# Chapter 10 #1 P

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• ### Current yield to maturity

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Comprehensive Problem Chapter 9 P.281

Mr. Rambo, President of Assault Weapons, inc. was pleased to hear that he had three offers from major defense companies for his latest missile firing automatic ejector. He will use a discount rate of 12% to evaluate each offer.

Offer I - \$500,000 now plus \$120,000 from the end of year 6 through 15. Also, if the product goes over \$50 million in cumulative sales by the end of year 15, he will receive an additional \$1,500,000. Rambo thought there was a 75% probability this would happen.

Offer II - 25% of the buyer's gross margin for the next 4 years. The buyer on this case is Air Defense, Inc. (ADI). Its gross margin is 65 percent. Sales for year 1 are projected to be \$1 million and then grow by 40% per year. This amount is paid today and is not discounted.

Offer III - A trust fund would be set up for the next nine years. At the end if that period, Rambo would receive the proceeds (and discount them back to the present at 12%). The trust funs called for semiannual payments for the next 9 years of \$80,000 (a total of \$160,000 per year). The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. To look up the future value of the annuity due in the tables, add 1 to n (18 +1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 12% annually (6% semiannually). Determine the present value of the trust fund's final value.

Required: Find the present value of each of the three offers and then indicate which one has the highest present value. You must show your work and show the tables.

Offer I PV = \$1,090,263.89

Offer II PV = \$1,154,400

Offer III PV = \$945,086.51

Offer II has the highest PV – Calculations are on the attached excel sheet

Chapter 10 #1 P.306

The Lone Star Company has \$1,000 par value bonds outstanding at 9 percent interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is:

a. 6 percent.

Present Value of Interest Payments

PVA = A * PVIFA (n = 20, I = 6%) Appendix D

PVA = 90 * 11.470 = \$1,032.30

Present Value of Principal Payment at Maturity

PV = FV * PVIF (n = 20, I = 6%) Appendix B

PV = 1,000 * .312 = \$312

Total Present Value

Present Value of Interest Payments \$1,032.30

Present Value of Principal Payments 312.00

Total Present Value or Price of the Bond \$1,344.30

b. 8 percent.

PVA = A * PVIFA (n = 20, I = 8%) Appendix D

PVA = \$90 * 9.818 = \$883.62

PV = FV * PVIF (n = 20, I = 8%) Appendix B

PV = \$1,000 * .215 = \$215

\$ 883.62

215.00

\$1,098.62

c. 12 percent

PVA = A * PVIFA (n = 20, I = 12%) Appendix D

PVA = \$90 * 7.469 = \$672.21

PV = FV * PVIF (n = 20, I = 12%) Appendix B

PV = \$1,000 * .104 = \$104

\$672.21

104.00

\$776.21

Chapter 10 #6 P. 306/307

The Hartford Telephone Company has a \$1,000 par value bond outstanding that pays 11 percent annual interest. The current yield to maturity on such bonds in the market is 14 percent. Compute the price of the bonds for these maturity dates:

a. 30 years.

PVA = A * PVIFA (n = 30, i = 14%) Appendix D

PVA = \$110 * 7.003 = \$770.33

PV = FV * PVIF (n = 30, i = 14%) Appendix B

PV = \$1,000 * 0.02 = \$20

\$770.33

20.00

\$790.33

b. 15 years.

PVA = A * PVIFA (n = 15, i = 14%) Appendix D

PVA = \$110 * 6.142 = \$675.62

PV = FV * PVIF (n = 15, i = 14%) Appendix B

PV = \$1,000 * .140 = \$140

\$675.62

140.00

\$815.62

c. 1 year.

PVA = A * PVIFA (n = 1, i = 14%) Appendix D

PVA = \$110 * .877 = \$96.47

PV = FV * PVIF (n = 1, i = 14%) Appendix B

PV = \$1,000 * .877 = \$877.00

\$ 96.47

877.00

\$973.47

Chapter 11 #5 P. 350

The Goodsmith Charitable Foundation, which is tax-exempt, issued debt last year at 8 percent to help finance a new playground facility in Los Angeles. This year the cost of debt is 20 percent higher; that is, firms that paid 10 percent for debt last year would be paying 12 percent this year.

a. If the Goodsmith Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on their cost last year and the 20 percent increase?

Kd = Yield (1 – T)

Yield = 8% * 1.20 = 9.6%

Kd = 9.6% (1 – 0) = 9.6% (1) = 9.6%

b. If the Foundation was found to be taxable by the IRS (at a rate of 35 percent) because it was involved in political activities, what would the aftertax cost of debt be?

Kd = 9.6% (1 – .35) = 9.6% (.65) = 6.24%

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