CAPITAL STRUCTURE :CHAPTERS 15 AND 16 BUSINESS RISK AND FINANCIAL RISK THE BUSINESS RISK OF A FIRM ( OR A PROJECT) RELATES TO THE VOLATILITY OF THE RETURN ON THE EQUITY OF ITS SHAREHOLDERS WHEN THE FIRM IS 100% EQUITY FINANCED, I.E., THE FIRM HAS NO DEBT AND HENCE UNLEVERED. FINANCIAL RISK RELATES TO THE ADDITIONAL RISK OF BANKRUPTCY DUE TO THE USE OF DEBT IN THE OPERATIONS. THUS, STOCK HOLDERS OF A FIRM WITH DEBT WILL HAVE TO BEAR THE BUSINESS RISK AS WELL AS THE FINANCIAL RISK DUE TO DEBT. BUSINESS RISK MAY BE INFLUENCED BY THE PRODUCT DEMAND VARIABILITY PRODUCT SALES PRICE VARIABILITY INPUT COST VARIABILITY ABILTY TO ADJUST OUTPUT PRICES FOR CHANGES IN INPUT COSTS ABILITY TO DEVELOP NEW PRODUCTS , TIMELY AND COST-EFFECTIVELY FOREIGN RISK EXPOSURE EXTENT TO WHICH OPERATING COSTS ARE FIXED: OPERATING LEVERAGE FOR A DISCUSSION OF THE ABOVE REFER TO PAGE 513 OF TEXT SINCE SUCH CHARACTERISTICS COULD VARY ACROSS INDUSTRIES AND ACROSS FIRMS IN AN INDUSTRY, BUSINESS RISK VARIES FROM INDUSTRY TO INDUSTRY AND AMONG FIRMS IN AN INDUSTRY. THE EFFECT OF OPERATING LEVERAGE AND RELATED CONCEPTS ARE ILLUSTRATED THRU THE FOLLOWING EXAMPLE: EXAMPLE TO ILLUSTRATE OPERATING LEVERAGE WORSE EXPECTED BETTER SALES (UNITS) 90,000 $ SALES (@ $50/UNIT) 4.5 M VARIABLE COST (@ $30/UNIT) 2.7 M CONTRIBUTION 1.8 M FIXED COSTS 1M ______ EBIT 0.8 M _______ CASE A (FIRM HAS NO DEBT) 100,000 5M 3M 2 1M ______ 1M ______ 110,000 5.5 M 3.3 M 2.2M 1M ______ 1.2 M _______ INTEREST TAXABLE INCOME TAX @ 40% 0 0.8 M 0.32 M ________ 0 1M 0.4 M ______ 0 1.2 M 0.48 M _______ NET INCOME 0.48 M _________ 0.6 M _______ 0.72 M _________ 0.2 M 0.6 M 0.24 M ________ 0.36 M _________ 0.2 M 0.8 M 0.32 M _______ 0.48 M ________ CASE B (FIRM HAS DEBT) INTEREST TAXABLE INCOME TAX @ 40% NET INCOME 0.2 M 1M 0.4 M _______ 0.6 M _______ DEGREES OF LEVERAGE DEGREE OF OPERATING LEVERAGE (DOL) = % CHANGE IN EBIT % CHANGE IN SALES DEGREE OF FINANCIAL LEVERAGE (DFL) = % CHANGE IN NI % CHANGE IN EBIT DEGREE OF TOTAL LEVERAGE (DTL) = % CHANGE NI % CHANGE IN SALES DTL = % CHANGE IN EBIT * % CHANGE IN NI % CHANGE IN SALES % CHANGE IN EBIT = DOL * DFL FOR CASE A (NO DEBT): DOL = 20/10 =2 DFL = 20/20 =1 DTL = 20/10 = 2 (OR 2 * 1) FOR CASE B (DEBT): DOL = 20/10 =2 DFL = 25/20 = 1.25 DTL = 25/10 = 2.5 (OR 2 * 1.25) CAPITAL STRUCTURE THEORY MILLER & MODIGLIANI (M&M) ASSUMPTIONS 1. BUSINESSRISK CAN BE MEASURED AND FIRMS WITH THE SAME BUSINESS RISK FALL IN A HOMOGENEOUS RISK CLASS AND COMMAND THE SAME BUSINESS RISK PREMIUM 2. INVESTORS (PRESENT AND PROSPECTIVE) HAVE HOMOGENEOUS EXPECTATIONS ABOUT EXPECTED