Question

Assume a bond today with a $10,000 face value, 10 years to maturity, and coupon rate of 4% paid semi-annually.

A) The price of this bond today, assuming a YTM of 4.2%, is: $Answer for coordinate 1

B) The price of this bond after six months from today, assuming a YTM of 3.1%, is: $Answer for coordinate 2

C) The current yield for this bond is: Answer for coordinate 3%

D) The capital gain for this bond is: Answer for coordinate 4%

Answer 1

A. Since the coupon is being paid semi-annually, the coupon rate will be 2%. The YTM will become 2.1%. The PV equation for the price of the bond will look like:

Price = 200/1.021^1 + 200/1.021^2 + ... + 200/1.021^20 + 10000/1.021^20 = $9,838.053

B. Now, the YTM will become 3.1/2 = 1.55%. So, the PV equation will look like:

Price = 200/1.0155^1 + 200/1.0155^2 + ... + 200/1.0155^19 + 10000/1.0155^19 = $10,735.71

C. The current yield is given as = Annual Coupon/Price of bond = 400/9838.053 = 4.065%

D. The capital gain for this bond will be = (10735.71-9838.053)/9838.053 = 9.1243%.