Question

. Last year Janet purchased a $1,000 face value corporate bond with an 10% annual coupon rate and a 20-year maturity. At the time of the purchase, it had an expected yield to maturity of 13.08%. If Janet sold the bond today for $1,051.15, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Given Information

FV	$1000
INTEREST	$100 ( 10% OF 1000)
YTM RATE	13.08%
YTM	20 Years
COMPOUNDING	Annually

Rate of return = Current yield    + Capital Gain Yield

= Annual interest / bond price + Current price / Price of the bond last year

Price of the bond = int [ 1 - ( 1 + r / 100) ^-n ] / r + FV / ( 1 + r /100) ⁿ

= 100 [ 1 - ( 1 + .1308) ^-20] / 0.1308 + 1000 / ( 1 + 0.1308)²⁰

= 100 [ 1 - 0.0855] / 0.1308 + 1000 / 11.68

= 699.15 + 85.6

= $ 784.75

Current yield = Annual interest / bond price

= 100 / 784.75

= 12.74%

Capital Gain Yield = Current price / Price of the bond last year - 1

= 1051.15 / 784.75 - 1  

= 1.339 - 1

= 0.339 %

Total Return = 12.74% + 0.339%

= 13.08%