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Unformatted text preview: payment, C. So, the price of the bonds if interest rates fall will be: P1 = $1,250 + C The selling price today of the bonds is the PV of the expected payoffs to the bondholders. To find the coupon rate, we can set the desired issue price equal to present value of the expected value of end of year payoffs, and solve for C. Doing so, we find: P0 = $1,000 = [.60(C + C / .13) + .40($1,250 + C)] / 1.11 C = $108.63 So the coupon rate necessary to sell the bonds at par value will be: Coupon rate = $108.63 / $1,000 Coupon rate = .1086 or 10.86% 335 9. a. The price of the bond today is the present value of the expected price in one year. So, the price of the bond in one year if interest rates increase will be: P1 = $80 + $80 / .09 P1 = $968.89 If interest rates fall, the price if the bond in one year will be: P1 = $80 + $80 / .06 P1 = $1,413.33 Now we can find the price of the bond today, which will be: P0 = [.35($968.89) + .65($1,413.33)] / 1.08 P0 = $1,164.61 b. If interest rates rise, the price of the bonds will fall. If the price of the bonds is low, the company will not call them. The firm would be foolish to pay the call price for something worth less than the call price. In this case, the bondholders will receive the coupon payment, C, plus the present value of the remaining payments. So, if interest rates rise, the price of the bonds in one year will be: P1 = C + C / .09 If interest rates fall, the assumption is that the bonds will be called. In this case, the bondholders will receive the call price, plus the coupon payment, C. The call premium is not fixed, but it is the same as the coupon rate, so the price of the bonds if interest rates fall will be: P1 = ($1,000 + C) + C P1 = $1,000 + 2C The selling price today of the bonds is the PV of the expected payoffs to the bondholders. To find the coupon rate, we can set the desired issue price equal to present value of the expected value of end of year payoffs, and solve for C. Doing so, we find: P0 = $1,000 = [.35(C + C / .09) + .65($1,000 + 2C)] / 1.08 C = $77.63 So the coupon rate necessary to sell the bonds at par value will be: Coupon rate = $77.633 / $1,000 Coupon rate = .0776 or 7.76% c. To the company, the value of the call provision will be given by the difference between the value of an outstanding, noncallable bond and the call provision. So, the value of a noncallable bond with the same coupon rate would be: Noncallable bond value = $77.63 / 0.06 = $1,293.88 336 So, the value of the call provision to the company is: Value = .65($1,293.88 – 1,077.63) / 1.08 Value = $130.15 10. The company should refund when the NPV of refunding is greater than zero, so we need to find the interest rate that results in a zero NPV. The NPV of the refunding is the difference between the gain from refunding and the refunding costs. The gain from refunding is the bond value times the difference in the interest rate, discounted to the present value. We must also consider that the interest payments are tax deductible, so the aftertax gain is: NPV = PV(Gain) – PV(Cost) The present value of the gain will be: Gain = $250,000,000(.08 – R) / R Since refunding would cost money today, we must determine the aftertax cost of refunding, which will be: Aftertax cost = $250,000,000(.12)(1 – .35) Aftertax cost = $19,500,000 So, setting the NPV of refunding equal to zero, we find: 0 = –$19,500,000 + $250,000,000(.08 – R) / R R = .0742 or 7.42% Any interest rate below this will result in a positive NPV from refunding. 11. In this case, we need to find the NPV of each alternative and choose the option with the highest NPV, assuming either NPV is positive. The NPV of each decision is the gain minus the cost. So, the NPV of refunding the 8 percent perpetual bond is: Bond A: Gain = $75,000,000(.08 – .07) / .07 Gain = $10,714,285.71 Assuming the call premium is tax deductible, the aftertax cost of refunding this issue is: Cost = $75,000,000(.085)(1 – .35) + $10,000,000(1 – .35) Cost = $10,643,750.00 Note that the gain can be calculated using the pretax or aftertax cost of debt. If we calculate the gain using the aftertax cost of debt, we find: Aftertax gain = $75,000,000[.08(1 – .35) – .07(1 – .35)] / [.07(1 – .35)] Aftertax gain = $10,714,285.71 337 Thus, the inclusion of the tax rate in the calculation of the gains from refunding is irrelevant. The NPV of refunding this bond is: NPV = –$10,643,750.00 + 10,714,285.71 NPV = $70,535.71 The NPV of refunding the second bond is: Bond B: Gain = $87,500,000(.09 – .0725) / .0725 Gain = $21,120,689.66 Assuming the call premium is tax deductible, the aftertax cost of refunding this issue is: Cost = ($87,500,000)(.095)(1 – .35) + $12,000,000(1 – .35) Cost = $13,203,125.00 The NPV of refunding this bond is: NPV = –$13,203,125.00 + 21,120,689.66 NPV = $7,917,564.66 Since the NPV of refunding both bonds is positive, both bond issues should be refunded. 12. The price of a zero coupon bond is the PV of the par, so: a. b. P0 = $1,000/1.04550 = $110.71 In one year, the bond will have 24 years to maturity, so the price will be: P1 = $1,000/1.04548 = $120.90 The interest deduction is the price of the bond at the end of the year, minus the price at the beginning of the year, so: Year 1 interest deduction = $120.90 – 110.71 = $10.19 The price of the bond when it has one year left to m...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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