Lecture 15- Exam 3

Lecture 15- Exam 3 - The Weighted Average The Cost of...

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Unformatted text preview: The Weighted Average The Cost of Capital - A Refresher Great Lakes Resources Inc. Great Equity has Book Value of $5 Million ® Estimated In-Ground Resource Value is $120 Estimated Million Million ® Extraction/Operating Costs Estimated at $60 Extraction/Operating Million Million ® Debt Financing Available @ 10% ® Similar Equity Investments Earn 16% ® What is the Minimum Acceptable After-Tax Cash What Flow? Tax rate = 30% ® Great Lakes Resources Inc. ® Return on Debt $60 MM * 10%*(1-0.3) = $ 4.2 MM ® Return to Shareholders $120 MM * 16% Minimum After-Tax Acceptable Cash Flow = $19.2 MM = $23.4 MM Great Lakes Resources Inc. Great Minimum Acceptable After-Tax Rate of Return Mkt Val Wt % Mkt % Debt $ 60 MM 0.33 7 2.33 Equity $120 MM 0.67 16 10.67 Total $180 MM 13.00 13% is the Firm’s Weighted Average 13% Great Lakes Resources Inc. ® 13%* $180MM = $23.4MM ® The The Firm’s Cost of Capital is the Minimum Acceptable After-Tax Rate of Return That Ensures ALL Long-Term Creditors Get Paid!! ALL Long-Term Great Lakes Resources Inc. How Did the Shareholders Decide on the 16% How Return ? They Could “Guess-timate” or They Could Use the Dividend Growth Model ividend rowth odel Where D1 = $1.00, P0 = $10.00 & g = 6% Where 6% DGM Would Predict A Risk-Adjusted Return of E[Ri] = D1/P0 + g E[R = $1.00/$10.00 + 0.06 = 16 % $1.00/$10.00 Great Lakes Resources Inc. How Did the Shareholders Decide on the 16% How Return ? They Could “Guess-timate” or They Could Use the Capital Asset Pricing apital sset ricing Model Where Rm = 17.1%, Rf = 6% & β L = 0.9 0.9 CAPM Would Predict A Risk-Adjusted Return of E[Ri] = Rf + (Rm - Rf) β L E[R = 6 + (17.1 - 6) (0.9) = 16 % (17.1 Great Lakes Resources Inc. CAPM Predicts That Shareholders Require CAPM Compensation in Proportional ( β ) to the Degree of Debt in the Firm. So, What Would a Debt-Free Firm Offer its Shareholders ? Debt-Free β L = β A * [ 1 + (Debt/Equity) * (1 - t)] 0.9 = β A * ( 1 + (0.5) * (0.7)) 0.9 β A = 0.67 E[Ri] = 6 + (17.1 - 6) (0.67) = 13.44 % Great Lakes Resources Inc. Suppose Great Lakes Decided it Needed to Suppose Borrow $70,000,000 in Debt Instead, What Return Would the Shareholders Require ? Return β L = β A * [ 1 + (Debt/Equity) * (1 - t)] β L = 0.67 * ( 1 + (7/12)(0.7)) β L = 0.94 Ri = Rf + (Rm - Rf ) β L = 6 + (17.1 - 6) (0.94) = 16.43% Great Lakes Resources Inc. Great So, The Minimum Acceptable Rate of So, Return Becomes: Return Mkt Val Wt % % Debt $ 70 MM 0.368 7 2.58 Equity $120 MM 0.632 16.43 10.38 Total $190 MM 12.96 12.96% is the Firm’s Weighted 12.96% Average Cost of Capital (WACC) ! Average Return Relationships Return Annual % Cost Cost Cost of Equity WACC Cost of Debt M = Optimal Capital Structure Leverage D/E Great Lakes Resources Inc. Suppose the 1st Year’s Income Statement is: Sales Expenses Interest Ebt Tax Net Income $ $ $ 80.0 MM 40.1 MM 4.2 MM 4.2 35.7 MM 15.7 MM 25.0 MM Great Lakes Resources Inc. ® $ 25.0 MM Minus $ 19.7 MM that the Shareholders’ 25.0 Expect = $5.3MM ! $5.3MM ® So, $ 5.3MM is the Additional Economic Value So, 5.3MM Added to the Company ! Added to ® If the ROIC Exceeds the Cost of Capital That’s If EVA !! EVA !! But . . . But The