Question

Consider a coupon bond with a 5% coupon rate. It will mature in one year and its yield to maturity is 10%. If the 1-year interest rate increases to 12% over the course of the year, what is the return on the bond?

Answer 1

$95.45

Step-by-step explanation:

First, we need to calculate the price of the bond using both yields to maturity

Current Price

Use the following formula to calculate the price of the bond

P = ( C x PVAF ) + ( F x PVF )

Where

F =Face value = $1,000

C =Coupon Payment = $1,000 x 5% = $50

PVAF = ( 1 - ( 1 + 10% )^-1 ) / 10% = 0.90909091

PVF = 1 / ( 1 + 10% )^1 = 0.90909091

Placing values in the formula

P = ( $50 x 0.90909091 ) + ( $1,000 x 0.90909091 )

P = $954.55

After 1 Year

The Bond will be matured on this time

At the of Maturity the price of the bond will be equal to the face value

Price of the bond = $1,000

Now calculate the return on the bond

Return on the bond = Coupon Interest + Price appreciation

Where

Coupon Interest = $50

Price appreciation = $1,000 - $954.55 = $45.45

Placing values in the formula

Return on the bond = $50 + $45.45 = $95.45