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# FUNDTECHOFIMAGING2 BE547

Penn

GPA 3.81

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This 33 page Class Notes was uploaded by Maida Feil on Monday September 28, 2015. The Class Notes belongs to BE547 at University of Pennsylvania taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/215360/be547-university-of-pennsylvania in Bioengineering at University of Pennsylvania.

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Date Created: 09/28/15

Chapter 15 Capital Structure Basic Concepts Since Alpha Corporation is an allequity firm its value is equal to the market value of its outstanding shares Alpha has 5000 shares of comm on stock outstanding worth 20 per share Therefore the value of Alpha Corporation is 100000 5000 shares 20 per share ModiglianiMiller Propositionl states that in the absence of taxes the value of a levered firm equals the value of an otherwise identical unlevered firm Since Beta Corporation is identical to Alpha Corporation in every way except its capital structure and neither firm pays taxes the value of the two firms should be equal ModiglianiMiller Propositionl No Taxes VL VU Alpha Corporation an unlevered firm is worth 100000 VU Therefore the value of Beta Corporation VL is 100000 The value of a levered firm equals the market value of its debt plus the market value of its equity VL B S The value ofBeta Corporation is 100000 VL and the market value of the firm s debt is 25000 The value ofBeta s equity is S 7 VL 7 B 100000 25000 75000 Therefore the market value of Beta Corporation s equity S is 75000 Since the market value of Alpha Corporation s equity is 100000 it will cost 20000 020 100000 to purchase 20 of the firm s equity Since the market value of Beta Corporation s equity is 75000 it will cost 15000 020 75000 to purchase 20 of the firm s equity Since Alpha Corporation expects to earn 350000 this year and owes no interest payments the dollar return to an investor who owns 20 of the firm s equity is expected to be 70000 020 350000 over the next year While Beta Corporation also expects to earn 350000 before interest this year it must pay 12 interest on its debt Since the market value of Beta s debt at the beginning of the year is 25000 Beta must pay 3000 012 25000 in interest at the end of the year Therefore the amount of the firm s earnings available to equity holders is 347000 350000 3000 The dollar return to an investor who owns 20 of the firm s equity is 69400 020 347000 The initial cost of purchasing 20 of Alpha Corporation s equity is 20000 but the cost to an investor of purchasing 20 of Beta Corporation s equity is only 15000 see part d In order to purchase 20000 worth of Alpha s equity using only 15000 of his own money the investor must borrow 5000 to cover the difference The investor must pay 12 interest on his borrowings at the end of the year Since the investor now owns 20 of Alpha s equity the dollar return on his equity investment at the end of the year is 70000 020 350000 However since he borrowed 5000 at 12 per annum he must pay 600 012 5000 at the end ofthe year Therefore the cash flow to the investor at the end of the year is 69400 70000 600 Notice that this amount exactly matches the dollar return to an investor who purchases 20 of Beta s equity Strategy Summary 1 Borrow 5000 at 12 2 Purchase 20 of Alpha s stock for a net cost of 15000 20000 5000 borrowed The equity of Beta Corporation is riskier Beta must pay off its debt holders before its equity holders receive any of the firm s earnings 1f the firm does not do particularly well all of the firm s earnings may be needed to repay its debt holders and equity holders will receive nothing A fir39m s debtequity ratio is the market value of the firm s debt divided by the market value of a firm s equity The market value of Acetate s debt 10 million and the market value of Acetate s equity is 20 million DebtEquity Ratio Market Value of Debt Market Value of Equity 10 million 20 million 12 Therefore Acetate s DebtEquity Ratio is 17 1n the absence of taxes a firm s weighted average cost of capital rwm is equal to rwacc B BS Us S 5rs where B the market value of the firm s debt S the market value of the firm s equity rB the pretax cost of a firm s debt rs the cost ofa firm s equity In this problem B 10000000 S 20000000 rB 14 The Capital Asset Pricing Model CAPlVl must be used to calculate the cost of Acetate s equity rs According to the CAPM rs rf BSErm 7 r where r the riskfree rate of interest Erm the expected rate of return on the market portfolio BS the beta of a firm s equity In this problem rf 8 Erm 18 BS 09 Therefore the cost of Acetate s equity is 139s rfBsE139m If 008 09 018 7 008 017 The cost of Acetate s equity rs is 17 Acetate s weighted average cost of capital equals rwacc B 03 IE S CBtSrs 10 million 30 million014 20 million 30 million017 13014 23017 016 Therefore Acetate s weighted average cost of capital is 16 According to ModiglianiMller Proposition 11 No Taxes 1395 1390 BSX1390 13913 where r0 the cost of capital for an allequity firm rs the cost of equity for a levered firm rB the pretax cost of debt In this problem rs 017 rB 014 B 10000000 S 20000000 Thus 017r0 12r07014 Solving for r0 r0 016 Therefore the cost of capital for an otherwise identical allequity firm is 16 This is consistent with ModiglianiMiller s proposition that in the absence of taxes the cost of capital for an allequity firm is equal to the weighted average cost of capital of an otherwise identical levered firm Since Unlevered is an allequity firm its value is equal to the market value of its outstanding shares Unlevered has 10 million shares of common stock outstanding worth 80 per share Therefore the value of Unlevered is 800 million 10 million shares 80 per share ModiglianiMiller Propositionl states that in the absence of taxes the value of a levered firm equals the value of an otherwise identical unlevered firm Since Levered is identical to Unlevered in every way except its capital structure and neither firm pays taxes the value of the two firms should be equa ModiglianiMiller Propositionl No Taxes VL VU Therefore the market value ofLevered lnc shauldbe 800 million also Since Levered has 45 million outstanding shares worth 100 per share the market value of Levered s equity is 450 million The market value of Levered s debt is 275 million The value of a levered firm equals the market value of its debt plus the market value of its equity Therefore the current market value of Levered Inc is VL B S 275 million 450 million 725 million The market value of Levered s equity needs to be 525 million 75 million higher than its current market value of 450 million for MIVI Proposition 1 to hold Since Levered s market value is less than Unlevered s market value Levered is relatively underpriced and an investor should buy shares of the rm s stock Since the market value of Knight s equity is 1714000 5 of the firm s equity costs 85700 005 1714000 Since the market value of Veblen s equity is 2400000 5 of the firm s equity costs 120000 005 2400000 In order to compare dollar returns the initial net cost of both positions should be the same Therefore the investor will borrow 34300 120000 87500 at 6 per annum when purchasing 120000 of Veblen s equity for a net cost of 85700 120000 34300 An investor who owns 5 of Knight s equity will be entitled to 5 of the firm s earnings