Chapter 15 Solutions

Transcript

Corporate Finance 9th edition Solutions Manual CHAPTER 15 LONG-TERM FINANCING:  AN  INTRODUCTION  Answers to Concepts Review and Critical Thinking Th inking Questions 1. The indenture indenture is a legal contract contract and can run into into 100 pages or more. Bond features which which would be included are: the basic terms of the bond, the total amount of the bonds issued, description of the  property used as security, repayment arrangements, call provisions, convertibility convertibility provisions, and details of protective covenants. 2. The differences between preferred stock and debt are: dividends on on preferred stock cannot cannot be deducted as interest expense expense when when determining determining a. The dividends taxable corporate income. From the individual investor’s point of view, preferred dividends are ordinary income for tax purposes. For corporate investors, 70% of the amount they receive as dividends from preferred stock are exempt from income taxes. liquidation (at bankruptcy), bankruptcy), preferred stock is is junior junior to debt and senior senior to common b. In case of liquidation stock. There is no legal obligation for firms to pay out preferred dividends dividends as opposed opposed to the obligated obligated c.  payment of interest on bonds. Therefore, firms cannot be forced into default if a preferred stock dividend is not paid in a given year. Preferred dividends can be cumulative or non-cumulative, and they can also be deferred indefinitely (of course, indefinitely deferring the dividends might have an undesirable effect on the market value of the stock). 3. Some firms can benefit from issuing preferred stock. The reasons can be: utilities can pass the tax disadvantage of issuing issuing preferred preferred stock on to their customers, customers, so a. Public utilities there is a substantial amount of straight preferred stock issued by utilities. reporting losses losses to to the IRS already already don’t have positive positive income income for any tax deductions, so b. Firms reporting they are not affected by the tax disadvantage of dividends versus interest payments. They may  be willing to issue preferred preferred stock. Firms that issue preferred preferred stock can avoid the threat of bankruptcy bankruptcy that exists with with debt debt c. financing because preferred dividends are not a legal obligation like interest payments on corporate debt. 4. The return return on non-convertible preferred stock stock is lower than than the return on corporate bonds bonds for two reasons: 1) Corporate investors receive 70 percent tax deductibility on dividends if they hold the stock. Therefore, they are willing to pay more for the stock; that lowers its return. 2) Issuing corporations are willing and able to offer higher returns on debt since the interest on the debt reduces their tax liabilities. Preferred dividends are paid out of net income, hence they provide no tax shield. Corporate investors are the primary holders of preferred stock since, unlike individual investors, investors, they can deduct 70 percent of the dividend when computing their tax liabilities. Therefore, they are willing to accept the lower return that the stock generates. 317 Corporate Finance 9th edition Solutions Manual 5. The following table summarizes the main difference between debt and equity: Repayment is an obligation of the firm Grants ownership of the firm Provides a tax shield Liquidation will result if not paid Debt Yes No Yes Yes Equity No Yes No No Companies often issue hybrid securities because of the potential tax shield and the bankruptcy advantage. If the IRS accepts the security as debt, the firm can use it as a tax shield. If the security maintains the bankruptcy and ownership advantages of equity, the firm has the best of both worlds. 6. There are two benefits. First, the company can take advantage of interest rate declines by calling in an issue and replacing it with a lower coupon issue. Second, a company might wish to eliminate a covenant for some reason. Calling the issue does this. The cost to the company is a higher coupon. A  put provision is desirable from an investor’s standpoint, so it helps the company by reducing the coupon rate on the bond. The cost to the company is that it may have to buy back the bond at an unattractive price. 7. It is the grant of authority by a shareholder to someone else to vote his or her shares. 8. Preferred stock is similar to both debt and common equity. Preferred shareholders receive a stated dividend only, and if the corporation is liquidated, preferred stockholders get a stated value. However, unpaid preferred dividends are not debts of a company and preferred dividends are not a tax deductible business expense. 9. A company has to issue more debt to replace the old debt that comes due if the company wants to maintain its capital structure. There is also the possibility that the market value of a company continues to increase (we hope). This also means that to maintain a specific capital structure on a market value basis the company has to issue new debt, since the market value of existing debt generally does not increase as the value of the company increases (at least by not as much). 10. Internal financing comes from internally generated cash flows and does not require issuing securities. In contrast, external financing requires the firm to issue new securities. 11. The three basic factors that affect the decision to issue external equity are: 1) The general economic environment, specifically, business cycles. 