Question

9. Predicting Bond Values (Use the chapter appendix to answer this problem.) The portfolio manager of Ludwig Company has excess cash that is to be invested for four years. He can purchase four-year Treasury notes that offer a 9 percent yield. Alternatively, he can purchase new 20-year Treasury bonds for $2.9 million that offer a par value of $3 million and an 11 percent coupon rate with annual payments. The manager expects that the required return on these same 20-year bonds will be 12 percent four years from now.

a. What is the forecasted market value of the 20-year bonds in four years?

b. Which investment is expected to provide a higher yield over the four-year period?

Answer 1

a.

C= coupon=11%*3 million= 330,000

n= periods remaining after 4 years= 20-4 =16

PV of 20-Year................PV of Remaining Bonds as of 4 years from now

= Coupon Payments +PV of Principal

= $330,000(PVIFA,i= 12%,n= 16) + $3,000,000(PVIF,i= 12%,n= 16)

= $330,000(6.9740) + $3,000,000(.1631)

= $2,301,420 + $489,300

= $2,790,720

b.

Company could achieve a yield of 9 percent on the Treasury notes with certainty.

By discounting the cash flow resulting from the alternative investment (20-year bonds) over the four-year investment horizon at 9 percent, we can determine whether the bonds offer a higher or lower yield.

The PV of the bonds as of today using a 9 percent discount rate is:

= $330,000(PVIFA,i= 9%,n= 4) + $2,790,720(PVIF,i= 9%,n= 4)

= $330,000(3.2397) + $2,790,720(.7084)

= $1,069,101 + $1,976,946

= $3,046,047

Since now the company would pay less for these bonds than the PV estimated here, this implies that yield to maturity on the Treasury bonds exceeds 9 percent.

Therefore, the Treasury bonds offer a higher yield than the Treasury notes.