Question

A $5,000 bond with a coupon rate of 6.5% paid semiannually has eight years to maturity and a yield to maturity of 7.8% . If interest rates rise and the yield to maturity increases to 8.1% , what will happen to the price of the bond?

a. fall by $82.87

b. rise by $82.87

c. fall by $99.44

d. The price of the bond will not change

Answer 1

Answer: Option a is correct

Face value=$5000
Coupon rate=6.5%
Semiannual coupon rate=6.5%/2=0.0325
Semiannual coupon payment=(Semiannual coupon rate)*(Face value)=0.0325*5000=162.5
Time period=8 years
When the coupon is paid semiannually, the number of periods=8*2=16
Yield to maturity=7.8%
Semiannual yield to maturity=7.8%/2=0.039

Now, if the interest rate rises, the yield to maturity rises to 8.1%, so the semiannual yield to maturity=8.1%/2=0.0405

We can determine the values using excel.

U V At ytm of 0.039 At ytm of 0.0405 1 2 Face value 5000 5000 3 Payment 162.5 162.5 Number of periods 4 16 16 5 Yield to maturity 0.039 0.0405 ($4,618.49) ($4,535.62) 6 Present value= 7 Formula used: PV(V5,V4,V3,V2) PV(W5,W4,W3,W2)

As the present values are cash outflows, they are shown as negative in excel.

Present value before rise in interest rate=$4,618.49
Present value after rise in interest rate=$4,535.62
Difference=4535.62-4618.49=-82.87

So, the price fell down by -$82.87