available to common stock holders at the end of each year While Knight s expected operating income is 300000 it must pay 60000 to debt holders before distributing any of its earnings to stockholders Knight s expected earnings available to stockholders is 240000 300000 60000 Therefore an investor who owns 5 of Knight s stock expects to receive a dollar return of 12000 005 240000 at the end of each year based on an initial net cost of 85700 An investor who owns 5 of Veblen s equity will be entitled to 5 of the firm s earnings at the end of each year Since Veblen is an allequity firm it owes none of its money to debt holders and can distribute all 300000 of its earnings to stockholders An investor who owns 5 of Veblen s equity will expect to receive a dollar return of 15000 at the end of each year However since this investor borrowed 34300 at 6 per annum in order to fund his equity purchase he owes 2058 006 34300 in interest payments at the end of each year This reduces his expected net dollar return to 12942 15000 2058 Therefore an investor who borrows 34300 at 6 per anunm in order to purchase 5 of Veblen s stock will expect to receive a dollar return of 12942 at the end of the year for an initial net cost of 85700 For a net cost of 85700 purchasing 5 of Veblen s equity yields a higher expected dollar return than purchasing 5 of Knight s equity Both of the above two strategies cost 85700 Since the dollar return to the investment in Veblen is higher all investors will choose to invest in Veblen over Knight The process of investors purchasing Veblen s equity rather than Knight s will cause the market value of Veblen s equity to rise and the market value of Knight s equity to fall Any differences in the dollar returns to the two strategies will be eliminated and the process will cease when the total market values of the two firms are equal Before the restructuring the market value of Grimsley s equity was 5000000 100000 shares 50 per share Since Grimsley issues 1000000 worth of debt and uses the proceeds to repurchase shares the market value of the firm s equity after the restructuring is 4000000 5000000 1000000 Because the firm used the 1000000 to repurchase 20000 shares the firm has 80000 100000 7 20000 shares outstanding after the restructuring Note that the market value of Grimsley s stock remains at 50 per share 4000000 80000 shares This is consistent with Modigliani and Miller s theory Since Ms Hannon owned 10000 worth of the firm s stock she owned 02 10000 5000000 of Grimsley s equity before the restructuring Ms Hannon also borrowed 2000 at 20 per annum resulting in 400 020 2000 of interest payments at the end of the year Let Y equal Grimsley s earnings over the next year Before the restructuring Ms Hannon s payout net of personal interest payments at the end of the year was 0002Y 400 After the restructuring the firm must pay 200000 020 1000000 in interest to debt holders at the end of the year before it can distribute any of its earnings to equity holders Also since the market value of Grimsley s equity dropped from 5000000 to 4000000 Ms Hannon s 10000 holding of stock now represents 025 10000 4000000 of the firm s equity For these two reasons Ms Hannon s payout at the end of the year will change After the restructuring Ms Hannon s payout at the end of the year will be 00025Y 200000 400 which simplifies to 00025Y 900 In order for the payout from her postrestructuring portfolio to match the payout from her pre restructuring portfolio Ms Hannon will need to sell 005 00025 7 0002 of Grimsley s equity She will then receive 02 of the firm s earnings just as she did before the restructuring Ignoring any personal borrowing or lending this will change Ms Hannon s payout at the end of the year to 0002Y 200000 which simplifies to 0002Y 400 Therefore Ms Hannon must sell 2000 00005 4000000 of Grimsley s stock and eliminate any personal borrowing in order to rebalance her portfolio Her new financial positions are Value of Total Total Grimsley Shares Borrowing Lending MsHannon 8000 Since Ms Finney owned 50000 worth of the firm s stock she owned 1 50000 5000000 of Grimsley s equity before the restructuring Ms Finney also lent 6000 at 20 per annum resulting in the receipt of 1200 020 6000 in interest payments at the end of the year Therefore before the restructuring MsFinney s payout net of personal interest payments at the end of the year was 001Y 1200 After the restructuring the firm must pay 200000 020 1000000 in interest to debt holders at the end of the year before it can distribute any of its earnings to equity holders Also since the market value of Grimsley s equity dropped from 5000000 to 4000000 Ms Finney s 50000 holding of stock now represents 125 50000 4000000 of the firm s equity For these two reasons Ms Finney s payout at the end of the year will change After the restructuring Ms Finney s payout at the end of the year will be 00125Y 200000 1200 which simplifies to 00125Y 1300 In order for the payout from her postrestructuring portfolio to match the payout from her pre restructuring portfolio Ms Finney will need to sell 025 00125 7 001 of Grimsley s equity She will then receive 1 of the firm s earnings just as she did before the restructuring Ignoring any personal borrowing or lending this will change Ms Finney s payout at the end of the year to 001Y 200000 which simplifies to 001Y 2000 In order to receive a net cash inflow of 1200 at the end of the year in addition to her 1 claim on Grimsley s earnings Ms Finney will need to receive 3200 1200 7 2000 in personal interest payments at the end of the year Since Ms Finney can lend at an interest rate of 20 per annum she will need to lend 16000 3200 020 in order to receive an interest payment of 3200 at the end of the year After lending 16000 at 20 per annum Ms Finney s new payout at the end of the year is 001Y 200000 3200 which simplifies to 001Y 1200 Therefore Ms Finney must sell 10000 00025 4000000 of Grimsley s stock and add 10000 more to her lending position in order to rebalance her portfolio Her new financial positions are Value of Total Total Grimsley Shares Borrowing Lending Ms Finney 40000 16000 Since Ms Grace owned 20000 worth of the firm s stock she owned 04 20000 5000000 of Grimsley s equity before the restructuring Ms Grace had no personal position in lending or borrowing Therefore before the restructuring Ms Grace s payout at the end of the year was 0004Y After the restructuring the firm must pay 200000 020 1000000 in interest to debt holders at the end of the year before it can distribute any of its earnings to equity holders Also since the market value of Grimsley s equity dropped from 5000000 to 4000000 Ms Grace s 20000 holding of stock now represents 05 20000 4000000 of the firm s equity For these two reasons Ms Grace s payout at the end of the year will change After the restructuring Ms Grace s payout at the end of the year will be 0005Y 200000 which simplifies to 0005Y 1000 In order for the payout from her postrestructuring portfolio to match the payout from her pre restructuring portfolio Ms Grace will need to sell 01 0005 7 0004 of Grimsley s equity She will then receive 04 of the firm s earnings just as she did before the restructuring This will change Ms Grace s payout at the end of the year to 0004Y 200000 which simplifies to 0004Y 800 In order to receive no net cash flow at the end of the year other than her 04 claim