Question

Bond X is noncallable and has 20 years to maturity, an 11% annual coupon, and a $1,000 par value. Your required return on Bond X is 12%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 10.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Answer:

You should be willing to pay $984.93 for Bond X

Explanation:

The price of a bond is equivalent to the present value of all the cash flows that are likely to accrue to an investor once the bond is bought. These cash-flows are the periodic coupon payments that are to be paid annually and the proceeds from the sale of the bond at the end of year 5.

During the 5 years, there are 5 equal periodic coupon payments that will be made. Given a par value equal to $1,000 and a coupon rate equal to 11% the annual coupon paid will be $1,000*0.11$ = $110. This stream of cash-flows is an ordinary annuity.

The  PV of the cash-flows = PV of the coupon payments + PV of the value of the bond at the end of year 5

Assuming that at the end of year 5 the yield to maturity on a 15-year bond with similar risk will be 10.5%, the price of the bond will be equal to :

 110*PV Annuity Factor for 15 periods at 10.5%+ $1,000* PV Interest factor with i=10.5% and n =15

= $110*\frac{[1-(1+0.105)^-^1^5]}{0.105}+ \frac{1,000}{(1+0.105)^1^5}$=$1,036.969123

therefore, the value of the bond today equals

110*PV Annuity Factor for 5 periods at 12%+ $1,036.969123* PV Interest factor with i=12% and n =5

= $110*\frac{[1-(1+0.12)^-^5]}{0.105}+ \frac{1,036.969123}{(1+0.12)^5}$=$984.93