Martin Shipping Lines issued bonds ten years ago at $2,700 per bond. The bonds had a 30-year...

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Martin Shipping Linesissued bonds ten years ago at $2,700 per bond. The bonds had a30-year life when issued, with semiannual payments at the thenannual rate of 10 percent. This return was in line with requiredreturns by bondholders at that point, as described below:
Â Â Â Â
Â Â Realrate of return 2 %
Â Â Inflation premium 4
Â Â Riskpremium 4
Â Â Total return 10 %
Â Â Â Â
Assume that today theinflation premium is only 2 percent and is appropriately reflectedin the required return (or yield to maturity) of the bonds.
Â Â Â Â Â Â
Compute the new priceof the bond.

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4.1 Ratings (588 Votes)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Martin Shipping LinesÂ Â Â Â Â Â

First compute the new required rate of return (yield to maturity).

Real rate of returnÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2%

Inflation premiumÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2%

Risk premiumÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4%

Total returnÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 8%

Then use this value to find the price of the bond.

Present Value of Interest Payments

PVA = A Ã— PVIFA (n = 20, i = 8%)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Appendix D

PVA = $270 Ã— 9.818 = $2,650.86

Present Value of Principal Payment at Maturity

PV = FV Ã— PVIF (n = 20, i = 8%)Â Â Â Appendix B

PV = $2,700 Ã— .215 = $580.5

The new price of the bond = $2,650.86+ $580.5 = $3,231.36

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