Question

You buy a bond with the following features: 6 years to maturity, face value of $1000, coupon rate of 4% (annual coupons) and yield to maturity of 2.1%. Just after you purchase the bond, the yield to maturity rises to 4.5%. What is the capital gain or loss on your bond? If the answer is a capital gain just enter the number. For example 581.65 If the answer is a capital loss enter a negative number. For example -841.47 Do not include the $ sign, just enter the number in dollars, rounded to the nearest cent (2 decimals). Hint: capital gain / loss = value of the bond now - initial value of the bond.

Answer 1

We know the formulae

YTM = (C + (F - P) / n) / ((F + P) / 2)

YTM = Yield to Maturity

C = Coupon or Interest Payment = 4 % of 1000 = $ 40

F = Face Value = $ 1000

P = Price = x

n = Years to Maturity = 6 years

2.1 % = ( 40 +( 1000-x) /6)/((1000+x)/2)

2.1% = (1240-x)/6/(1000+x) /2

Bond price = 1106.08 $

if ytm = 4.5 %

4.5% = (1240-x)/6/(1000+x) /2

Bond price = 974.22 $

Therefore capital loss = -131.86 $

=974.22-1106.08