Question

An investor is looking at two bonds. The first is a Treasury bond that has an annual coupon rate of 5%, matures in 10 years and with a $1,000 par value. The second is zero-coupon bond with a 3% yield to maturity that matures in 10 years. The market rate of interest is currently at 3%.

a) Compute the current price of the coupon-bearing Treasury bond? (15 pts)

b) Interest rates are forecast to rise by 50 basis points (0.5%) over the next year. Compute the rate of return on the coupon-bearing Treasury bond? (15 pts)

c) If instead, interest rates decline by 50 basis points, should you invest in the zero-coupon bond or the coupon-bearing Treasury bond and why? Show calculations. (20 pts)

Answer 1

It is assumed that coupon frequency is semi annual.

Part (a): Current price of coupon bearing Treasury Bond= $1,171.69

Part (b): If interest rate is increased by 50 basis points over one year, return on coupon bearing bond

= -2.708482% (negative)

Calculations of coupon bond are given at the end of this answer.

Part (c ): If interest rate is declined by 50 basis points over one year, return on coupon bond= 9.903381%

Current price of zero coupon bond (P0)= F/(1+r)^n

Where F= Face value (100), r= interest rate (3%) and n= period (10 years)

Plugging the inputs, Current Price= 100/(1+3%)^10 = $74.409391

If the interest rate declines by 50 basis points over one year,

Revised r= 2.5% and n=9 years

Price of zero coupon bond (P1) = 100/(1+2.5%)^9 =$80.072836

Return on zero coupon bond= (P1-P0)/P0

= (80.072836- 74.409391)/ 74.409391 = 7.611196%

Since the return on coupon bearing bond is higher, the same is opted.

Calculations of coupon bond as follows: