Question

Bonds of Food Corporation with a par value of $1,000 sell for $960, matures in four years and have a 7% annual coupon rate paid annually, the interest rate will be 10%, 8%, and 11% respectively. Calculate the Realized compound yield.

Answer 1

Answer-

The realized compound yield is the rate of return one would earn if all the coupon payments are reinvested.

Given

FV = $ 1000
PV = $ 960
Number of years = 4
Annual coupon = 7 % annually = 7 % x $ 1000 = 0.07 x $ 1000 = $ 70

The interet rates are 10 % , 8 % and 11 %

Since the coupon payments are $ 70 / year and are reinvested at 10 % , 8 % and 11 %

Coupon payments are worth = $ 70 x ( 1.10 ) x ( 1.08) x ( 1.11) + $ 70 x ( 1.08) x ( 1.11) + $ 70 x (1.11)

= $ 70 x 1.31868 + $ 70 x 1.1988 + $ 70 x 1.11

= $ 92.31 + $ 83.916 + $ 77.7

= $ 253.926

The total return from the investment = $ 1000 + $ 253.926 = $ 1253.926

The present value or purhase price = $ 960

The realized compound yield or return is

$ 960 x ( 1+r)4  = $ 1253.926  

By using financial calculator we get

PV = ( $ 960)
FV = $ 1253.926
N= 4
PMT = $ 0
I/Y = r = ?

I/Y = r = 6.9 %

Therefore the realized compound yield = 6.9 %