Question

Suppose you buy a bond that will pay $10,000 principal at the end of 10 years. No coupon interest payments are made on the bond. (It is a zero coupon bond.) If the yield to maturity of similar zero coupon bonds is 6 percent per year:

A. What is the current price of the bond?

B. What will be the price of the bond if the market yield to maturity instantaneously increases to 8 percent per year?

C. What will the price be if the yield to maturity instantaneously declines to 4 percent per year?

D. Explain the relationship among the prices.

Answer 1

A. Current price of the bond will be the present value of all future cash flows from the bond.

Since there will be no coupon interest payments, so the present value calculation will include only the principal payment after 10 years

We now look the present value table to find out the present value of $1 at 6% after 10 years. It comes $0.558 .

So, current price of the bond = Pesent value of $10000 at 6% for 10 years

= 0.558 * $10000 = $5580

B) Price of the bond with yield to maturity of 8% will be the present value of $10000 at 8% for 10 years.

We now look the present value table to find out the present value of $1 at 8% after 10 years. It comes $0.463 .

So, price of the bond with 8% yield to maturity = Pesent value of $10000 at 8% for 10 years

= 0.463 * $10000 = $4630

C) Price of the bond with yield to maturity of 4% will be the present value of $10000 at 4% for 10 years.

We now look the present value table to find out the present value of $1 at 4% after 10 years. It comes $0.676 .

So, price of the bond with 4% yield to maturity = Pesent value of $10000 at 4% for 10 years

= 0.676 * $10000 = $6760

D) Price yield relationship is given below:

Yield to maturity Price of the bond

6% $5580

8% $4630

4% $6760

So, from the above table we can clearly see that, as the yield to maturity increases, price of the bond decreases and as the yield to maturity decreases, price of the bond increases. Means there is inverse relationship between the yield to maturity and priceof the bond.