Question

In: Finance

You are examining three bonds with a par value of $1,000 (you receive $1,000 at​ maturity)...

You are examining three bonds with a par value of $1,000 (you receive $1,000 at​ maturity) and are concerned with what would happen to their market value if interest rates​ (or the market discount​ rate) changed. The three bonds are

Bond A—a bond with 6 years left to maturity that has an annual coupon interest rate of 9 ​percent, but the interest is paid semiannually.

Bond B—a bond with 9 years left to maturity that has an annual coupon interest rate of 9 ​percent, but the interest is paid semiannually.

Bond C—a bond with 17 years left to maturity that has an annual coupon interest rate of 9 ​percent, but the interest is paid semiannually.

What would be the value of these bonds if the market discount rate were

a. 9 percent per year compounded​ semiannually?

b. 5 percent per year compounded​ semiannually?

c. 14 percent per year compounded​ semiannually?

d. What observations can you make about these​ results?

Solutions

Expert Solution

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = YTM/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = (years remaining until maturity * 2)

pmt = -1000 * coupon rate / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = -1000 (face value receivable on maturity)

The bond prices are calculated as below :

d]

The observations are :

  • Higher the market discount rate, lower the bond price
  • Lower the market discount rate, higher the bond price
  • Longer the bond maturity, more sensitive the bond to changes in the market discount rate

jeff jeffy answered 2 years ago
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