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

33.8%

Step-by-step explanation:

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

`p=(A(1-(1+r)^(-n) )/(r) + (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=(100(1-1.1384^(-20) )/(0.1384) + (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 =
`(994.79)/(743.31) -1=0.3383`

= 33.8% profit (rate of return).