2) The level of stock prices, and 3) The availability of  positive NPV projects. 12. When a company has dual class stock, the difference in the share classes are the voting rights. Dual share classes allow minority shareholders to retain control of the company even though they do not own a majority of the total shares outstanding. Often, dual share companies were started by a family, taken public, but the founders want to retain control of the company. 13. The statement is true. In an efficient market, the callable bonds will be sold at a lower price than that of the non-callable bonds, other things being equal. This is because the holder of callable bonds effectively sold a call option to the bond issuer. Since the issuer holds the right to call the bonds, the  price of the bonds will reflect the disadvantage to the bondholders and the advantage to the bond issuer (i.e., the bondholder has the obligation to surrender their bonds when the call option is exercised by the bond issuer.) 318 Corporate Finance 9th edition Solutions Manual 14. As the interest rate falls, the call option on the callable bonds is more likely to be exercised by the  bond issuer. Since the non-callable bonds do not have such a drawback, the value of the bond will go up to reflect the decrease in the market rate of interest. Thus, the price of non-callable bonds will move higher than that of the callable bonds. 15. Sinking funds provide additional security to bonds. If a firm is experiencing financial difficulty, it is likely to have trouble making its sinking fund payments. Thus, the sinking fund provides an early warning system to the bondholders about the quality of the bonds. A drawback to sinking funds is that they give the firm an option that the bondholders may find distasteful. If bond prices are low, the firm may satisfy its sinking fund obligation by buying bonds in the open market. If bond prices are high though, the firm may satisfy its obligation by purchasing bonds at face value (or other fixed  price, depending on the specific terms). Those bonds being repurchased are chosen through a lottery. Solutions to Questions and Problems  NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is  found without rounding during any step in the problem.  Basic 1. If the company uses straight voting, the board of directors is elected one at a time. You will need to own one-half of the shares, plus one share, in order to guarantee enough votes to win the election. So, the number of shares needed to guarantee election under straight voting will be: Shares needed = (600,000 shares / 2) + 1 Shares needed = 300,001 And the total cost to you will be the shares needed times the price per share, or: Total cost = 300,001 × $39 Total cost = $11,700,039 If the company uses cumulative voting, the board of directors are all elected at once. You will need 1/( N  + 1) percent of the stock (plus one share) to guarantee election, where  N  is the number of seats up for election. So, the percentage of the company’s stock you need is: Percent of stock needed = 1/( N  + 1) Percent of stock needed = 1 / (7 + 1) Percent of stock needed = .1250 or 12.50% 319 Corporate Finance 9th edition Solutions Manual So, the number of shares you need to purchase is:  Number of shares to purchase = (600,000 × .1250) + 1  Number of shares to purchase = 75,001 And the total cost to you will be the shares needed times the price per share, or: Total cost = 75,001 × $39 Total cost = $2,925,039 2. If the company uses cumulative voting, the board of directors are all elected at once. You will need 1/( N  + 1) percent of the stock (plus one share) to guarantee election, where  N  is the number of seats up for election. So, the percentage of the company’s stock you need is: Percent of stock needed = 1/( N  + 1) Percent of stock needed = 1 / (3 + 1) Percent of stock needed = .25 or 25% So, the number of shares you need is:  Number of shares to purchase = (5,800 × .25) + 1  Number of shares to purchase = 1,451 So, the number of additional shares you need to purchase is:  New shares to purchase = 1,451 – 300  New shares to purchase = 1,151 3. If the company uses cumulative voting, the board of directors are all elected at once. You will need 1/( N  + 1) percent of the stock (plus one share) to guarantee election, where  N  is the number of seats up for election. So, the percentage of the company’s stock you need is: Percent of stock needed = 1/( N  + 1) Percent of stock needed = 1 / (3 + 1) Percent of stock needed = .25 or 25% So, the number of shares you need to purchase is:  Number of shares to purchase = (1,200,000 × .20) + 1  Number of shares to purchase = 300,001 And the total cost will be the shares needed times the price per share, or: Total cost = 300,001 × $9 Total cost = $2,700,009 320 Corporate Finance 9th edition Solutions Manual 4. Under cumulative voting, she will need 1/( N   + 1) percent of the stock (plus one share) to guarantee election, where  N   is the number of seats up for election. So, the percentage of the company’s stock she needs is: Percent of stock needed = 1/( N  + 1) Percent of stock needed = 1 / (6 + 1) Percent of stock needed = .1429 or 14.29% Her nominee is guaranteed election. If the elections are staggered, the percentage of the company’s stock needed is: Percent of stock needed = 1/( N  + 1) Percent of stock needed = 1 / (3 + 1) Percent of stock needed = .25 or 25% Her nominee is no longer guaranteed election. 