Question

Last year Janet purchased a $1,000 face value corporate bond with an 9% annual coupon rate and a 25-year maturity. At the time of the purchase, it had an expected yield to maturity of 9.31%. If Janet sold the bond today for $968.89, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.

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Answer 1

Coupon Interest rate = 9%

Par value of bond = $1,000.00

Interest per coupon (1000*9%) = $90.00

YTM rate 9.31%

No. of years to Maturity 25

Calculation of purchase price of bond @ 9.31% YTM

Annual Interest received = 90.00

Cumulative P.V.F. @ 9.31 % for 25 Years =

(1- ((1/(1.0931)^25)))/0.0931 9.580884862

Present value of interest received (90*9.5808848) $862.28

Maturity amount received = 1000

P.V.F. @ 9.31 % for 25 th year = 0.1080196193

(1/(1+0.0931)^25)

Present value of Maturity amount(1000*0.1080196) $108.02

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Price of bond $970.30

So, price of bond is $970.30

Calculation of rate of return for past year

Sale price of bond = 968.89

purchase price of bond= 970.3

Annual interest earned during last year 90

Rate of return earned = ((sale price - purchase price) + annual interest received ) / purchase price

((968.89-970.30)+90) / 970.30

0.09130165928 or 9.13%

So, rate of return earned during last year is 9.13%