Question

A bond has a par value of \(1,000, a time to maturity of 10 years, and a coupon rate of 8% with interest paid annually. If the current market price is \)800, what will be the approximate capital gain yield of this bond over the next year if its yield to maturity remains unchanged?

Short answer

The capital gain yield will be $11.70

Step-by-step solution

Given information

PV = $-800

FV = $1000

PMT = 80

t = 9

Calculation of price, maturity years, YTM and Bond equivalent YTM

Yield To Maturity = (Face Value/Current Bond Price)^(1/Years To Maturity)−1

= (1000 / 800) )^(1/9)−1

= 11.46%

Calculation of capital gain yield

PV = -800

FV = $1000

PMT = 80

t = 9

i = 11.46%

The current yield = 80 / 800 = 10%

YTM = Current yield + Capital gain yield

11.46 = 10 + Capital gain yield

Capital gain = 1.46% of PV

New price = $811.70

Thus capital gain yield = $811.70 - $800

= $ 11.70