5. Zero coupon bonds are priced with semiannual compounding to correspond with coupon bonds. The  price of the bond when purchased was: P0 = $1,000 / (1 + .035) 50 P0 = $179.05 And the price at the end of one year is: P0 = $1,000 / (1 + .035) 48 P0 = $191.81 So, the implied interest, which will be taxable as interest income, is: Implied interest = $191.81 – 179.05 Implied interest = $12.75 6. 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 = $60(PVIFA 7%,58) + $1,000(PVIF7%,58) P1 = $859.97 If interest rates fall, the price if the bond in one year will be: P1 = $60(PVIFA 3.5%,58) + $1,000(PVIF3.5%,58) P1 = $1,617.16  Now we can find the price of the bond today, which will be: P0 = [.50($859.97) + .50($1,617.16)] / 1.055 2 P0 = $1,112.79 For students who have studied term structure, the assumption of risk-neutrality implies that the forward rate is equal to the expected future spot rate. 321 Corporate Finance 9th edition Solutions Manual b. 7. If the bond is callable, then the bond value will be less than the amount computed in part a. If the bond price rises above the call price, the company will call it. Therefore, bondholders will not pay as much for a callable bond. The price of the bond today is the present value of the expected price in one year. The bond will be called whenever the price of the bond is greater than the call price of $1,150. First, we need to find the expected price in one year. If interest rates increase next year, the price of the bond will be the  present value of the perpetual interest payments, plus the interest payment made in one year, so: P1 = ($100 / .12) + $100 P1 = $933.33 This is lower than the call price, so the bond will not be called. If the interest rates fall next year, the  price of the bond will be: P1 = ($100 / .07) + $100 P1 = $1,528.57 This is greater than the call price, so the bond will be called. The present value of the expected value of the bond price in one year is: P0 = [.40($933.33) + .60($1,150)] / 1.10 P0 = $966.67  Intermediate 8. 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 / 0.13 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. 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% 322 Corporate Finance 9th edition Solutions Manual 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, non-callable bond and the call provision. So, the value of a noncallable bond with the same coupon rate would be:  Non-callable bond value = $77.63 / 0.06 = $1,293.88 323 Corporate Finance 9th edition Solutions Manual 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 = $10,714,285.71 324 Corporate Finance 9th edition Solutions Manual 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. P0 = $1,000/1.045 50 = $110.71 b. In one year, the bond will have 24 years to maturity, so the price will be: P1 = $1,000/1.045 48 = $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 maturity will be: P24 = $1,000/1.045 2 = $915.73 Year 24 interest deduction = $1,000 – 915.73 = $84.27 325 Corporate Finance 9th edition Solutions Manual c. Previous IRS regulations required a straight-line calculation of interest. The total interest received by the bondholder is: Total interest = $1,000 – 110.71 = $889.29 The annual interest deduction is simply the total interest divided by the maturity of the bond, so the straight-line deduction is: Annual interest deduction = $889.29 / 25 = $35.57 d . The company will prefer straight-line methods when allowed because the valuable interest deductions occur earlier in the life of the bond. 13. a. The coupon bonds have an 8% coupon which matches the 8% required return, so they will sell at par. The number of bonds that must be sold is the amount needed divided by the bond price, so:  Number of coupon bonds to sell = $30,000,000 / $1,000 = 30,000 The number of zero coupon bonds to sell would be: Price of zero coupon bonds = $1,000/1.04 60 = $95.06  Number of zero coupon bonds to sell = $30,000,000 / $95.06 = 315,589 b. The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So: Coupon bonds repayment = 30,000($1,040) = $31,200,000 The repayment of the zero coupon bond will be the par value times the number of bonds issued, so: Zeroes: repayment = 315,589($1,000) = $315,588,822 Challenge 14. To calculate this, we need to set up an equation with the callable bond equal to a weighted average of the noncallable bonds. We will invest X percent of our money in the first noncallable bond, which means our investment in Bond 3 (the other noncallable bond) will be (1 – X). The equation is: C2 = C1 X + C3(1 – X) 8.25 = 6.50 X + 12(1 – X) 8.25 = 6.50 X + 12 – 12 X X = 0.68182 326 Corporate Finance 9th edition Solutions Manual So, we invest about 68 percent of our money in Bond 1, and about 32 percent in Bond 3. This combination of bonds should have the same value as the callable bond, excluding the value of the call. So: P2 P2 P2 = 0.68182P1 + 0.31819P3 = 0.68182(106.375) + 0.31819(134.96875) = 115.4730 The call value is the difference between this implied bond value and the actual bond price. So, the call value is: Call value = 115.4730 – 103.50 = 11.9730 Assuming $1,000 par value, the call value is $119.73. 15. In general, this is not likely to happen, although it can (and did). The reason that this bond has a negative YTM is that it is a callable U.S. Treasury bond. Market participants know this. Given the high coupon rate of the bond, it is extremely likely to be called, which means the bondholder will not receive all the cash flows promised. A better measure of the return on a callable bond is the yield to call (YTC). The YTC calculation is the basically the same as the YTM calculation, but the number of periods is the number of periods until the call date. If the YTC were calculated on this bond, it would be positive. 327