WACC is Only Appropriate for Projects of AVERAGE Risk !! AVERAGE Risk This Raises the Question of Division This Costs of Capital When a Firm has Divisions That are Engaged in Projects of Different Risk Levels CAPM CAPM Is Usually Used When the Shares are Is Publicly Traded. Publicly But with Some Minor Adjustments Can be But Easily Applied to Corporate Divisions or Privately-Held Companies Privately-Held The Main Trick is to Consider Only AfterTax Cash Flows to the Equity Holder Hi-Lo Inc. Hi-Lo H i- L o I n c . H o ld in g C o m p a n y w it h P u b lic ly I s s u e d S h a r e s L o D iv is io n T rades B ank of C anada B onds 1 0 0 % o w n e d b y H i- L o I n c . 4 0 % o f T o t a l O p e r a t io n s H i D iv is io n M a n u f a c t u r e s C a r B a t t e r ie s 1 0 0 % o w n e d b y H i- L o I n c . 6 0 % o f T o t a l O p e r a t io n s Hi-Lo Inc. Hi-Lo Suppose the Holding Company has a 50:50 Suppose Debt to Equity Ratio and a 40% Tax Rate Debt Also, Let’s Say the Industry Avgs. are Also, β A(TB) = 0, β A(MFG) = 1.2, Rf = 8% and Rm = 14% What is the Appropriate Risk-Adjusted Rate of What Return for Each Division ? Hi-Lo Inc. Hi-Lo Let’s Consider the T-Bond Division β L(TB) = β Α (TB) * [ 1 + (Debt/Equity) (1 - t)] = 0 Therefore; E[RTB] = Rf + (Rm - Rf) β L(TB) = 8 + ( 14 - 8) ( 0 ) 14 = 8% Hi-Lo Inc. Hi-Lo Let’s Consider the Battery Division β L(MFG) = β A(Mfg) * [ 1 + (Debt/Equity) (1 - t)] = 1.2 1.2 * [ 1 + ( 1 ) (0.6)] = 1.92 1.92 Therefore; E[RMFG] = Rf + (Rm - Rf) β L(MFG) = 8 + ( 14 - 8) ( 1.92 ) 14 = 19.52 % Hi-Lo Inc. Hi-Lo Let’s Consider the Holding Company E[R] = 8% (0.4) + 19.52% (0.6) = 14.91 % E[β L(Hi-Lo)] = 0 (0.4) + 1.92 (0.6) = 1.152 Check; E[RHi-Lo] = Rf + (Rm - Rf) β L(Hi-Lo) = 8 + ( 14 - 8) ( 1.152 ) 14 = 14.91 % What About Privately Held Companies ? Held Suppose You Are Thinking of Lending to A Small Suppose Privately-Held (NuBeer) Brewery. You Don’t Know Too Much About it But it Needs Funds for Expansion. The Project is Estimated to Yield 12.1% After-Tax. The Firm Has $400,000 in Debt and $907,100 in Equity. The In Its Last Fiscal Year, Net Income was $146,400. NuBeer Pays Only 30% in Taxes Due to Large Depreciation Expenses. Depreciation What About Privately Held Companies ? Held Suppose The Average Firm in the Beer Industry Suppose has a 1:2 Debt to Equity Ratio, a β L = 1 .6 9 , and a 40% Tax Rate. Let Rm = and 10% and Rf = 6% 10% First, Determine What β A(IND) Should Be. β L(IND) = β A(IND) * [ 1 + (Debt/Equity) (1 - t)] 1.69 = β A(IND) * [ 1 + (1/2) (1 - 0.4)] βA = 1.3 What About Privately Held Companies ? Held Second, Recalculate β L(NuBeer) For NuBeer β L(NuBeer) = β A(IND) * [ 1 + (Debt/Equity) (1 - t)] = 1.3 * [ 1 + (400/907.1) (1 - 0.30)] = 1.70 1.3 E[RNuBeer] = Rf + (Rm - Rf) β L(NuBeer) = 6 + ( 10 - 6) ( 1.70 ) 10 = 12.8 % Summary Summary 1. Determine the Risk-Free Rate - Usually a T-Bill or T-Bond Rate 2. Determine the Market Risk Premium - Usually a Market Index Return Minus the T-Bill/Bond Yield 3. Determine Beta - Use a Comparable Company’s Beta and Adjust for Debt : Equity Differences What If We Wanted to Know More . . . ? Know ® This This Method Also Uses Comparable Companies As Proxies. Generally, We Estimate Cash Flows or Earnings (or Both !) Out to Some Point, Say 5 Yrs. And Then Use Either a P/E Multiplier