EARNINGS, RISK, ETC. 3. CAPITAL MARKETS ARE PERFECT (NO BROKERAGE COSTS) 4. ANY AMOUNT OF BORROWING AND LENDING CAN BE TRANSACTED AT THE SAME INTEREST RATE –RISK-FREE RATE- BY INDIVIDUALS AND FIRMS 5. BORROWING DECISION IS A ONE-TIME DECISION 6. FIRMS HAVE NO GROWTH AND ALL CASH FLOWS ARE PERPETUITIES 7. EBIT IS NOT AFFECTED BY DEBT 8. BANCRUPTCY IS POSSIBLE, BUT THERE ARE NO BANKRUPTCY COSTS 9. AGENCY PROBLEM MAY BE PRESENT BUT THERE ARE NO AGENCY COSTS WITH THE ABOVE ASSUMPTIONS, M&M EXAMINED WHETER VL = VU VL < VU VL > VU THEY EXAMINED THE ABOVE RELATIONSHIPS UNDER: A. NO CORPORATE TAXES AND NO PERSONAL TAXES B. NO PERSONAL TAXES, BUT CORPORATE TAXES EXIST LATER, MILLER EXAMINED THE RELATIONSHIPS UNDER: BOTH CORPORATE AND PERSONAL TAXES EXIST WITHOUT TAXES (NO CORPORATE OR PERSONAL TAXES) VL = VU = EBIT/ rSU rSL = rSU + RISK PREMIUM = rSU + (rSU-rD) * (D/S) (16-1) (16-2) WACCL = WACCU = rSU REFER TO FIG. 16-1 (LEFT) PROBLEM 16-2 a. VU = EBIT rsU = b. rsU = 10.0%. $2 million 0.10 = $20 million. (Given) rsL = rsU + rsU - rd)(D/S)= 10%+(10%-5%)($10/$10)= 15.0%. c. SL = EBIT rd D $2 0.05($10) = = $10 million. 0.15 rsL SL + D = VL = VU + TD. $10 + $10 = $20 = VL = $20 + (0)$10 = $20 million. d. WACCU = rsU = 10%. For Firm L, we know that WACC must equal rsU = 10% according to Proposition I. But, we can demonstrate this as follows: WACCL = (D/V)rd + (S/V)rs = ($10/$20)5% +($10/$20)15% = 2.5% + 7.5% = 10.0%. e. VL = $22 million is not an equilibrium value according to MM. Here’s why. Suppose you owned 10 percent of Firm L’s equity, worth 0.10($22 million - $10 million) = $1.2 million. You could (1) sell your stock, (2) borrow an amount (at 5%) equal to 10 percent of Firm L’s debt, or 0.10($10 million) = $1 million, and (3) end up with $1.2 million + $1 million = $2.2 million. You could spend $2 million to buy 10% of Firm U’s stock, and invest $200,000 in risk-free debt. Your cash stream would now be 10 percent of Firm U’s flow, or 0.10(EBITU) = 0.10($2 million) = $200,000, plus the return on the $200,000 of risk-free debt, minus the 0.05($1 million) = $50,000 interest expense for $150,000 plus the return on the extra $200,000. Before the arbitrage, your return was 10 percent of the $2 million - 0.05($10 million) = $1.5 million, or $150,000. Investors would do this arbitrage until VL = VU = $20 million. WITH CORPORATE TAXES ONLY (NO PERSONAL TAXES) VU = EBIT*(1-T)/ rSU (16-5) VL = VU + T*D (16-4) rSL = rSU + RISK PREMIUM = rSU + (rSU-rD) * (1-T) * (D/S) (16-6) WACCL < WACCU REFER TO FIG. 16-1 (RIGHT) PROBLEM 16-3 $2(1 0.4) EBIT (1 T ) = = $12 million. 