Answer:
Rate of return
30 year bond = 42%
20 year bond = 45%
Explanation:
First of all find current yield on 30 year maturity bond
We will use PV of annuity formula to calculate current YTM
Coupon Payment = 6.7% x 1000 = $67
$881.17 =( $67( 1- ( 1 + r )^-30 ) / r ) + ( 1000 / ( 1 + r )^30 )
r = 0.0773 = 7.73%
Current YTM is 7.73%
Now calculate the current yield for 20 years maturity bond
Coupon Payment = 6.2% x 1000 = $62
893.1 = ( ( $62 x ( 1 - ( 1 + r )^-20 ) / r ) + ( 1000 / ( 1 + r )^20 )
r = 0.0723 = 7.23%
As given
5 years from now the YTM on 30 Year bond will be 7.70% and on 20 Year bond will be 7.20%.
Now calculate
Price of the 30 year bond Bond after 5 year at YTM of 7.7%
Price of the Bond = ( $67 x ( 1 - ( 1 + 0.077 )^-(30-5) ) / 0.077 )+( 1000 / ( 1 + 0.077 )^(30-5) ) = $890.46
Price of the 20 year bond Bond after 5 year at YTM of 7.2%
Price of the Bond = ((6.7%*1000)*(1-(1+0.072)^-15)/0.072)+(1000/(1+0.072)^15)
( $62 x ( 1 - ( 1 + 0.072 )^-(20-5) ) / 0.072 )+( 1000 / ( 1 + 0.072 )^(20-5) ) = $910.06
Increase in price of 30 year bond = $890.46 - $881.17 = $9.29
Increase in price of 30 year bond = $910.06 - $893.1 = $16.96
Future value of Coupon payment for 5 years
30 year bond = 67 x ( 1.072^5 -1 ) / 0.072 = $386.84
20 year bond = 62 x ( 1.072^5 -1 ) / 0.072 = $357.97
Total return = FV of Coupon payment + Price increase
30 year bond = $386.84 + $9.29 = $396.13
20 year bond = $357.97 + $16.96 = $374.93
Rate of return =
30 year bond = $396.13 / $881.17 = 0.45 = 45%
20 year bond = $374.93 / $893.1 = 0.42 = 42%