on Grimsley s earnings Ms Grace will need to receive 800 0 7 800 in interest payments at the end of the year Since Ms Grace can lend at an interest rate of 20 per annum she will need to lend 4000 800 020 in order to receive an interest payment of 800 at the end of the year After lending 4000 at 20 per annum MsGrace s new payout at the end of the year is 0004Y 200000 800 which simplifies to 0004Y Therefore Ms Grace must sell 4000 0001 4000000 of Grimsley s stock and lend 4000 in order to rebalance her portfolio Her new financial positions are Value of Total Total Grimsley Shares Borrowing Lending MsGrace 16000 4000 According to ModiglianilLiller the weighted average cost of capital rwm for a levered firm is equal to the cost of equity for an unlevered firm in a world with no taxes Since Rayburn pays no taxes its weighted average cost of capital after the restructuring will equal the cost of the firm s equity before the restructuring Therefore Rayburn s weighted average cost of capital will be 18 after the restructuring According to ModiglianiMiller Proposition H No Taxes rs r0 BSr0 7 r5 where r0 the cost of capital for an allequity firm rs the cost of equity for a levered firm rB the pretax cost of debt In this problem r0 7 018 r3 010 B 400000 5 1600000 The cost of Rayburn s equity after the restructuring is rs ro CBSXro 7 r13 018 400000 1600000018 010 018 14018 7 010 20 Therefore Rayburn s cost of equity after the restructuring will be 20 In accordance with ModiglianiMiller Proposition II No Taxes the cost of Rayburn s equity will rise as the firm adds debt to its capital structure since the risk to equity holders increases with leverage In the absence of taxes a firm s weighted average cost of capital rwm is equal to rwm B Bts Us S CBtSrs where B the market value of the firm s debt S the market value of the firm s equity rB the pretax cost of the firm s debt rs the cost of the firm s equity In this problem B 400000 S 1600000 rB 10 rs 7 20 Rayburn s weighted average cost of capital after the restructuring will be rwacc BCBSIB SCBSrs 400000 2000000010 1600000 2000000020 15010 45020 018 Consistent with part a Rayburn s weighted average cost of capital after the restructuring remains at 18 Strom is an allequity firm with 250000 shares of comm on stock outstanding where each share is worth 20 Therefore the market value of Strom s equity before the buyout is 5000000 250000 shares 20 per share Since the firm expects to earn 750000 per year in perpetuity and the appropriate discount rate to its unlevered equity holders is 15 the market value of Strom s assets is equal to a perpetuity of 750000 per year discounted at 15 Therefore the market value of Strom s assets before the buyout is 5000000 750000 015 Strom s marketvalue balance sheet prior to the announcement of the buyout is Strom Inc Assets 5000000 Debt E uit 5000000 Total Assets 5000000 Total D E 5000000 According to the efficientmarket hypothesis Strom s stock price will change immediately to re ect the NPV of the project Since the buyout will cost Strom 300000 but increase the firm s annual earnings by 120000 into perpetuity the NPV of the buyout can be calculated as follows NPVBUYOUT 300000 120000 015 500 000 Remember that the required return on the acquired firm s earnings is also 15 per annum The market value of Strom s equity will increase immediately after the announcement to 5500000 5000000 500000 Since Strom has 250000 shares of common stock outstanding and the market value of the firm s equity is 5500000 Strom s new stock price will immediately rise to 22 per share 5500000 250000 shares after the announcement of the buyout According to the ef cientmarket hypothesis Strom s stock price will immediately rise to 22 per share after the announcement of the buyout After the announcement Strom has 250000 shares of common stock outstanding worth 22 per share Therefore the market value of Strom s equity immediately after the announcement is 5500000 250000 shares 22 per share The NPV of the buyout is 500000 Strom s marketvalue balance sheet after the announcement of the buyout is Stro n Inc Old Assets 5000000 Debt NPVBuyour 500000 Equity 5500000 Total Assets 5500000 Total D E 5500000 Strom needs to issue 300000 worth of equity in order to fund the buyout The market value of the firm s stock is 22 per share after the announcement Therefore Strom will need to issue 136363636 shares 300000 22 per share in order to fund the buyout Strom will receive 300000 136363636 shares 22 per share in cash after the equity issue This will increase the firm s assets by 300000 Since the firm now has 2636363636 250000 136363636 shares outstanding where each is worth 22 the market value of the firm s equity increases to 5800000 2636363636 shares 22 per share Strom s marketvalue balance sheet after the equity issue will be lt S Stro n Inc Old Assets 5000000 Debt Cash 300000 Equity 5800000 NPVBUYOUT 500000 Total Assets 5800000 Total D E 5800000 When Strom makes the purchase it will pay 300000 in cash and receive the present value of its competitor s facilities Since these facilities will generate 120000 of earnings forever their present value is equal to a perpetuity of 120000 per year discounted at 15 PVNEW mums 1 20000 0 l 5 800000 Strom s marketvalue balance sheet after the buyout is Stro n Inc Old Assets 5000000 Debt PVNEWFACEHIES 800000 Equity 5800000 Total Assets 5800000 Total D E 5800000 The expected return to equity holders is the ratio of annual earnings to the market value of the firm s equity Strom s old assets generate 750000 of earnings per year and the new facilities generate 120000 of earnings per year Therefore Strom s expected earnings will be 870000 per year Since the firm has no debt in its capital structure all of these earnings are available to equity holders The market value of Strom s equity is 5800000 The expected return to Strom s equity holders is 15 870000 5800000 Therefore adding more equity to the firm s capital structure does not alter the required return on the firm s equity 39 In the absence of taxes a firm s weighted average cost of capital rwm is equal to BBS rB SBSrs where B the market value of the firm s debt S the market value of the firm s equity rB the pretax cost of the firm s debt rs the cost of the firm s equity rwacc In this problem B 0 S 5800000 rB 0 rs 15 Strom s weighted average cost of capital after the buyout is B BS rB S BSrs 0 58000000 5800000 58000000l5 rwacc 1o15 015 Therefore Strom s weighted average cost of capital after the buyout is 15 if Strom issues equity to fund the purchase After the announcement the value of Strom s assets will increase by the 500000 the net present value of the new facilities Under the efficientmarket hypothesis the market value of Strom s equity Will immediately rise to re ect the NPV of the new facilities Therefore the market value of Strom s equity Will be 5500000 5000000 500000 after the announcement Since the firm has 250000 shares of common stock outstanding Strom s new stock price will be 22 per share 5500000 250000 Strom s marketvalue balance sheet after the announcement is Stro n Inc Old Assets 5000000 Debt NPVBuyouT 500000 Equity 5500000 Total Assets 5500000 Total D E 5500000 Strom will receive 300000 in cash after the debt issue The market value of the firm s debt will be 300000 Strom s marketvalue balance sheet after the debt issue will be Stro n Inc Old Assets 5000000 