0.10 rsU a. VU = VL = VU + TD = $12 + (0.4)$10 = $16 million. VL = D + SL OR SL = VL – D = 16 – 10 = 6 Million b. rsU = 0.10 = 10.0%. rsL = rsU + (rsU - rd)(1 - T)(D/S) = 10% + (10% - 5%)(0.6)($10/$6) = 10% + 5% = 15.0%. c. SL = ( EBIT rd D)(1 T) [$2 0.05($10)]0.6 = = $6 million. 0.15 rsL VL = SL + D = $6 + $10 = $16 million. d. WACCU WACCL = rsU = 10.00%. = (D/V)rd(1 - T) + (S/V)rs = ($10/$16)5%(0.6) + ($6/$16)15% = 7.50%. WITH CORPORATE AND PERSONAL TAXES VU = EBIT*(1-TC) * (1-TS) rSU * (1-TS) (16-8) VL = VU + {1- [(1-TC) * (1-TS)/(1-Td]}* D (16-12) PROBLEM 16-4 a. VU = EBIT (1 TC )(1 Ts ) EBIT (1 TC ) $2(0.6) = = = $12 0.10 rsU (1 Ts ) rsU million. b. VL = VU + 1 (1 TC )(1 Ts ) D (1 Td ) (0.6)( 0.8) = $12 + 1 $10 (0.72) = $12 + [1 - 0.67]$10 = $12 + 0.33($10) = $15.33 million. VL = $15.33 million. Gain from leverage = $3.33 million. c. The gain from leverage under Miller is 0.33($10) = $3.33 million. The gain from leverage in Problem 16-3 is 0.4($10) = $4 million. Thus, the addition of personal tax rates reduced the value of the debt financing. d. VU = VL = $20 million. Gain from leverage = $0.00. e. VU = $12 million. VL = $16 million. Gain from leverage = $4 million. f. VU = $12 million. VL = $16 million. Gain from leverage = $4.0 million. Note that the gain from leverage is the same as in Part (e) and will be the same value, as long as Td = Ts. CAPITAL STRUCTURE THEORY, HAMADA MODEL AND PURE PLAY APPROACH bL = bU[1 + (1 - T)(D/S)] rsU = rRF + (rM - rRF)bU rsL = rsU + (rsU - rRF)(1 - T)(D/S) PROBLEM 16-1 a. bL = bU[1 + (1 - T)(D/S)]. bU = bL 1.8 1 .8 = = = 1.125. 1 .6 1 (1 T )( D / S) 1 (1 0.4)( 0.5 / 0.5) b. rsU = rRF + (rM - rRF)bU = 10% + (5%)1.125 = 10% + 5.625% = 15.625%. c. $2 Million Debt: VL = VU + TD = $10 + 0.25($2) = $10.5 million. rsL = rsU + (rsU - rRF)(1 - T)(D/S) = 15.625% + (15.625% - 10%)(0.75)($2/$8.5) = 15.625 + 5.625% (0.75)($2/$8.5) = 16.62%. $4 Million Debt: VL = $10 + 0.25($4) = $11.0 million. rsL = 15.625% + 5.625%(0.75)($4/$7) = 18.04%. $6 Million Debt: VL = $10 + 0.25($6) = $11.5 million. rsL= 15.625% + 5.625% (0.75)($6/$5.5) = 20.23%. CAPITAL STRUCTURE THEORY THE TRADE-OFF MODEL THE MODELS OF M&M WITH CORPORATE TAXES AND THE MILLER MODEL WITH CORPORATE AND PERSONAL TAXES IMPLY THAT DEBT IS BENEFICIAL AND CAPITAL STRUCTURE SHOULD BE CLOSE TO 100% DEBT FOR FIRM VALUE MAXIMIZATION. HOWEVER, WITH THE EXCEPTION OF A FEW FIRMS, THE OBSERVED DEBT LEVEL IS BETWEEN 0% AND 100% ALSO, DIFFERENT INDUSTRIES HAVE DIFFERENT AVERAGE DEBT LEVELS. HOW CAN THIS BE EXPLAINED? MODELS USING FINANCIAL DISTRESS (BANKRUPTCY) COSTS AND