Question

National Steel's 20-year, $1,000 par value bonds pay 9 percent interest annually. The market price of the bonds is $900 and your required rate of return is 12 percent.

a. Compute the bond's expected rate of return.

b. Determine the value of the bond to you, given your required rate of return.

c. Should you purchase the bond?

Answer 1

Answer a.

Par Value = $1,000
Current Price = $900

Annual Coupon Rate = 9.00%
Annual Coupon = 9.00% * $1,000
Annual Coupon = $90

Time to Maturity = 20 years

Let Annual YTM be i%

$900 = $90 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -900
PMT = 90
FV = 1000

I = 10.19%

Expected Rate of Return = 10.19%

Answer b.

Par Value = $1,000
Annual Coupon = $90
Time to Maturity = 20 years
Required Return = 12%

Value of Bond = $90 * PVIFA(12%, 20) + $1,000 * PVIF(12%, 20)
Value of Bond = $90 * (1 - (1/1.12)^20) / 0.12 + $1,000 / 1.12^20
Value of Bond = $775.92

Answer c.

No, you should not purchase this bond as its expected rate of return is lower than the required rate of return.