Debt 300000 Cash 300000 Equity 5500000 NPVBUYOW 500000 Total Assets 5800000 Total D E 5800000 Strom will pay 300000 in cash for the facilities Since these facilities will generate 120000 of earnings forever their present value is equal to a perpetuity of 120000 per year discounted at 15 PVNEW mums 120000 015 800000 Strom s marketvalue balance sheet after the buyout will be Stro n Inc Old Assets 5000000 Debt 300000 PVNEWFACEHIES 800000 Equity 5500000 Total Assets 5800000 Total D E 5800000 The expected return to equity holders is the ratio of annual earnings to the market value of the firm s equity Strom s old assets generate 750000 of earnings per year and the new facilities generate 120000 of earnings per year Therefore Strom s earnings Will be 870000 per year Since the firm has 300000 worth of 10 debt in its capital structure the firm must make 30000 010 300000 in interest payments Therefore Strom s net earnings are only 840000 870000 30000 The market value of Strom s equity is 5500000 lt The expected return to Strom s equity holders is 1527 840000 5500000 Therefore adding more debt to the firm s capital structure increases the required return on the firm s equity This is in accordance with ModiglianiMller Proposition H In the absence of taxes a firm s weighted average cost of capital rwm is equal to rwacc B 03 Us S CBtSrs where B the market value of the firm s debt S the market value of the firm s equity rB the pretax cost of the firm s debt rs the cost of the firm s equity In this problem B 300000 5 5500000 rB 10 rs 1527 Strom s weighted average cost of capital after the buyout will be rwacc BCBSIB SCBSrs 300000 5800000010 5500000 580000001527 358010 55580152D 015 Therefore Strom s weighted average cost of capital after the buyout will be 15 regardless of whether the rm issues debt or equity Without the power plant the Gulf expects to earn 27 million per year into perpetuity Since Gulf is an allequity firm and the required rate of return on the firm s equity is 10 the market value of Gulfs assets is equal to the present value of a perpetuity of 27000000 per year discounted at 10 PVPerpetuity C r 27000000 010 270000000 Therefore the market value of Gulfs assets before the firm announces that it will build a new power plant is 270000000 Since Gulf is an allequity firm the market value of Gulfs equity is also 270000000 Gulf s marketvalue balance sheet before the announcement of the buyout is made is Gulf Power Assets 270000000 Debt E uit 270000000 Total Assets 270000000 Total D E 270000000 Since the market value of Gulf s equity is 270 million and the firm has 10 million shares outstanding Gulf s stock price before the announcement to build the new power plant is 27 per share 270 million 10 million shares E According to the efficientmarket hypothesis the market value of Gulf s equity will change immediately to re ect the net present value of the project Since the new power plant will cost Gulf 20 million but will increase the firm s annual earnings by 3 million in perpetuity the NPV of the new power plant can be calculated as follows 20 million 3 million 010 10 million NPVN39EW POWER PLANT Remember that the required return on the firm s equity is 10 per annum Therefore the market value of Gulf s equity will increase to 280 million 270 million 10 million immediately after the announcement Gulf s marketvalue balance sheet after the announcement will be Gulf ower Old Assets 270000000 Debt NPVPOWER pLANT 10000000 Equity 280000000 Total Assets 280000000 Total D E 280000000 Since Gulf has 10 million shares of comm on stock outstanding and the total market value of the firm s equity is 280 million Gulfs new stock price will immediately rise to 28 per share 280 million 10 million shares after the firm s announcement Gulf needs to issue 20 million worth of equity in order to fund the construction of the power plant The market value of the firm s stock will be 28 per share after the announcement Therefore Gulf will need to issue 71428571 shares 20 million 28 per share in order to fund the construction of the power plant 39 Gulf will receive 20 million 71428571 shares 28 per share in cash after the equity issue Since the firm now has 1071428571 10 million 71428571 shares outstanding where each share is worth 28 the market value of the firm s equity increases to 300000000 1071428571 shares 28 per share Gulf s marketvalue balance sheet after the equity issue will be Gulf ower Old Assets 270000000 Debt Cash 20000000 Equity 300000000 NPVPOWER PLANT 10000000 Total Assets 300000000 Total D E 300000000 Gulf will pay 20000000 in cash for the power plant Since the plant will generate 3 million in annual earnings forever its present value is equal to a perpetuity of 3 million per year discounted at 10 PVNEW pOWERpLANT 3 million 010 30 million Gulf s marketvalue balance sheet after the construction of the power plant will be lt Gulf ower Old Assets 270000000 Debt PVPOWER pLANT 30000000 Equity 300000000 Total Assets 300000000 Total D E 300000000 Since Gulf is an allequity firm its value will equal the market value of its equity Therefore the value of Gulf Power will be 300 million if the rm issues equity to nance the construction of the power plant Under the efficientm arket hypothesis the market value of the firm s equity will immediately rise by 10 million following the announcement to re ect the NPV of the power plant Therefore the total market value of Gulf s equity will be 280 million 270 million 10 million after the firm s announcement Gulfs marketvalue balance sheet after the announcement will be Gulf ower Old Assets 270000000 Debt NPVPOWER PLANT 10000000 Equity 280000000 Total Assets 280000000 Total D E 280000000 Since the firm has 10 million shares of common stock outstanding Gulf s new stock price will be 28 per share 280 million 10 million shares Gulf will receive 20 million in cash after the debt issue The market value of the firm s debt will be 20 million Gulfs marketvalue balance sheet after the debt issue will be Gulf ower Old Assets 270000000 Debt 20000000 Cash 20000000 Equity 280000000 NPVPOWER PLANT 10000000 Total Assets 300000000 Total D E 300000000 39 Gulf will pay 20 million in cash for the power plant Since the plant will generate 3 million of earnings forever its present value is equal to a perpetuity of 3 million per year discounted at 10 3 million 010 30 million PVPOWER PLANT Gulf s marketvalue balance sheet after it builds the new power plant is Gulf ower Old Assets 270000000 Debt 20000000 PVPOWER pLANT 30000000 Equity 280000000 Total Assets 300000000 Total D E 300000000 iv lt lt The value of a levered firm is the sum of the market values of the firm s debt and equity Since the market value of Gulfs debt will be 20 million and the market value of Gulf s equity will be 280 million the value of Gulf Power will be 300 million if the firm decides to issue debt in order to fund the outlay for the power plant Therefore the value of Gulf Power will be 300 million regardless of whether the rm issues debt or equity to fund the construction of the new power plant According to ModiglianiMller Proposition H No Taxes rs 1390 BSXro 7 r3 where r0 the required return on an unlevered firm s equity rs the required return on a firm s equity rB the required return on a firm s debt r0 010 rB 008 B 20 million S 280 million In this problem The required return on Gulf s levered equity is rs 1390 BSXro 7 I13 