AGENCY COSTS OF DEBT ALONG WITH TAX BENEFITS OF DEBT (DUE TO TAX DEDUCTIBILITY OF INTEREST) ARE CALLED TRADE-OFF MODELS. THESE MODELS SEEK TO EXPLAIN THE OPTIMUM CAPITAL STRUCTURE AS THE DEBT LEVEL AT WHICH THE TAX-SHELTERING BENEFITS OF DEBT ARE OFFSET BY THE FINANCIAL DISTRESS (BANKRUPTCY) AND AGENCY COSTS THAT ARISE DUE TO DEBT AND INCREASE WITH DEBT LEVEL: VL = VU + TAX BENEFITS OF DEBT (SAY,T*D) - PV OF EXPECTED FINANCIAL DISTRESS COSTS - PV OF EXPECTED AGENCY COSTS REFER TO FIG. 15-1 HERE ONLY FINANCIAL DISTRESS COSTS ARE SHOWN. IT IS EASY TO INCLUDE THE EFFECTS OF AGENCY COSTS IN THE DIAGRAM Also refer to power point slides 40-50 as well as discussion in chapter 15 of text (pages 519-530) FINDING OPTIMUM CAPITAL STRUCTURE WITH BANKRUPTCY AND AGENCY COSTS 1. FIND VU 2. ESTIMATE BANKRUPTCY COSTS AND THEIR PRESENT VALUE 3. ESTIMATE THE PROBABILITY OF BANKRUPTCY AT DIFFERENT DEBT LEVELS 4. ESTIMATE THE EXPECTED PV OF BANKRUPTCY COSTS AT DIFFERENT DEBT LEVELS AS (2) * (3) 5. ESTIMATE PV OF EXPECTED AGENCY COSTS AT DIFFERENT DEBT LEVELS 6. FOR EACH DEBT LEVEL FIND VL = VU + T*D – (4) – (5) 7. THE OPTIMUM CAPITAL STRUCTURE (DEBT LEVEL) IS WHERE VL IS MAXIMUM PROBLEM LLL IN. IS CURRENTLY UNLEVERED, WITH A VALUE OF $30 MILLION. IT WILL CONTINUE TO BE IN THE 40% TAX BRACKET. THE COMPANY HAS ESTIMETED THAT THE PV OF ITS BANKRUPTCY COSTS WOULD BE $8 MILLION. LLL INC. HAS ESTIMATED THE PROBABILITIES OF BANKRUPTCY AND EXPECTED PV OF AGENCY COSTS AT DIFFERENT DEBT LEVELS AS FOLLOWS: DEBT $ MILLION PROB. OF BANKRUPTCY EXPECTED PV OF AGENCY COSTS ($ MILLION) 0 0 0.25 5 .1 10 0.3 20 0.5 30 35 0.8 0.95 0.5 0.75 1.0 1.5 3.0 FIND THE OPTIMUM LEVEL OF BORROWING (OPTIMUM CAPITAL STRUCTURE) FORR LLL INC. SOLUTION 1. VU = $ 50 MILLION (GIVEN) 2. PV OF BANKRUPTCY COSTS = $ 8 MILLION (GIVEN) 3. PROBABILITY OF BANKRUPTCY AT DIFFERENT DEBT LEVELS IS GIVEN ABOVE IN THE PROBLEM 4. EXPECTED PV OF BANRUPTCY COSTS AT DIFFERENT DEBT LEVELS DEBT $ MILLION 0 5 10 20 30 35 PROBABILITY OF BANKRUPTCY 0 0.1 0.3 0.5 0.8 0.95 EXPECTED PV OF BANKRUPTCY COSTS=(2)*(3)$ MILLION 0 0.8 2.4 4.0 6.4 7.60 5. EXPECTED PV OF AGENCY COSTS $ MILLION 0.25 0.5 0.75 1.0 1.5 3.0 6.FIND VL = VU + T*D – (4) – (5) (1) DEBT VU (2) T*D (3) (4) EXPECTED EXPECTED PV OF PV OF BANKRUPTCY AGENCY COSTS COSTS (5) VL=(1)+(2) -(3)-(4) 0 50 0 0 0.25 49.75 5 50 2 0.8 0.50 50.70 10 50 4 2.4 0.75 50.85 20 50 8 4.0 1.00 53.00 30 50 12 6.4 1.50 54.10 35 50 14 7.6 3.00 53.40 SINCE VALUE IS A MAXIMUM OF $54.10 MILLION AT A DEBT LEVEL OF $30 MILLION, OPTIMUM LEVEL OF BORROWING (OPTIMUM CAPITAL STRUCTURE) IS $30 MILLION