Question

1.An issue of bonds with par of $1,000 matures in 8 years and pays 8% p.a. interest semi-annually. The market price of the bonds is $1,205 and your required rate of return is 9%.

(a) Calculate the bonds expected rate of return.

(b) Calculate the value of the bond to you, given your required rate of return.

(c) Should you purchase the bond? (State the reason for your decision.)

Answer 1

Answer a.

Par Value = $1,000
Current Price = $1,205

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $1,000
Semiannual Coupon = $40

Time to Maturity = 8 years
Semiannual Period to Maturity = 16

Let semiannual YTM be i%

$1,205 = $40 * PVIFA(i%, 16) + $1,000 * PVIF(i%, 16)

Using financial calculator:
N = 16
PV = -1205
PMT = 40
FV = 1000

I = 2.437%

Semiannual YTM = 2.437%
Annual YTM = 2 * 2.437%
Annual YTM = 4.87%

Answer b.

Par Value = $1,000
Semiannual Coupon = $40
Semiannual Period to Maturity = 16

Annual Rate of Return = 9%
Semiannual Rate of Return = 4.50%

Expected Price = $40 * PVIFA(4.50%, 16) + $1,000 * PVIF(4.50%, 16)
Expected Price = $40 * (1 - (1/1.045)^16) / 0.045 + $1,000 / 1.045^16
Expected Price = $943.83

Answer c.

Expected price of bond is lower than the current market price of bond. So, we should not purchase this bond.