010 20 million 280 million0lO 008 010 114010 7 008 1014 Therefore the required return on Gulf s levered equity is 1014 39 In the absence of taxes a firm s weighted average cost of capital rwm is equal to rwacc BCBSIB SCBSrs where B the market value of the firm s debt S the market value of the firm s equity rB the required return on the firm s debt rs the required return on the firm s equity In this problem B 20 million S 280 million rB 8 rs 1014 Gulfs weighted average cost of capital after the construction of the new power plant is rwacc BBS 13913 t SBS139s 20 million 300 million008 280 million 300 million0lOl4 115008 141501014 010 Therefore Gulf s weighted average cost of capital will be 10 following either debt or equity nancing False A reduction in leverage will decrease both the risk of the stock and its expected return 1510 1511 a Modigliani and Miller state that in the absence of taxes these two effects exactly cancel each other out and leave the price of the stock and the overall value of the firm unchanged False ModiglianiMiller Proposition 11 No Taxes states that the required return on a firm s equity is positively related to the firm s debtequity ratio rs r0 BSr0 7 rB Therefore any increase in the amount of debt in a firm s capital structure will increase the required return on the firm s equity Assumptions of the Modigliani1Liller theory in a world without taxes 1 Individuals can borrow at the same interest rate at which the firm borrows Since investors can purchase securities on margin an individual s effective interest rate is probably no higher than that for a firm Therefore this assumption is reasonable when applying M1l s theory to the real world If a firm were able to borrow at a rate lower than individuals the firm s value would increase through corporate leverage As M1l Propositionl states this is not the case in a world with no taxes 2 There are no taxes In the real world firms do pay taxes In the presence of corporate taxes the value of a firm is positively related to its debt level Since interest payments are deductible increasing debt reduces taxes and raises the value of the firm 3 There are no costs of financial distress 1n the real world costs of financial distress can be substantial Since stockholders eventually bear these costs there are incentives for a firm to lower the amount of debt in its capital structure This topic will be discussed in more detail in later chapters Since Digital has 1 million shares of common stock outstanding with each share worth 10 the value of the firm s equity is 10 million 1 million shares 10 per share Therefore 1 of the firm s equity costs 100000 001 10 million 1f 1Lichael borrows 20 of the cost it will cost him 80000 net of debt to purchase 1 of Digital s equity 1f 1Lichael borrows 40 of the cost it will cost him 60000 net of debt to purchase 1 of Digital s equity 1f 1Lichael borrows 60 of the cost it will cost him 40000 net of debt to purchase 1 of Digital s equity Since Michael purchased 1 of the Digital s equity he has a right to 1 of the firm s annual earnings Since the firm is expected to generate 1500000 of earnings per year Michael will receive a cash inflow of 15000 1f 1Lichael wishes to borrow 20 of the purchase price of his investment he will need to borrow 20000 020 100000 and fund 80000 of the purchase on his own Since the interest rate on this debt is 10 per annum Michael will owe 2000 010 20000 in interest payments at the end of the year Therefore if Michael borrows 20 of the purchase price the expected return on his investment will be 1625 15000 2000 80000 1512 a If 1Lichael Wishes to borrow 40 of the purchase price of his investment he will need to borrow 40000 040 100000 and fund 60000 of the purchase on his own Since the interest rate on this debt is 10 per annum Michael Will oWe 4000 010 40000 in interest payments at the end of the year Therefore if Michael borrows 40 of the purchase price the expected return on his investment will be 1833 15000 4000 60000 1f 1Lichael Wishes to borrow 60 of the purchase price of his investment he will need to borrow 60000 060 100000 and fund 40000 of the purchase on his own Since the interest rate on this debt is 10 per annum Michael will oWe 6000 010 60000 in interest payments at the end of the year Therefore if Michael borrows 60 of the purchase price the expected return on his investment will be 2250 15000 6000 40000 Before the announcement of the stock repurchase plan the market value of the Locomotive s outstanding debt is 75 million The ratio of the market value of the firm s debt to the market value of the firm s equity is 40 The market value of Locomotive s equity can be calculated as follows Since B 75 million and BS 40 75 million S 040 S 1875 million The market value of the firm s equity prior to the announcement is 1875 million The value of a levered firm is equal to the sum of the market value of the firm s debt and the market value of the firm s equity The market value of Locomotive Corporation a levered firm is VL B S 75 million 1875 million 2625 million Therefore the market value of Locomotive Corporation is 2625 million prior to the stock repurchase announcement According to M1l Propositionl No Taxes changes in a firm s capital structure have no effect on the overall value of the firm Therefore the value of the firm will not change after the announcement of the stock repurchase plan The market value of Locomotive Corporation will remain at 2625 million after the stock repurchase announcement The expected return on a firm s equity is the ratio of annual earnings to the market value of the firm s equity Locomotive expects to generate 375 million in earnings per year Before the restructuring Locomotive has 75 million of 10 debt outstanding The firm was scheduled to pay 750000 75 million 010 in interest at the end of each year Therefore annual earnings before the stock repurchase announcement are 3000000 3750000 750000 Since the market value of the firm s equity before the announcement is 1875 million the expected return on the firm s levered equity rs before the announcement is 016 3 million 1875 million The expected return on Locomotive s levered equity is 16 before the stock repurchase plan is announce According to ModiglianiMiller Proposition 11 No Taxes rs ro BSXro 7 Us Where r0 the expected return on the assets of an allequity firm rs the expected return on the equity of a levered firm rB the pretax cost of debt In this problem rs 016 rB 010 B 75 million S 1875 million Thus 016 r0 75 million 1875 millionr0 7 010 016 r0 040r0 7 010 Solving for r0 r0 01429 Therefore the expected return on the equity of an otherwise identical allequity rm is 1429 This problem can also be solved in the following way r0 Earnings Before Interest VU Locomotive generates 3750000 of earnings before interest According to ModiglianiMller Proposition 1 in a world with no taxes the value of a levered firm equals the value of an otherwise identical unlevered firm Since the value ofLocomotive as a levered firm is 2625 million 75 1875 and since the firm pays no taxes the value ofLocomotive as an unlevered firm VU is also 2625 million r0 375 million 2625 million 01429 1429 According to ModiglianiMller Proposition 11 No Taxes rs ro BSXro 7 Us Where r0 the expected return on the assets of an allequity firm rs the expected return on the equity of a levered firm rB the pretax cost of debt for a