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 13.84%. If Janet sold the bond today for $994.79, 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

Answer:

33.8%

Explanation:

Purchase price of the bond will be computed using the formula below.

$p=\frac{A(1-(1+r)^{-n} }{r} + \frac{F}{(1+r)^{n} }$

where A = annual coupon = 10% * 1000 = 100

r = yield to maturity = 0.1384

n = time to maturity = 20 years

F = face value = $1,000

p = price of the bond.

$p=\frac{100(1-1.1384^{-20} }{0.1384} + \frac{1,000}{(1.1384)^{20} }\\p = 668.4721 + 74.8346\\p = 743.31$

Therefore, if Janet sold the bond a year later for $994.79,

the profit on sale = $\frac{994.79}{743.31} -1=0.3383$

= 33.8% profit (rate of return).