Answer:
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%
