Assume interest payments are on an annual basis. 1). Burns Fire and Casualty Company has $1,000 par value bonds outstanding at 1 % interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is: a). 6% b). 8% C). 12%

a. 6 percent yield to maturity

Present Value of Interest Payments

PVA = A x PVIFA (n = 20, i = 6%) Appendix D

PVA = $110 x 11.470 = $1,261.70

Present Value of Principal Payment at Maturity

PV = FV x FVIF (n = 20, i = 6%) Appendix B

PV = 1,000 x .312 = $312

Present Value of Interest Payment $1,261.70

Present Value of Principal Payment 312.00

Total Present Value or Price of the Bond $1,573.70

b. 8 percent yield to maturity
PVA = A x PVIFA (n = 20, i = 8%) Appendix D
PVA = $110 x 9.818 = $1,079.98
PV = FV x PVIF (n = 20, i = 8%) Appendix B
PV = $1,000 x .215 = $215
$1,079.98
215.00
$1,294,88
c. 12 percent yield to maturity
PVA = A x PVIFA (n = 20, i = 12%) Appendix D
PVA = $110 x 7.469 = $821.59
PV = FV x PVIF (n = 20, i = 12%) Appendix B
PV = $1,000 x .104 = $104
$821.59
104.00
$925.59

11). Jim Busby calls his broker to inquire about purchasing a bond of Disk Storage Systems. His broker quotes a price of $1,180. Jim is concerned that the bond might be overpriced based on the facts involved. The $1,000 par value bond pays 14% interest, and it has 25 years remaining until maturity. The current yield to maturity on similar bonds is 12%. Compute the new price of the bond and comment on whether you think it is overpriced in the marketplace. Explain the rationale behind each of these valuation calculations. Do you observe a common theme?

Present Value of Interest Payments

PVA = A x PVIFA (n = 25, i = 12%) Appendix D

PVA = $140 x 7.843 = $1,098.02

Present Value of Principal Payment at Maturity

PV = FV x PVIF (n = 25, i = 12%) Appendix B

PV = $1,000 x .059 = $59

$1,098.02

59.00

$1,157.02

The bond has a value of $1,157.02. This indicates his broker is quoting too high a price at $1,180.