or A Cash Flow Multiplier to Get A Terminal Value. Value. ® Generally, We are Assuming the Company Will Generally, Grow Faster Than the Industry Avg At First and Then Slow Down. and Allmein Inc. Allmein Comprises 2 Divisions Alloil and Allchem. It is the Comprises Industry Practice to Value Chemical Holdings Based on a P/E Multiplier (6.5-7.5) and to Value Oil Assets on the Basis of Cash Flow Multipliers ( 3-4). Assets Allmein Has 80.55MM Shares Outstanding and Allmein Spends $125MM per Year on Administrative Expenses. Expenses. If Allchem Will Earn Approx. $140MM and Alloil If Will Have $150MM In Cash Flow What is Your Estimate of the Shareholders’ Equity ? Estimate Allmein Inc. Allchem NI => $140MM, P/E 6.5 - 7.5 Allchem P/E 6.5 * (140MM/80.55MM shares) = $ 11.30 6.5 11.30 7.5 * (140MM/80.55MM shares) = $ 13.04 7.5 13.04 ® Alloil Alloil CF =>$150MM, P/CF 3 - 4 P/CF 3 * (150MM/80.55MM) = $ 5.59 4 * (150MM/80.55MM) = $ 7.45 Corp Division (125MM/80.55MM) = -$ 1.55 Corp -$ Total $ 15.34 - $ 18.94 Value of Shareholders’ Equity (times 80.55 MM shs) $ 1,235.6MM - $ 1,525.6MM 1,235.6MM ® When Good Deals When Are Bad Deals Are The WACC The Revisited (Again)! Great Lakes Resources Inc. Suppose Great Lakes Decided it Needed to Suppose Borrow $70,000,000 in Debt Instead, What Return Would the Shareholders Require ? Return β L = β A * [ 1 + (Debt/Equity) * (1 - t)] β L = 0.67 * ( 1 + (7/12)(0.7)) β L = 0.94 Ri = Rf + (Rm - Rf ) β L = 6 + (17.1 - 6) (0.94) = 16.43% Great Lakes Resources Inc. Great So, The Minimum Acceptable Rate of So, Return Becomes: Return Mkt Val Wt % % Debt $ 70 MM 0.368 7 2.58 Equity $120 MM 0.632 16.43 10.38 Total $190 MM 12.96 12.96% is the Firm’s Weighted 12.96% Average Cost of Capital (WACC) ! Average What if . . . ? What Great Lakes Wants the Additional $10MM to Great Invest at 11% (This Project Would Be of The Invest Same Risk As The Current Business But in A Slightly Different Area) Arguing That Any Slightly Time They Can Borrow at Less Than The Investment’s Return They Will Make Money Investment’s Do You Lend Them The Money ? Before the Investment Before EBIT - Interest EBT Taxes Net Income $33.4MM (From Existing Assets) $33.4MM 6.0MM ( $60MM @ 10%) $27.4MM 8.2MM ( @ 30%) $19.2MM (÷ $120MM = 16%) $120MM After the Investment After EBIT + Investment Investment - Interest Interest EBT Taxes Net Income $33.4MM $33.4MM 1.1MM 7.0MM $27.5MM 8.3MM $19.2MM (From Existing Assets) (From ( $10MM @ 11%) ( $70MM @ 10%) ( @ 30%) (÷ $120MM = 16%) $120MM Implications Implications Shareholders Did Not Receive Adequate Shareholders Compensation (Shortfall of $516,000 Compensation [0.43%*$120MM] ). [0.43%*$120MM] Importantly, This Shortfall is Not the Result of Misfortune But of Poor Managerial DecisionMisfortune Making. It Was A Negative NPV Project. Sufficient Errors of This Type Will Inevitable Lead to Insolvency. Lead Remember Remember Hi-Lo Inc. H i- L o In c . H o ld in g C o m p a n y w it h P u b lic ly Is s u e d S h a r e s L o D iv is io n T ra d e s B a n k o f C a n a d a B o n d s 1 0 0 % o w n e d b y H i- L o In c . 4 0 % o f T o t a l O p e r a t io n s After-Tax Cost-of-Funds Cost-of-Funds 14.91% 14.91% H i D iv is io n M a n u f a c t u r e s C a r B a t t e r ie s 1 0 0 % o w n e d b y H i- L o In c . 