.02 - $1,014.05 + $72) / $1,014.05 = 7%

after tax HPR:

(-$1.03 x 0.8) / $1,014.05 = -0.08%

($72 x 0.7) / $1,014.05 = 4.97%

total = 4.89%

c. If you expect their yields to maturity to be 6% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your aftertax rate of return be on each?

zero coupon bond = $1,000 / (1 + 6%)⁹ = $591.90

before tax holding period return = ($591.90 - $508.35) / $508.35 = 16.44%

after tax HPR = 16.44% x 0.8 = 13.15%

6.2% coupon bond:

PV of face value = $1,000 / (1 + 6%)⁹ = $591.90

PV of coupon payments = $62 x 6.8017 (PV annuity factor, 6%, 10 periods) = $421.71

market price = $1,013.61

before tax holding period return = ($1,013.61 - $943.81 + $62) / $943.81 = 13.96%

after tax HPR:

($69.80 x 0.8) / $943.81 = 5.92%

($62 x 0.7) / $943.81 = 4.60%

total = 10.52%

7.2% coupon bond:

PV of face value = $1,000 / (1 + 6%)⁹ = $591.90

PV of coupon payments = $72 x 6.8017 (PV annuity factor, 6%, 10 periods) = $489.72

market price = $1,081.62

before tax holding period return = ($1,081.62 - $1,014.05 + $72) / $1,014.05 = 13.76%

after tax HPR:

($67.57 x 0.8) / $1,014.05 = 5.33%

($72 x 0.7) / $1,014.05 = 4.97%

total = 10.30%

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