levered firm 1513 a Notice that the term 13 S represents the firm s debttoequity ratio After the stock repurchase announcement the firm s expected debttoequity ratio changes from 40 to 50 As shown in part c the expected return on the equity of an otherwise identical allequity firm is 1429 To determine the expected return on Locomotive s equity after the stock repurchase announcement the appropriate variables are re 01429 rB 010 BS 050 The expected return on Locomotive s levered equity after the stock repurchase announcement is 139s 1390 BSXTO 13913 01429 0 001429 7 010 01644 Therefore the expected return on Locomotive s equity is 1644 after the stock repurchase announcement ModiglianiMiller Proposition 1 states that in a world with corporate taxes VL VU TCB VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure where In this problem VL 1700000 B 500000 Tc 034 If the firm were financed entirely by equity the value of the firm would be VU VL TCB 1700000 7 034500000 1530000 Therefore the value of this rm would be 1530000 if it were financed entirely by equity While the firm generates 306000 of annual earnings before interest and taxes it must make interest payments of 50000 500000 010 Interest payments reduce the firm s taxable income Therefore the firm s pretax earnings are 256000 306000 50000 Since the firm is in the 34 tax bracket it must pay taxes of 87040 034 256000 at the end of each year Therefore the amount of the rm s annual aftertax earnings is 168960 256000 87040 These earnings are available to the stockholders The following table summarizes this solution EBIT 306000 Interest 50000 PreT ax Earnings 256000 Taxes at 34 87040 AfterTax Earnings 168960 1514 1515 ModiglianiMller Proposition 1 states that in a world with corporate taxes VL VU TCB Where VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure Since the firm is an allequity firm with 175000 shares of common stock outstanding currentl worth 20 per share the market value of this unlevered firm VU is 3500000 175000 shares 20 per share The firm plans to issue 1000000 debt and is subject to a corporate tax rate of 30 In this problem VU 3500000 Tc 0 B 1000000 The market value of a levered firm is VL VU TCB 3500000 0301000000 3800000 The value of a levered firm is equal to the sum of the market value of its debt and the market value of its equity That is the value of a levered firm is VL S B Rearranging this equation the market value of the firm s levered equity S is S VL 7 B 3800000 1000000 2800000 Therefore the market value of the rm s equity is 2800000 after the rm announces the stock repurchase plan The value of an allequity firm is the present value of its aftertax expected earnings vU EBIT1Tc ro Where VU the value of an unlevered firm E 1T the firm s expected annual earnings before interest and taxes Tc the corporate tax rate r0 the aftertax required rate of return on an allequity firm In this problem EBlT 2500000 Tc 034 r0 020 1516 7 0 P The value of Strider Publishing is VU EBITXI39TCH 1390 2500000l 034 020 8250000 Therefore the value of Strider Publishing as an allequity firm is 8250000 ModiglianiMller Proposition 1 states that in a world with corporate taxes VL VU TCB VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure where In this problem VU 8250000 Tc 034 B 600000 The value of Strider Publishing will be vL vU TCB 8 50000 034600000 8454000 Therefore the value of Strider Publishing Company will be 8454000 if it issues 600000 of debt and repurchases stock Since interest payments are tax deductible debt lowers the firm s taxable income and creates a tax shield for the firm This tax shield increases the value of the firm The ModiglianiMiller assumptions in a world with corporate taxes are 1 There are no personal taxes 2 There are no costs of financial distress 3 The debt level of a firm is constant through time Both personal taxes and costs of financial distress will be covered in more detail in a later chapter ModiglianiMiller Proposition 1 states that in a world with corporate taxes VL VU TCB VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure where The value of an unlevered firm is the present value of its aftertax earnings vU EBIT1Tc ro 1517 7 0 Where VU the value of an unlevered firm EBIT the firm s expected annual earnings before interest and taxes Tc the corporate tax rate r0 the aftertax required rate of return on an allequity firm In this problem EBIT 1200000 Tc 035 r0 012 The value of Gibson as an unlevered firm VU CEBITXITc ro 12000001 035 012 6500000 The value of Gibson if it were an allequity rm is 6500000 Since Gibson s pretax cost of debt is 8 per annum and the firm makes interest payments of 200000 per year the value of the firm s debt must be 2500000 200000 008 As a check notice that 8 annual interest on 2500000 of debt yields 200000 008 2500000 of interest payments per year The current value of Gibson s debt is 2500000 Thus VU 6500000 Tc 035 B 2500000 The total market value of Gibson is VL VU TCB 6500000 0352500000 7375000 Therefore the total market value of Gibson is 7375000 If there are no costs of financial distress or bankruptcy increasing the level of debt in a firm s capital structure Will always increase the value of a firm This implies that every firm Will want to be financed entirely 100 by debt if it Wishes to maximize its value This conclusion is not applicable in the real world since it does not consider costs of financial distress bankruptcy or other agency costs that might offset the benefit of increased leverage These costs will be discussed in further detail in later chapters The expected return on a firm s equity is the ratio of annual aftertax earnings to the market value of the firm s equity Green expects 1500000 of pretax earnings per year Because the firm is subject to a corporate tax rate of 40 it must pay 600000 worth of taxes every year Since the firm has no debt in its capital structure and makes no interest payments Green s annual aftertax expected earnings are 900000 1500000 600000 The market value of Green s equity is 10000000 ST 0 Therefore the expected return on Green s unlevered equity is 9 900000 10000000 Notice that perpetual annual earnings of 900000 discounted at 9 yields a market value of the firm s equity of10000000 900000 009 Green is an allequity firm The present value of the firm s aftertax earnings is 10000000 1500000 600000 009 Green s marketvalue balance sheet before the announcement of the debt issue is Green Assets 10000000 Debt lEquity 10000000 Total Assets 10000000 TotalD E 10000000 Since the market value of Green s equity is 10000000 and the firm has 500000 shares of common stock outstanding the price of Green s stock is 20 per share 10000000 500000 shares before the announcement of the debt issue ModiglianiMiller Proposition 1 states that in a world with corporate taxes VL VU TCB Where VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure When Green announces the debt issue the value of the firm will increase by the present value of the tax shield on the debt Since Green plans to issue 2000000 of debt and the firm is subject to a corporate tax rate of 40 the present value of the firm s tax shield is PVTax Shield TCB 0402000000 800000 Therefore the value of Green Manufacturing will increase by 800000 as a result of the debt issue The value of Green Manufacturing after the repurchase announcement is VL VU TCB 10000000 0402000000 10800000 