Question

A $1,000 maturity value bond has 15 years left to maturity. The bond has an 8.5% coupon rate and pays interest annually.

a. If you want to earn a 7% rate of return, how much would you be willing to pay today for this bond?

b. Suppose you buy the bond for the value you calculated in part a. After holding the bond for two years and receiving two interest payments, you sell the bond for $1,032.43. What annual, compound rate of return have you earned over this two year period? Show that PVget equals PVgiveup. (Try 3%, 7% or 8%)

c. Suppose you buy the bond for the value you calculated in part a. After holding the bond for two years and receiving two interst payments, you sell the bond. What price must you receive (at time 2) to earn your desired 7% rate of return?

Answer 1

Answer a.

Par Value = $1,000
Time to Maturity = 15 years
Annual Coupon = 8.50%*$1,000 = $85
Rate of Return = 7%

Current Price = $85 * PVIFA(7%, 15) + $1,000 * PVIF(7%, 15)
Current Price = $85 * (1 - (1/1.07)^15) / 0.07 + $1,000 / 1.07^15
Current Price = $1,136.62

Answer b.

Purchase Price = $1,136.62
Annual Coupon = $85
Period = 2 years
Selling Price = $1,032.43

Let rate of return earned be i%

$1,136.62 = $85/(1+i) + $85/(1+i)^2 + $1,032.43/(1+i)^2

Using financial calculator:
N = 2
PV = -1136.62
PMT = 85
FV = 1032.43

I = 2.96%

Rate of Return = 2.96% or 3%

Answer c.

Purchase Price = $1,136.62
Annual Coupon = $85
Period = 2 years
Required Rate of Return = 7%

Let selling price be $x

$1,136.62 = $85/1.07 + $85/1.07^2 + $x/1.07^2
$1,136.62 = $153.682 + $x*0.8734
$x * 0.8734 = $982.938
$x = $1,125.42

So, selling price is $1,125.42