Question

(Bond valuation) You own a bond that pays $120 in annual interest, with a $1,000 par value. It matures in 15 years. Your requires rate of return is 10 percent.

a. Calculate the value of the bond.

b. How does the value change if your required rate of return (1) increases to 16 percent or (2) decreases to 8 percent?

c. Explain the implications of your answers in part (b) as they relate to interest rate risk, premium bonds, and discount bonds.

d. Assume that the bond matures in 5 years instead of 15 years. Recompute your answers in part (b).

e. Explain the implications of your answers in part (d) as they relate to interest rate risk, premium bonds, discount bonds.

(round all answers to nearest cent or two decimal places)

Answer 1

Answer a.

Face Value = $1,000
Annual Coupon = $120
Time to Maturity = 15 years
Annual Interest Rate = 10%

Value of Bond = $120 * PVIFA(10%, 15) + $1,000 * PVIF(10%, 15)
Value of Bond = $120 * (1 - (1/1.10)^15) / 0.10 + $1,000 / 1.10^15
Value of Bond = $1,152.12

Answer b.

If interest rate increases to 16%:

Value of Bond = $120 * PVIFA(16%, 15) + $1,000 * PVIF(16%, 15)
Value of Bond = $120 * (1 - (1/1.16)^15) / 0.16 + $1,000 / 1.16^15
Value of Bond = $776.98

Percentage Change in Value = ($776.98 - $1,152.12) / $1,152.12
Percentage Change in Value = -0.3256 or -32.56%

If interest rate decreases to 8%:

Value of Bond = $120 * PVIFA(8%, 15) + $1,000 * PVIF(8%, 15)
Value of Bond = $120 * (1 - (1/1.08)^15) / 0.08 + $1,000 / 1.08^15
Value of Bond = $1,342.38

Percentage Change in Value = ($1,342.38 - $1,152.12) / $1,152.12
Percentage Change in Value = 0.1651 or 16.51%

Answer c.

If the interest rate is greater than the coupon rate, then price of will be lower than the par value.
If the interest rate is smaller than the coupon rate, then price of will be greater than the par value.

Answer d.

If interest rate increases to 16%:

Value of Bond = $120 * PVIFA(16%, 5) + $1,000 * PVIF(16%, 5)
Value of Bond = $120 * (1 - (1/1.16)^5) / 0.16 + $1,000 / 1.16^5
Value of Bond = $869.03

If interest rate decreases to 8%:

Value of Bond = $120 * PVIFA(8%, 5) + $1,000 * PVIF(8%, 5)
Value of Bond = $120 * (1 - (1/1.08)^5) / 0.08 + $1,000 / 1.08^5
Value of Bond = $1,159.71

Answer e.

Bond with higher maturity period is risky and value of bond show more change due to change in interest rate.