Since the firm has not yet issued any debt Green s equity is also worth 10800000 Green s marketvalue balance sheet after the announcement of the debt issue is Green Old Assets 10000000 Deb PV Tax Shie d 800000 E uit 10800000 Total Assets 10800000 TotalDE 10800000 d F 239 Since the market value of Green s equity after the announcement of the debt issue is 10800000 and the firm has 500000 shares of common stock outstanding the price of Green s stock is 2160 per share 10800000 500000 shares after the announcement of the debt issue after the 39 r Therefore 39 Green s stock price will rise to 2160 per share Green will issue 2000000 worth of debt and use the proceeds to repurchase shares of common stock Since the price of Green s stock after the announcement will be 2160 per share Green can repurchase 9259259 shares 2000000 2160 per share as a result of the debt issue Green will repurchase 9259259 shares with the proceeds from the debt issue Since Green had 500000 shares of common stock outstanding and repurchased 9259259 as a result of the debt issue the firm will have 40740741 500000 7 9259259 shares of common stock outstanding after the repurchase Green will have 40740741 shares of common stock outstanding after the repurchase After the restructuring has taken place Green will have 2000000 worth of debt in its capital structure The value of Green after the restructuring is 10800000 The value of a levered firm is equal to the sum of the market value of its debt and the market value of its equity That is the value of a levered firm is VL S B Rearranging this equation the market value of the Green s levered equity after the announcement of the debt issue is VL 7 B 10800000 2000000 8800000 Green s marketvalue balance sheet after the restructuring is Green Old Assets 10000000 lDeb 2000000 PV Tax Shied 800000 E uit 8800000 Total Assets 10800000 TotalD E 10800000 Since the market value of Green s equity after the restructuring is 8800000 and the firm has 40740741 shares of common stock outstanding the price of Green s stock will be 2160 per share 8800000 40740741 shares after the restructuring Therefore Green s stock price will remain at 2160 per share after the restructuring has taken place g According to ModiglianiMller Proposition 11 with corporate taxes 1395 1390 BSX1390 l39BX1 Tc Where r0 the required return on the equity of an unlevered firm rs the required return on the equity of a levered firm rB the pretax cost of debt for a levered firm 1518 Tc the corporate tax rate B the market value of the firm s debt S the market value of the firm s equity In this problem r0 009 see part a 06 rB 7 Tc 040 B 2000000 S 8800000 The required return on Green s levered equity after the restructuring is 139s 1390 BSXTO rB17 Tc 009 2000000 8800000009 7 0061 7 040 009 5220090061 7 040 r 0941 Therefore the required return on Green s levered equity after the restructuring is 941 ModiglianiMller Proposition 1 states that in a world with corporate taxes VL VU TCB where VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure The value of an unlevered firm is the present value of its aftertax earnings VU EBIT1T cl ro where VU the value of an unlevered firm EBlT the firm s expected annual earnings before interest and taxes Tc the corporate tax rate r0 the aftertax required rate of return on an allequity firm In this problem EBIT 4000000 Tc 035 ro 015 The value of Holland if it were unlevered is VU EBITXIle ro 40000001 035 015 17 333 333 The value of Holland if it were an allequity firm is 17333333 Holland currently has 10000000 of debt in its capital structure and is subject to a corporate tax rate of 35 0 Thus VU 17333333 Tc 0 35 B 10000000 The value of Holland is VL VU TCB 17333333 03510000000 20833333 Therefore the value of Holland is 20833333 According to ModiglianiMiller Proposition 11 with corporate taxes 1395 1390 BSX1390 l39BX1 Tc Where r0 the required return on the equity of an unlevered firm rs the required return on the equity of a levered firm rB the pretax cost of debt Tc the corporate tax rate B the market value of the firm s debt S the market value of the firm s equity In this problem r0 015 rB 010 Tc 035 B 10000000 S 10833833 The required return on Holland s levered equity is 139s 1390 BSXTO l39BX1 Tc 015 10000000 10833833015 7 01017 035 015 09230015 0101 7 030 018 Therefore the cost of Holland s levered equity is 18 In a world with corporate taxes a firm s weighted average cost of capital rwm is equal to rwacc B CBtS1 7 Tc Us S BSi rs Where B the market value of the firm s debt S the market value of the firm s equity rB the required return on the firm s debt rs the required return on the firm s equity Tc the corporate tax rate The value of Holland s debt is 10000000 Since the value of the firm 20833833 is the sum of the value of the firm s debt and the value of the firm s equity the market value of the firm s equity is 10833833 20833833 10000000 Thus B 10000000 S 10833833 1519 rB 010 rs 018 Tc 035 Holland s weighted average cost of capital is rwacc BCBS1 Tc rB t S CBtSrs 10000000 208338331 7 035010 10833833 20833833018 0481 7 035010 052018 01248 Therefore Holland s weighted average cost of capital is 1248 In a world with corporate taxes a firm s weighted average cost of capital rwm is equal to rwacc BCBS1 Tc rB S CBtSrs where B BS the firm s debttovalue ratio S BS the firm s equitytovalue ratio rB the pretax cost of debt rs the cost of equity for a levered firm Tc the corporate tax rate While the problem does not list Williamson s debttovalue ratio or William son s equitytovalue ratio it does say that the firm s debttoequity ratio is 25 If Williamson s debttoequity ratio is 25 B S 25 Solving for B B 25 S The above formula for rmcc uses the following ratio B BS Since B 25 S BBS 25 S 25 S S 25 S 35 S 25 35 07143 Williamson s debttovalue ratio is 7143 The above formula for rmcc also uses the following ratio S BS Since B 25 S Williamson s equitytovalue ratio S 25S S S 35 S 1 35 02857 Williamson s equitytovalue ratio is 2857 ST 0 In order to solve for the cost of Williamson s equity capital rs set up the following equation B BSl 7 Tc rB S BSrs rwacc 015 7 071431 7 o35010 0285005 rs 703625 Therefore the cost of Williamson s equity capital is 3625 According to ModiglianilIiller Proposition II with corporate taxes 1395 1390 BSX1390 l39BX1 Tc Where r0 the cost of equity for an unlevered firm rs the cost of equity for a levered firm rB the pretax cost of debt Tc the corporate tax rate B S the firm s debttoequity ratio In this problem rs 03625 rB 010 Tc 035 BS 25 In order to solve for the cost of Williamson s unlevered equity r0 set up the following equation rs r0 BSr0 7 rBl 7 Tc 03625 r0 25r0 7 010l 7 035 r0 020 Therefore Williamson s unlevered cost of equity is 20 If Williamson s debttoequity ratio is 075 the cost of the firm s equity capital rs will be rs r0 BSr0 7 rBl 7 Tc 020 075020 7 010l 7 035 02488 If Williamson s debttoequity ratio is 075 B S 075 Solving for B B 075 S A firm s debttovalue ratio is B BS Since B 075 S Williamson s debttovalue ratio 075 S 075 S S 075 Sl75 S 075 175 04286 Williamson s debttovalue ratio is 4286 A firm s equitytovalue ratio is S BS Since B 075 S Williamson s equitytovalue ratio S 075S S s 175 S 1 175 05714 Williamson s equitytovalue ratio is 5714 Williamson s weighted average cost of capital rwm is rwm BCBS1 Tc r13 t S Btsrs 042861 7 035010 0571402488 017 Therefore