Question

Interest Rate Risk. Consider two bonds, a 3-year bond paying an annual coupon of 5% and a 10-year bond also with an annual coupon of 5%. Both currently sell at face value. Now suppose interest rates rise to 10%. (LO6-3) a. What is the new price of the 3-year bonds? b. What is the new price of the 10-year bonds? c. Do you conclude that long-term or short-term bonds are more sensitive to a change in interest rates?

Answer 1

a. $875.66

b. $692.77

c. Long-term bonds are more sensitive to a change in interest rate in comparison to short-term bond.

Step-by-step explanation:

a.

The new price will be equal to the present value of 03 annual coupon payments of $50 each ( 1,000 *5%) plus the present value of principal repayment of $1,000 in three year time; discounted at 10% which is calculated as:

( 50/0.1) * [ 1-1.1^(-3) ] + 1,000/1.1^3 = $875.66

b.

The new price will be equal to the present value of 10 annual coupon payments of $50 each ( 1,000 *5%) plus the present value of principal repayment of $1,000 in teen year time; discounted at 10% which is calculated as:

( 50/0.1) * [ 1-1.1^(-10) ] + 1,000/1.1^10 = $692.77

c.

As short-term bond's decrease its price less than long-term bond does, it can be concluded that Long-term bonds are more sensitive to a change in interest rate in comparison to short-term bond.

Answer 2

Check the following explanation

Step-by-step explanation:

Assume face value of both bond be $ 1,000

A)price of a 3 year bond = (PVAF@10%,3 * interest ) +(PVF@10%,3 * Face value)

=(2.48685 * 50 ) +(.75131 * 1000)

= 124.34 + 751.31

= $ 875.65

B)Price of a 10 year bond = (PVAF@10%,10 *interest) +(PVF@10%,10 * Face value)

=(6.14457 *50) + (.38554 *1000)

= 307.23 + 385.54

= $ 692.77

c)Long term bonds are more sensitive to short term bonds .This is so because longer the duration ,higher is the risk .so when interest rate changes ,longer duration prices will fall morethan by short term bonds.