Question

Bond P is a premium bond with a 13% coupon. Bond D is a 8% coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 10%, and have 20 years to maturity. What is the current yield for bond P? For Bond D? If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P? For Bond D? Explain your answers and the interrelationship among the various types of yields.

Answer 1

Given,

13% Bond P and 8% bond D which are at premium and discount respectively has YTM of 10% and 20 years to maturity.

Since bond face value is not given in the question we assume $1000 as face value for computation of yield.

Computation of Current yield of the bonds :

Bond P :

Current price of the bond is calculated by computing present value of interest and terminal value.

Current price of the bond = (13% 1000) PvAF(10%,20y) + (1000 PvF(10%,20y)

= (130 8.514) + (1000 0.148644) = 1255.46

Current yield = Interest Current price of the bond

= 130 1255.46 =0.1035 10.35%

Bond D :

Current price of the bond = (8% 1000) PvAF(10%,20y) + (1000 PvF(10%,20y)

= (80 8.514) + (1000 0.148644) = 829.746

Current yield = 80 829.746 =0.0964 9.64%

Computation of capital gain yield of the bond over next year

Bond P :

Price of the bond after one year = (13% 1000) PvAF(10%,19y) + (1000 PvF(10%,19y)

= (130 8.365) + (1000 0.16351) = 1250.96

Capital gain yield = [Price of the bond after one year - price of the bond as on today] Price of the bond as on today

= [1250.96 - 1255.46]1255.46 100 = %

Bond D :

Price of the bond after one year = (8% 1000) PvAF(10%,19y) + (1000 PvF(10%,19y)

= (80 8.365) + (1000 0.16351) = $832.71

Capital gain yield = [832.71 - 829.746]829.746 100 = 0.357%

Current yield increases where as capital gain yield keeps decreasing over the period. This happens when the bond is at premium(interest rate > Yield to maturity).

Current yield decreases where as capital gain yield keeps increasing over the period. This happens when the bond is at discount(Interest rate < Yield to maturity).

Therefore current yield and capital yield move in opposite direction for the same bond.

The above mentioned value in colour is negative value