1. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1 Chapter 16 Capital Structure Decisions: Part II

2. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2 Topics in Chapter MM models, with and without corporate taxes MM proofs Miller model, with corporate and personal taxes Extension to MM when there is growth and the tax shield is risky Equity as an option

3. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 3 Value = + + ··· + FCF 1 FCF 2 FCF ∞ (1 + WACC) 1 (1 + WACC) ∞ (1 + WACC) 2 Free cash flow (FCF) Market interest rates Firm’s business risk Market risk aversion Firm’s debt/equity mix Cost of debt Cost of equity Weighted average cost of capital (WACC ) Net operating profit after taxes Required investments in operating capital − = Determinants of Intrinsic Value: The Capital Structure Choice

4. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 4 Who are Modigliani and Miller (MM)? They published theoretical papers that changed the way people thought about financial leverage. They won Nobel prizes in economics because of their work. MM’s papers were published in 1958 and 1963. Miller had a separate paper in 1977. The papers differed in their assumptions about taxes.

5. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 5 What assumptions underlie the MM and Miller Models? Firms can be grouped into homogeneous classes based on business risk. Investors have identical expectations about firms’ future earnings. There are no transactions costs. (More...)

6. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 6 All debt is riskless, and both individuals and corporations can borrow unlimited amounts of money at the risk-free rate. All cash flows are perpetuities. This implies perpetual debt is issued, firms have zero growth, and expected EBIT is constant over time. (More...)

7. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 7 MM’s first paper (1958) assumed zero taxes. Later papers added taxes. No agency or financial distress costs. These conditions are necessary for MM to prove their propositions on the basis of investor arbitrage.

8. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. MM Detailed Assumptions Company U is Unlevered. It has no debt. Company is Levered. It has debt amount D, with interest rate r d. Both companies are identical except for debt. Same EBIT. Zero growth, so no net additions to capital. The required return on U’s equity is r sU. The required return on L’s equity is r sL. Debt is riskless and investors can borrow as well as lend at this rate. 8

9. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. MM with Zero Taxes (1958) Proposition I: V L = V U. Steps in proof: Show that total investor cash flows are the same for both firms. Show that if V L ≠V U, then investors can create arbitrage profits. But this would lead to buying and selling activities that would drive V L and V U, to the same value. 9

10. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Annual Cash Flow to U’s Investors (CF U ) Cash flow to shareholders: No growth, so dividends equal net income (NI). No interest payments or taxes, so NI =EBIT. No debt, so no debtholders. CF U = EBIT. 10

11. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Annual Cash Flow to L’s Investors (CF L ) Debtholders receive interest payments, so their cash flow is: r d D Zero taxes, so the cash flow to shareholders is: EBIT − r d D CF L = r d D + (EBIT − r d D) = EBIT 11

12. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Cash Flows and Firm Values Note that CF U = EBIT = CF L U has no debtholders, so V U = S U L has debtholders, so V L = S L + D Proposition I: V L = S L + D = V U = S U. The value of a levered firm is equal to the value of the firm if it had no debt. 12

13. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proof By Using an Arbitrage Argument If V L ≠ V U, then an investor could: Sell the expensive asset Buy the cheaper asset Have money left over Have zero net future annual cash flow. This would be arbitrage, which should not exist in well-functioning markets. 13

14. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Suppose V L > V U Get cash by selling 1% of V L Use this cash to create a portfolio that reproduces L’s cash flows exactly, but is cheaper than V L : Borrow 1% of D at an interest rate of r d. Buy 1% of U 14

15. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Summary of Transactions Initial Cash FlowSell 1% of S L Borrow 1% of DBuy 1% of U Total Net Initial Cash Flow +0.01(S L )+0.01(D)−0.01(S U ) 0.01(S L + D – S U ) = 0.01(V L − V U ) > 0 15 Annual Cash Flows Sell 1% of S L Borrow 1% of DBuy 1% of U Total Net Annual Cash Flow Annual dividends −0.01(EBIT−r d D)+0.01(EBIT) +0.01(r d D) Annual interest−0.01(r d D) Annual total−0.01(EBIT−r d D)−0.01(r d D) +0.01(EBIT) 0

16. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The arbitrage opportunity Start off with no money! Sell 1% of L’s stock, borrow an amount equal to 1% of D, and buy 1% of U. The initial CF for this position is positive since we assumed V L > V U. Net annual cash flows are zero. This means after you enter the position, you have money in your pocket and no other net cash flows. 16

17. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. But arbitrage can’t last long! Everyone would engage in the arbitrage transactions: Selling pressure would cause V L to fall Buying pressure would cause V U to rise All of this would take place until V L = V U 17

18. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Example… Suppose we have the following data: EBIT = $100 for U and L. r sU = 10%. r d = 6%. L has D = 250. (Debt is zero for U.) 18

19. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Firm Values in Example V U = S U = EBIT/ r sU V U = 100/0.10 = $1,000. V L = S L + D (= V U because of Proposition I ) S L = V L − D S L = $1,000 − $250 = $750. 19

20. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Dividends in Example U’s only cash flow is a dividend to shareholders. With no debt, no taxes, and no growth: Dividend U = EBIT= $100 L pays interest, so its dividend (which is also its net income) is: Dividend L = EBIT − r d D Dividend L = $100 − 0.06($250) = $85 20

21. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Suppose S L = $800, instead of $750. Initial Cash Flow Sell 1% of S L Borrow 1% of DBuy 1% of U Total Net Initial Cash Flow +0.01($800) = $8 +0.01($250) = $2.5−0.01($1,000) = −$10 $8 + $2.5 −$10 = $0.50 21 Annual Cash Flows Sell 1% of S L Borrow 1% of DBuy 1% of U Total Net Annual Cash Flow Annual dividends −0.01($85) = −$8.50 +0.01($100) = $10 −$8.50 + $10 = $1.50 Annual interest −0.01(0.06 x $250) = −$1.50 −$1.50 Annual total −$8.50−$1.50$10$0 You have no net annual cash flows, but you have $0.50 in your pocket as a risk-free profit from the position.

22. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. How will investors use this? Investors will bid up the price of U, and bid down the price of L until V L = V U. What if there is no short selling? Then investors who were considering purchasing L would, instead, purchase U and borrow on their own accounts. They get the same annual cash flows but the initial investment is less. So no one would purchase L at this price, and the price of L’s stock would have to drop until V L = V U. 22

23. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. In our example In our example, investors will buy U’s stock and borrow rather than buy L’s stock. L is too expensive. This will bid down the price of L’s stock below $800. This will continue until S L + 250 = 1,000, or S L = $750. Here, investors use homemade leverage to reproduce L’s cash flows, but cheaper. 23

24. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. What if V L < V U Then reverse the position. Buy 1% of L, sell 1% of U and invest 0.01(D) in a bond paying interest of r d. Annual net cash flows are still 0, just like before. Because now V L < V U you have money left over, but no net annual liability. 24

25. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. How will investors use this? Investors will bid up the price of L, and bid down the price of U until V L = V U. What if there is no short selling? Then investors who were considering purchasing U would, instead, purchase L and lend (invest in bonds) on their own accounts. They get the same annual cash flows as U but the initial investment is less. No one would purchase U at this price, and the price of U’s stock would have to drop until V L = V U. 25

26. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Suppose S L = $700, instead of $750. Initial Cash FlowSell 1% of S U Lend 1% of DBuy 1% of S L Total Net Initial Cash Flow +0.01($1000) = $10 −0.01($250) = −$2.5 −0.01($700) = −$7 $10 − $2.5 −$7 = $0.50 26 Annual Cash Flows Sell 1% of S U Lend 1% of DBuy 1% of S L Total Net Annual Cash Flow Annual dividends −0.01($100) = −$10 +0.01($85) = $8.5 −$10 + $8.5 = $1.50 Annual interest 0.01(0.06 x $250) = $1.50 $1.50 Annual total−$10$1.50$8.5$0 You have no net annual cash flows, but you have $0.50 in your pocket as a risk-free profit from the position. You have duplicated L’s position with homemade leverage again.

27. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. MM no Taxes Proposition II Proposition II: r sL = r sU + (r sU – r d )(D/S L ) Proof: Just solve the following equation from Proposition I for r sL : (Algebra hint on next page) 27

28. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. To do the algebra… To solve, note that by definition EBIT on the right hand side can be rewritten as EBIT = S L r sL + r d D Plug this into the equation on the previous slide. This makes the algebra a good deal easier! 28

29. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. In our example r sU = 10%, D = $250, S L = $750, r d = 6%. r sL = 10% + (10% - 6%)(250/750) = 11.3333% To check, the present value of L’s dividends at r sL is $85/0.113333 = $750. This must be L’s stock price if there is to be no arbitrage. 29

30. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. MM with Corporate Taxes (1963) V L = V U + V Tax shield = V U + TD The value of a levered company is equal to its value if it had no debt plus the value of the interest tax shield. 30

31. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proof of Proposition I Begin by expressing U’s and L’s cash flows to investors in a way that can be compared to cash flows of known assets. As shown by MM’s arbitrage proof, assets with the same cash flows must have the same values. Start with U: U’s annual CF = EBIT(1 – T) 31

32. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. L’s Annual Cash Flows The annual cash flows to L are the dividends plus the interest payments: L’s Annual CF = (EBIT – r d D)(1 – T) + r d D = EBIT(1 – T) + r d DT The first part, EBIT(1 – T), is the same as the cash flow to U. The second part, is the debt tax shield. 32

33. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proof of Proposition I with taxes cont.. The first term, EBIT(1 – T), is equal to U’s cash flows. Therefore, the first term’s value is equal to the value of an unlevered firm, V U. Otherwise, arbitrage would be possible. 33

34. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proof of Proposition I with taxes cont.. The second term, the debt tax shield, is a perpetual stream of cash flows equal to r d DT. Its value depends on the discount rate. Modigiani and Miller assumed the appropriate discount rate was the required return on debt, r d, so the tax shield value is: Value of tax shield = r d TD/r d = TD. 34

35. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proof of Proposition I with taxes cont.. The total value of the levered firm is: V L = V U + TD In other words, the value of a levered firm is equal to the value of an unlevered firm plus the value of side effects due to leverage. 35

36. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Our example Consider firms U and L, both with EBIT = $100 and T = 40%. r sU = 10%, D = $150 for L, r d = 6%. CF to U = Dividends = 100(1-0.40) = $60 per year V U = $60/0.10 = $600. This is different from before because now we have taxes. 36

37. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Our example continued… CF to L = Dividends + interest = (100 – 150x0.06)(1-0.40) + 150x0.06 = 54.6 + 9 = 63.6. But this isn’t a useful way to look at it. Instead, rewrite it as: = 100x0.60 + 150x0.06x0.40 per year = 60 + 3.6 = 63.6 = CF to U + Debt tax shield = EBIT(1-T) + r d TD 37

38. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Our example: L’s cash flows EBIT(1-T) Tax Shield Annual CF: $60 $3.60 Disc. rate: 10% 6% PV: 60/0.1 = $600 3.6/0.06 = $60 V L = V U + V TS V L = V U + V TS = $600 + $60 = $660. 38

39. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proposition II with taxes r sL = r sU + (r sU – r d )(1 – T)(D/S) The required rate of return to a levered stock is the unlevered return plus a premium that depends on the tax rate, the rate on debt, and the amount of debt. 39

40. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proof of Proposition II with taxes Proposition I says that V L = S L + D = V U + V TS S L + D = S U + V TS = EBIT(1 – T)/r sU + TD Algebra (with a hint on the next page) gives the result of Proposition II. 40

41. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. to do the algebra… Since S L = (EBIT – r d D)(1 – T)/r sL you can solve for EBIT(1 – T): EBIT(1 – T) = S L r sL + r d D(1 – T) Plug this expression for EBIT(1 – T) into the right hand side of: S L + D = S U + V TS = EBIT(1 – T)/r sU + TD and solve for r sL to get the Proposition II result. 41

42. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Our example r sU = 10%, T = 40%, r d = 6% V L = $660, D = $150, so S L = $510 r sL = 10%+(10% - 6%)(1-0.40)(150/510) = 10.706% To check, L’s dividends are $54.6. Their present value at r sL is 54.6/0.10706 = $510, which is S L. 42

43. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 43 Another Numerical Illustration of the MM Propositions Firms U and L are in same risk class. EBIT U = EBIT L = $500,000. Firm U has no debt; r sU = 14%. Firm L has $1,000,000 debt at r d = 8%. The basic MM assumptions hold. There are no corporate or personal taxes.

44. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 44 V U = = = $3,571,429. V L = V U = $3,571,429. EBIT r sU $500,000 0.14 1. Find V U and V L.

45. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 45 V L = D + S = $3,571,429 $3,571,429 = $1,000,000 + S S = $2,571,429. 2. Find the market value of Firm L’s debt and equity.

46. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 46 r sL = r sU + (r sU - r d )(D/S) = 14.0% + (14.0% - 8.0%) ( ) = 14.0% + 2.33% = 16.33%. $1,000,000 $2,571,429 3. Find r sL.

47. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 47 WACC= w d r d + w ce r s = (D/V)r d + (S/V)r s = ( ) (8.0%) + ( ) (16.33%) = 2.24% + 11.76% = 14.00%. $1,000,000 $3,571,429 $2,571,429 $3,571,429 4. Proposition I implies WACC = r sU. Verify for L using WACC formula.

48. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 48 Without taxes Cost of Capital (%) 26 20 14 8 020406080100 Debt/Value Ratio (%) rsrs WACC rdrd MM Relationships Between Capital Costs and Leverage (D/V)

49. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 49 The more debt the firm adds to its capital structure, the riskier the equity becomes and thus the higher its cost. Although r d remains constant, r s increases with leverage. The increase in r s is exactly sufficient to keep the WACC constant.

50. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 50 Value of Firm, V (%) 43214321 00.51.01.52.02.5 Debt (millions of $) VLVL VUVU Firm value ($3.6 million) With zero taxes, MM argue that value is unaffected by leverage. Graph value versus leverage.

51. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 51 With corporate taxes added, the MM propositions become: Proposition I: V L = V U + TD. Proposition II: r sL = r sU + (r sU - r d )(1 - T)(D/S). V, S, r s, and WACC for Firms U and L (40% Corporate Tax Rate)

52. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 52 Notes About the New Propositions 1.When corporate taxes are added, V L ≠ V U. V L increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm. 2.r sL increases with leverage at a slower rate when corporate taxes are considered.

53. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 53 Note:Represents a 40% decline from the no taxes situation. V L = V U + TD= $2,142,857 + 0.4($1,000,000) = $2,142,857 + $400,000 = $2,542,857. V U = = = $2,142,857. EBIT(1 - T) r sU $500,000(0.6) 0.14 1. Find V U and V L.

54. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 54 V L = D + S = $2,542,857 $2,542,857= $1,000,000 + S S= $1,542,857. 2. Find market value of Firm L’s debt and equity.

55. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 55 = 14.0% + (14.0% - 8.0%)(0.6) ( ) = 14.0% + 2.33% = 16.33%. $1,000,000 $1,542,857 3. Find r sL. r sL = r sU + (r sU - r d )(1 - T)(D/S)

56. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 56 WACC L = (D/V)r d (1 - T) + (S/V)r s = ( ) (8.0%)(0.6) + ( ) (16.33%) = 1.89% + 9.91% = 11.80%. When corporate taxes are considered, the WACC is lower for L than for U. $1,000,000 $2,542,857 $1,542,857 $2,542,857 4. Find Firm L’s WACC.

57. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 57 Cost of Capital (%) 26 20 14 8 020406080100 Debt/Value Ratio (%) rsrs WACC r d (1 - T) MM: Capital Costs vs. Leverage with Corporate Taxes

58. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 58 Under MM with corporate taxes, the firm’s value increases continuously as more and more debt is used. Value of Firm, V (%) 43214321 00.51.01.52.02.5 Debt (Millions of $) VLVL VUVU TD MM: Value vs. Debt with Corporate Taxes

59. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 59 Miller’s Proposition I: V L = V U + [ 1 - ] D. T c = corporate tax rate. T d = personal tax rate on debt income. T s = personal tax rate on stock income. (1 - T c )(1 - T s ) (1 - T d ) Miller Model with Corporate and Personal Taxes

60. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Proof of Miller’s Model with Corporate and Personal Taxes The proof is similar to that of the MM model with corporate taxes. Begin by expressing U’s and L’s cash flows to investors in a way that can be compared to cash flows of known assets. 60

61. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Investor Cash Flows with Corporate and Personal Taxes Start with U’s after-tax cash flow to its investors: U’s annual CF = EBIT(1 – T c )(1 – T s ) 61

62. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. L’s Annual After-Tax Cash Flows to Investors The annual cash flows to L’s investors are the dividends plus the interest payments: L’s Annual CF = (EBIT – r d D)(1 – T c )(1 – T s ) + r d D(1 − T d ) With a lot of algebra, these cash flows can be rewritten as shown on the next slide. 62

63. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 63 L’s Annual After-Tax Cash Flows to Investors after Rearranging + 1 − r d D (1− T c )(1− T s ) (1 − T d ) L’s annual CF = EBIT(1 – T c )(1 – T s ) The first part, EBIT(1 – T c )(1 – T s ), is the same as the cash flow to U. The second part, is the debt tax shield.

64. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Miller’s Model: The Value of the Operating Cash Flows The first term, EBIT(1 – T c )(1 – T s ), is equal to U’s cash flows. Therefore, the first term’s value is equal to the value of an unlevered firm, V U. Otherwise, arbitrage would be possible. 64

65. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Miller’s Model: The Value of the Tax Shield The second term, the debt tax shield, is a perpetual stream of cash flows. Miller assumed the appropriate discount rate was the required return on debt, r d, so the tax shield value is 65 1 − D (1− T c )(1− T s ) (1 − T d )

66. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 66 Miller’s Model: Total Value of a Levered Firm V L = V U + 1 − D (1− T c )(1− T s ) (1 − T d ) As in the MM model with corporate taxes, the value of a levered firm is equal to the value of an unlevered firm plus the value of side effects due to leverage. However, the side effects in the Miller model include personal tax effects.

67. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 67 V L = V U + [ 1 - ] D = V U + (1 - 0.75)D = V U + 0.25D. (1 - 0.40)(1 - 0.12) (1 - 0.30) Example: T c = 40%, T d = 30%, and T s = 12%. Value rises with debt; each $100 increase in debt raises L’s value by $25.

68. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 68 Miller vs. MM Model with Corporate taxes If only corporate taxes, then V L = V U + T c D = V U + 0.40D. Here $100 of debt raises value by $40. Thus, personal taxes lowers the gain from leverage, but the net effect depends on tax rates. (More...)

69. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 69 If T s declines, while T c and T d remain constant, the slope coefficient (which shows the benefit of debt) is decreased. A company with a low payout ratio gets lower benefits under the Miller model than a company with a high payout, because a low payout decreases T s.

70. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 70 Why do personal taxes lower value of debt? Corporate tax laws favor debt over equity financing because interest expense is tax deductible while dividends are not. (More...)

71. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 71 However, personal tax laws favor equity over debt because stocks provide both tax deferral and a lower capital gains tax rate. This lowers the relative cost of equity vis-a- vis MM’s no-personal-tax world and decreases the spread between debt and equity costs. Thus, some of the advantage of debt financing is lost, so debt financing is less valuable to firms.

72. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 72 What does capital structure theory prescribe for corporate managers? MM, No Taxes: Capital structure is irrelevant- -no impact on value or WACC. MM, Corporate Taxes: Value increases, so firms should use (almost) 100% debt financing. Miller, Personal Taxes: Value increases, but less than under MM, so again firms should use (almost) 100% debt financing.

73. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 73 Do firms follow the recommendations of capital structure theory? Firms don’t follow MM/Miller to 100% debt. Debt ratios average about 40%. However, debt ratios did increase after MM. Many think debt ratios were too low, and MM led to changes in financial policies.

74. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 74 How is analysis different if firms U and L are growing? Under MM (with taxes and no growth) V L = V U + T D This assumes the tax shield is discounted at the cost of debt. Assume the growth rate is 7% The debt tax shield will be larger if the firms grow:

75. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 75 7% growth, TS discount rate of r TS Value of (growing) tax shield = V TS = r d TD/(r TS –g) So value of levered firm = V L = V U + r d TD/(r TS – g)

76. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 76 What should r TS be? The smaller is r TS, the larger the value of the tax shield. If r TS < r sU, then with rapid growth the tax shield becomes unrealistically large—r TS must be equal to r U to give reasonable results when there is growth. So we assume r TS = r sU.

77. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 77 Levered cost of equity In this case, the levered cost of equity is r sL = r sU + (r sU – r d )(D/S) This looks just like MM without taxes even though we allow taxes and allow for growth. The reason is if r TS = r sU, then larger values of the tax shield don't change the risk of the equity.

78. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 78 Levered beta If there is growth and r TS = r sU then the equation that is equivalent to the Hamada equation is b L = b U + (b U - b D )(D/S) Notice: This looks like Hamada without taxes. Again, this is because in this case the tax shield doesn't change the risk of the equity.

79. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 79 Relevant information for valuation EBIT = $500,000 T = 40% r U = 14% = r TS r d = 8% Required reinvestment in net operating assets = 10% of EBIT = $50,000. Debt = $1,000,000

80. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 80 Calculating V U NOPAT = EBIT(1-T) = $500,000 (.60) = $300,000 Investment in net op. assets = EBIT (0.10) = $50,000 FCF = NOPAT – Inv. in net op. assets = $300,000 - $50,000 = $250,000 (this is expected FCF next year)

81. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 81 Value of unlevered firm, V U Value of unlevered firm = V U = FCF/(r sU – g) = $250,000/(0.14 – 0.07) = $3,571,429

82. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 82 Value of tax shield, V TS and V L V TS = r d TD/(r sU – g) = 0.08(0.40)$1,000,000/(0.14-0.07) = $457,143 V L = V U + V TS = $3,571,429 + $457,143 = $4,028,571

83. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 83 Cost of equity and WACC Just like with MM with taxes, the cost of equity increases with D/V, and the WACC declines. But since r sL doesn't have the (1-T) factor in it, for a given D/V, r sL is greater than MM would predict, and WACC is greater than MM would predict.

84. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 84 Cost of Capital for MM and Extension

85. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 85 What if L's debt is risky? If L's debt is risky then, by definition, management might default on it. The decision to make a payment on the debt or to default looks very much like the decision whether to exercise a call option. So the equity looks like an option.

86. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 86 Equity as an option Suppose the firm has $2 million face value of 1-year zero coupon debt, and the current value of the firm (debt plus equity) is $4 million. If the firm pays off the debt when it matures, the equity holders get to keep the firm. If not, they get nothing because the debtholders foreclose.

87. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 87 Equity as an option The equity holder's position looks like a call option with P = underlying value of firm = $4 million X = exercise price = $2 million t = time to maturity = 1 year Suppose r RF = 6%  = volatility of debt + equity = 0.60

88. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 88 Use Black-Scholes to price this option V C = P[N(d 1 )] - Xe -r RF t [N(d 2 )] d 1 =  t 0.5 d 2 = d 1 -  t 0.5 ln(P/X) + [r RF + (  2 /2)]t

89. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 89 Black-Scholes Solution V = $4[N(d 1 )] - $2e -(0.06)(1.0) [N(d 2 )]. ln($4/$2) + [(0.06 + 0.36/2)](1.0) d 1 = (0.60)(1.0) = 1.5552. d 2 =d 1 – (0.60)(1.0) = d 1 – 0.60 = 1.5552 – 0.6000 = 0.9552.

90. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 90 N(d 1 ) = N(1.5552) = 0.9401 N(d 2 ) = N(0.9552) = 0.8383 Note: Values obtained from Excel using NORMSDIST function. V = $4(0.9401) - $2e-0.06(0.8303) = $3.7604 - $2(0.9418)(0.8303) = $2.196 Million = Value of Equity

91. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 91 Value of Debt The value of debt must be what is left over: Value of debt = Total Value – Equity = $4 million – 2.196 million = $1.804 million

92. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 92 This value of debt gives us a yield Debt yield for 1-year zero coupon debt = (face value / price) – 1 = ($2 million/ 1.804 million) – 1 = 10.9%

93. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 93 How does  affect an option's value? Higher volatility  means higher option value.

94. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 94 Managerial Incentives When an investor buys a stock option, the riskiness of the stock (  ) is already determined. But a manager can change a firm's  by changing the assets the firm invests in. That means changing  can change the value of the equity, even if it doesn't change the expected cash flows:

95. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 95 Managerial Incentives So changing  can transfer wealth from bondholders to stockholders by making the option value of the stock worth more, which makes what is left, the debt value, worth less.

96. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 96 Value of Debt and Equity for Different Volatilities

97. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 97 Bait and Switch Managers who know this might tell debtholders they are going to invest in one kind of asset, and, instead, invest in riskier assets. This is called bait and switch and bondholders will require higher interest rates for firms that do this, or refuse to do business with them.

98. © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 98 If the debt is risky coupon debt If the risky debt has coupons, then with each coupon payment management has an option on an option—if it makes the interest payment then it purchases the right to later make the principal payment and keep the firm. This is called a compound option.