Question

Sampson food company has a 14% annual coupon interest rate on a $1,000 par value bond with 15 years left to maturity. Bonds of same maturity now sell to yield 12% return.

(a) How much would you be willing to pay for one of these bonds today? Why?              

(b) If the bond is selling for $ 1,150 what is the yield to maturity?

(c) Will you buy this bond? Explain in detail what key factors you will consider in making your decision.

Answer 1

Answer a.

Face Value = $1,000

Annual Coupon = 14% * $1,000
Annual Coupon = $140

Time to Maturity = 15 years
Annual Yield = 12%

Expected Price = $140 * PVIFA(12%, 15) + $1,000 * PVIF(12%, 15)
Expected Price = $140 * (1 - (1/1.12)^15) / 0.12 + $1,000 / 1.12^15
Expected Price = $1,136.22

Maximum amount paid for this bond is $1,136.22

Answer b.

Face Value = $1,000
Annual Coupon = $140
Time to Maturity = 15 years
Current Price = $1,150

Let annual YTM be i%

$1,150 = $140 * PVIFA(i%, 15) + $1,000 * PVIF(i%, 15)

Using financial calculator:
N = 15
PV = -1150
PMT = 140
FV = 1000

I = 11.82%

Yield to Maturity = 11.82%

Answer c.

YTM is lower than the required return and current price is higher than the expected price. Therefore, we should not buy this bond.