6 0 % o f T o t a l O p e r a t io n s After-Tax Cost-of-Funds 8% After-Tax Cost-of-Funds 19.52% What if . . . ? What Hi-Lo Needs $5M to Expand the Battery Hi-Lo Making Division. They Argue They Have Calculated the NPV of This Decision Based Upon the Hi-Lo’s 14.91% WACC and a 10 Year Life. Assume They Accurately Estimate Earning $1.1M (Annually) After-Tax. Do You Lend Them The Money ? Do Evaluation The Analysis Performed by Hi-Lo is: PV of Benefits: $1.1MM * PVA(10 Yrs, 14.91%) = $ 5.5MM 5.5MM Cash Outflow: 5.0MM NPV $ 0.5MM BUT . . . Is This Right ? NO ! ! NO The Required Return of The Battery The Division is 19.52% Not 14.91% . . So Division PV of Benefits: $1.1MM * PVA(10 Yrs, 19.52%) = $ 4.7MM 4.7MM Cash Outflow: NPV 5.0MM 5.0MM -$ 0.3MM This Expansion is a Loser ! ! Implications Implications If We Use the Holding Company 14.91% as the If Discount Rate to Evaluate the Two Divisions’ After-Tax Cash Flows ..... After-Tax Then, in General, We Will Accept Battery Projects We Should Really Reject, and . . . . . We Will Reject T-Bond Projects We Should Really Accept ! Accept Hi-Flyer Corp. Hi-Flyer Has A 50:50 Debt-Equity Ratio on $200MM Capitalization. The Owner Who Also Held the Outstanding Loan at 8% Has Died. Taxes are 30%, And The Return on Equity is 15% (Rf = 5%, Rm = 10% and β L = 2. The Firm’s Net Income is $15MM. 2. The New Owners Must Refinance the Loan (@11%) to Payout the Original Owner’s Estate. They Also Have A $ 25MM Opportunity Which Will Yield $4.2MM/Yr Over the Next 10 Years & Want to Borrow $12.5MM Do You Lend Them The Money ? Do Hi-Flyer Corp. Hi-Flyer Before The Refinancing the WACC is: Mkt Val Wt % Debt $100 MM 0.5 5.6 Equity $100 MM 0.5 15.0 Total $200 MM % 2.8 7.5 10.3 PV of Benefits - Cash Outflow: $4.2MM * PVA(10 Yrs, 10.3%) - $25MM = $ 0.5MM 10.3% $25MM 0.5MM Hi-Flyer Corp. Hi-Flyer After The Refinancing Mkt Val Debt $112.5MM Equity $112.5MM Total $225.0MM the WACC is: Wt % 0.5 7.7 0.5 15.0 % 3.9 7.5 11.4 11.4 PV of Benefits - Cash Outflow: $4.2MM * PVA(10 Yrs, 11.4%) - $25MM = -$ 0.7 MM 11.4% $25MM -$ Hi-Flyer Corp. (Part 2) Hi-Flyer Suppose The New Owners Also Had to Buy Out the Suppose Equity at a 15% Premium as Well as Refinance the Loan (@11%) the What is the WACC After the Purchase But Before any New Project ? Before Hi-Flyer Corp. (Part 2) Hi-Flyer The First Thing We Have to Do is ReCalculate the Expected Return to the Calculate Shareholders. Shareholders. β L = β A * [ 1 + (Debt/Equity) * (1 - t)] 2 = β A * ( 1 + (100/100)(0.7)) β A = 1.18 So, the New β L Will Be: So, β L = 1.18 * ( 1 + (100/115)(0.7)) = 1.90 Hi-Flyer Corp. (Part 2) Hi-Flyer And the new Expected Return on Equity Will And Be: Be: Ri = Rf + (Rm - Rf ) β L = 5 + (10 - 5) (1.9) = 14.5% (10 Hi-Flyer Corp. (Part 2) Hi-Flyer After The Refinancing Mkt Val Debt $100.0MM Equity $115.0MM Total $215.0MM the WACC is: Wt % 0.47 7.7 0.53 14.5 % 3.6 7.7 11.3 So, The Minimum Acceptable After-Tax Rate So, of Return on Assets is 11.3% ? of Hi-Flyer Corp. (Part 2) Hi-Flyer The Assets Must Be Equal to $ 215MM and They The Should Earn $ 215MM * 11.3% = 24.3MM After-Tax ! BUT ! ! $ 15MM is Goodwill Arising From the Purchase and is NOT (Necessarily) a Producing Asset. So, the is NOT (Necessarily) So, Producing Assets Must Earn 24.3/200 = 12.15% Producing ...
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