Question

Bond X is noncallable and has 20 years to maturity, a 11% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 7%. How much should you be willing to pay for Bond X today

Answer 1

Present value = $1,170.68

Step-by-step explanation:

The value of the bond in 5 years will be:

PV of face value = $1,000 / (1 + 7%)¹⁵ = $362.45

PV of coupon payments = $110 x 9.1079 (PVIFA, 15 periods, 7%) = $1,001.87

Total value = $1,364.32

The current value of the bond is:

PV of face value = $1,364.32 / (1 + 12%)⁵ = $774.15

PV of coupon payments = $110 x 3.6048 (PVIFA, 5 periods, 12%) = $396.53

Present value = $1,170.68