Question

Assume a bond today with a $10,000 face value, 5 years to maturity, and coupon rate of 2.5% paid semi-annually.

A) The price of this bond today, assuming a YTM of 3.4%, is:

B) The price of this bond after six months from today, assuming a YTM of 1.8%, is:

C) The current yield for this bond is:

D) The capital gain for this bond is:

Answer 1

Ans. Face value of the bond, F = $10000

Years to maturity, n = 5 years

Number of coupons paid, N = 5*2 = 10

Coupon rate, c = 2.5%

Coupon, C = c*F = $250

A) Using formula for price of the bond with yield = 3.4% or 0.034

Price of the bond, P = 250*[(1-1/(1+0.034)^10)/0.034] + 10000/(1+0.034)^10

=> P = $9589.36

B) After six months, coupon payment left = 9

Using price of the bond formula at yield of 1.8% or 0.018

P' = 250*[(1-1/(1+0.018)^9)/0.018] + 10000/(1+0.018)^9

=> P' = $10576.85

C) Current Price of the bond at yield of 1.8%
=> P = 250/[(1-1/(1+0.018)^10)/0.018] + 10000/(1+0.018)^10

=> P = $10333.28

C) Capital Gain = (P' - P)/P = (10576.85 - 10333.28)/10333.28 = 2.357%

* Please don’t forget to hit the thumbs up button, if you find the answer helpful.