Williamson s weighted average cost of capital rwacc is 17 if the rm s debtt0 equity ratio is 075 If Williamson s debttoequity ratio is 15 then the cost of the firm s equity capital rs will be 1395 1390 BSXTO l39BXl Tc 020 15020 7 01017 035 75 If Williamson s debtequity ratio is 15 B S 15 Solving for B B 15 S A firm s debttovalue ratio is B BS Since B 15 S Williamson s debttovalue ratio 15 S 15 S S 15 S25 S 15 25 060 Williamson s debttovalue ratio is 60 A firm s equitytovalue ratio is S BS Since B 15 S Williamson s equitytovalue ratio S 15S S S 25 S 1520 7 1 25 040 Williamson s equitytovalue ratio is 40 Williamson s weighted average cost of capital rwm is BBS17 Tc1B s BSrs 0601 7 035010 04002975 0158 rwacc Therefore Williamson s weighted average cost of capital rwacc is 158 if the rm s debtto equity ratio is 15 The value of an unlevered firm is the present value of its aftertax earnings VU EBITxlT cl ro Where VU the value of an unlevered firm E BIT the firm s expected annual earnings before interest and taxes Tc the corporate tax rate r0 the aftertax required rate of return on an allequity firm In this problem EBIT 100000 T c 040 r0 025 The value of General Tools GT as an unlevered firm is VU CEBITxlTc ro 1000001 040 025 240000 The value of General Tools is 240000 as an allequity rm ModiglianiMller Proposition I states that in a world with corporate taxes VL VU TCB VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure Where In this problem VU 240000 Tc 040 B 100000 If GT borrows 100000 and uses the proceeds to purchase shares the firm s value will be VL vU TCB 240000 040100000 1521 280000 Therefore the value of General Tools will be 280000 if the rm adds 100000 of debt to its capital structure If Stephenson Wishes to maximize the overall value of the firm it should use debt to finance the 100 million purchase Since interest payments are tax deductible debt in the firm s capital structure will decrease the firm s taxable income creating a tax shield that Will increase the overall value of the firm Since Stephenson is an allequity firm with 15 million shares of common stock outstanding worth 3250 per share the market value of the firm is 4875 million 15 million shares 3250 per share Stephenson s marketvalue balance sheet before the announcement of the land purchase is quot 39 Real Estate Assets 487500000 Debt Equity 487500000 Total Assets 487500000 Total D E 487500000 As a result of the purchase the firm s pretax earnings will increase by 25 million per year in perpetuity These earnings are taxed at a rate of 40 Therefore after taxes the purchase increases the annual expected earnings of the firm by 15 million 25 million1 040 Since Stephenson is an allequity firm the appropriate discount rate is the firm s unlevered cost of equity capital r0 which is 125 NPVPurchase 100000000 250000001 7 040 0125 100000000 15 million 0125 20000000 Therefore the net present value of the land purchase is 20 million After the announcement the value of Stephenson Will increase by 20 million the net present value of the purchase Under the efficientmarket hypothesis the market value of the firm s equity Will immediately rise to re ect the NPV of the project Therefore the market value of Stephenson s equity Will be 5075 million 4875 million 20 million after the firm s announcement Stephenson s marketvalue balance sheet after the announcement is quot 39 Real Estate Old Assets 487500000 Debt NPVPROJ39ECT 20000000 Equity 507500000 Total Assets 507500000 Total D E 507500000 Since the market value of the firm s equity is 5075 million and the firm has 15 million shares of common stock outstanding Stephenson s stock price after the announcement Will be 3383 per share 5075 million 15 million shares Stephenson s stock price after the announcement is 3383 per share E Since Stephenson must raise 100 million to finance the purchase and the firm s stock is worth 3383 per share Stephenson must issue 2955956 shares 100 million 3383 per share in order to finance the purchase Stephenson must issue 2955956 shares in order to finance the initial outlay for the purchase Stephenson will receive 100 million 2955956 shares 3383 per share in cash as a result of the equity issue This will increase the firm s assets and equity by 100 million Stephenson s marketvalue balance sheet after the equity issue is 39 Real Estate Old Assets 487500000 Debt Cash 100000000 Equity 607500000 NPVPROJ39ECT 20000000 Total Assets 607500000 Total D E 607500000 Since Stephenson issued 2955956 shares in order to finance the purchase the firm now has 17955956 15000000 2955956 shares outstanding Stephenson will have 17955956 shares of common stock outstanding after the equity issue Since the market value of the firm s equity is 6075 million and the firm has 17955956 shares of common stock outstanding Stephenson s stock price after the equity issue will be 3383 per share 6075 million 17955956 million shares Stephenson s stock price after the equity issue remains at 3383 per share The project will generate 25 million of additional annual pretax earnings forever These earnings will be taxed at a rate of 40 Therefore after taxes the project increases the annual earnings of the firm by 15 million 25 million1 040 The present value of these cash flows is equal to a perpetuity making annual payments of 15 million discounted at 125 15 million0125 120 million Plli ROJ39ECT Stephenson s marketvalue balance sheet after the purchase has been made is Real Estate u Old Assets 487500000 Debt PVPROJ39ECT 120000000 Equity 607500000 Total Assets 607500000 ITotalD E 607500000 ModiglianiMller Proposition 1 states that in a world with corporate taxes VL VU TCB VL the value of a levered firm VU the value of an unlevered firm Tc the corporate tax rate B the value of debt in a firm s capital structure where F As was shown in part c Stephenson will be worth 6075 million if it finances the purchase with equity If it were to finance the initial outlay of the project with debt the firm would have 100 million worth of 8 debt outstanding Thus VU 6075 million Tc 040 B 100 million 1f Stephenson chooses to finance the purchase using debt the firm s market value will be VL VU TCB 6075 million 040100 million 6475 million Therefore Stephenson will be worth 6475 million if it chooses to nance the purchase with debt After the announcement the value of Stephenson will immediately rise by the PV of the project Since the market value of the firm s debt is 100 million and the value of the firm is 6475 million the market value of Stephenson s equity must be 5475 million 6475 million 100 million Stephenson s marketvalue balance sheet after the debt issue is 39 Real Estate VU 607500000 Debt 100000000 TCB 40000000 Equity 547500000 Total Assets 647500000 Total D E 647500000 Since the market value of the Stephenson s equity is 5475 million and the firm has 15 million shares of comm on stock outstanding Stephenson s stock price after the debt issue will be 3650 per share 5475 million 15 million shares Stephenson s stock price after the debt issue will be 3650 per share If Stephenson uses equity in order to finance the project the firm s stock price will remain at 3383 per share If the firm uses debt in order to finance the project the firm s stock price will rise to 3650 per share Therefore debt nancing maximizes the per share stock price of a firm s equity

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