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Date Created: 11/01/15
Example IV computing WACC Big Oil has the following sources of financing A bank loan of 200 mn interest 7 12year 8 per year coupon paid annually bonds of face value 200 mn Assume current interest rate is 9 YTM 100 mn shares of par value 1 trading at a current price of 12 share Retained earnings of 300 mn What s WACC of Big Oil Assume 3085 for firm s stock riskfree rate of 6 market premium of 9 and tax rate of 35 Answer Key MV of bank loans 200 mn MV of bonds 12 coupon payments of 8200 mn 16 mn and face value of 200 mn rYTM 9 so PV of bonds CFs 18568 ie MV of bonds 18568 mn MV of equity 100mn12 1200 mn NOTE Retained earnings are included in the market value of equity so you should not include them segarately again Answer Key continued rd9 YTM on bonds 7 interest paid on bank loans Using CAPM re608591365 MV WeightageMVlTota required return Bank debt 20000 0126 7 Longterm bonds 18568 0117 9 Total debt 38568 Equity 120000 0757 1365 Firm value 158568 WACC 012671035 01179103507571365 So WACC116 F305 Intermediate Corporate Finance Practice Problems WACC Questions You will nd the answers on the next page 1 Given the following information for Huntington Power Co nd the WACC Assume that the company s tax rate is 35 o The company has 4000 bonds outstanding The bonds are 7coupon bonds semiannual with 20 years remaining maturity They are currently selling at 103 ofthe face value which is 1000 There are 90000 shares of common stock outstanding selling for 57 share The equity beta is 11 O The company also has 13000 preferred shares outstanding The face value of preferred shares is 100 they pay a dividend of 6 per year in perpetuity and are currently trading at 104 share 0 0 Assume that the riskfree rate is 6 and the market risk premium is 8 2 Titan Mining Corporation has the following securities outstanding 9 million shares of common stock 05 million shares of 7 per year preferred stock and 120000 85 coupon bonds with semiannual coupon payments The common stock currently sells for 34 per share and has a beta of 120 The preferred stock currently sells for 83 per share The bonds have 15 years to maturity and sell at 93 of face value The market risk premium is 10 Tbills are yielding 5 and Titan s taX rate is 35 a What is the rm s market value capital structure b If Titan is evaluating a new investment project that has the same risk as the rm s typical project what rate would you use to discount its cash ows Answers 1 N Let s rst compute the costs of debt equity and preferred stock 0 Cost of debt Rd This should equal the YTM on the bonds It is given that bond price 103 offace value 1030 Therefore the YTM 6725 set PV1030 PMT35 N40 Pyr2 and compute Iyr So Rd 6725 Using CAPM Re 6 118 148 o For preferred stock Rp dividend price 6100104 5769 0 Next let s compute the MVs ofall securities 0 MV of debt D 4000 bonds 1030 bond 4120000 0 MV of equity E 90000 shares 57 share 5130000 0 MV ofpreferred stock P 13000104 1352000 0 Total value V DEP 10602000 Therefore WACC 4120 X 6725 X l 035 5130 X 148 1352 X 5769 10602 10602 10602 9596 Let s first compute the costs of debt equity and preferred stock 0 Cost of debt Rd This should equal the YTM on the bonds It is given that bond price 93 offace value 930 Therefore the YTM 9379 set PV930 PMT 425 N 30 Pyr2 and compute Iyr So Rd 9379 Using CAPM Re 5 1210 17 For preferred stock Rp dividend price 710083 8434 00 Next let s compute the MVs ofall securities 0 MV of debt D 120000 bonds 930 bond 111600000 0 MV of equity E 9000000 shares 34 share 306000000 0 MV ofpreferred stock P 50000083 41500000 0 Total value V DEP 459100000 a The market value capital structure of the rm is as follows 0 111600459100 2431 debt 0 306000459100 6665 equity 0 41500459100 904 preferred stock b WACC can be computed as under 111600 459100 13575 gtlt 9379 X 1 035 36 000 X17 w WACC 7 9100 459100 X 8434 Capital Structure ModiglianiMiller Propositions Class 22 F305 Intermediate Corporate Finance Professor Jun Yang Outline More on cost of capital and capital structure Given an existing capital structure what is WACC Variations in cost of capital Does capital structure matter If capital structure changes what happens to WACC The concept of perfect markets APV approach Relaxing first assumption of perfect markets corporate tax Introducing unlevered beta Required reading RWJordan Chapter 15 From Last Class WACC An average of the rate of return on a portfolio of all the firm39s secun es WACC measures what aftertax returns a firm s investors Mg expect How to use WACC Calculate the corresponding free cash flows Discount these free cash flows using the WACC Where should we use WACC Value an investmentproject a firm s division and entire firms Eg in a takeover situation or to compare your valuation with that of the financial markets say for your share repurchase decisions Make capital budgeting decisions using the NPV approach As a hurdle rate for line managers eg to determine whether they get a bonus or not irom last class 3 steps in calculating WACC Suppose a capital structure is given Individual rate of returns Calculate the required return on each security in the firm s financing mix The weight Calculate the market value of each security as a proportion of the firm39s value The sum of all weights must be 1 Take the weighted average Calculate a weighted average of the required returns What is a firm s capital structure Definition The mix of financial securities or financial claims with which a firm funds itself Financial securities are claims on future cash flows They may also give the holder of the security various ownership or control rights Commonly seen financial securities 7 E lk39 Debt Common stock Preferred stock m ll 39 Convertible securities warrants convertible debt convertible preferred WEE u39imu Bait QIQEH SEE Does Capital Structure Matter In a world with perfect and complete capital markets the value of a levered firm is the SAME AS the value of an unlevered firm MM Capital Structure is a part of a much larger value creating equation At Sears as in most companies creating shareholder value is the main governing objective There is considerable effort aimed at achieving the lowest longterm cost of capital by managing the capital structure That leads to a discussion in which we determine ourtarget capital structure I can tell you we have dug seriously into the capital structure question Alice Peterson VicePresident and Treasurer of Sears Motivation Main questions that we will address Does capital structure affect firm value ie the combined value of all of firm s securities If so how do we determine the optimal capital structure that maximizes firm value Outline of chapter Capital structure in a perfect market Modigliani Miller propositions on irrelevancy of leverage Capital structure with imperfections Text reference RWampJaffe Chapter 15 16 Modigliani amp Miller Propositions MampM propositions tell us how capital structure matters in a perfect world once we understand these we can better understand how amp why imperfections matter Some trivia Most if not all of corporate finance theory came from MM propositions Franco Modigliani and Merton Miller were both awarded the Nobel prize separately at least in part for their work on capital structure Perfect amp complete capital market Perfect capital market is one in which there are no taxes is no default ie bankruptcy risk are no agency problems ie no conflict of interest between managers shareholders and debtholders is no asymmetric information ie investors know as much as managers do Individuals have as much access to cheap debt as corporations MM Debt Irrelevance Proposition In a world with perfect and complete capital markets the value of a levered firm is the SAME AS the value of an unlevered firm Note 1 By value of firm we mean the combined value of all securities that the firm has issued Note 2 Levered firm is a firm with debt ie with Ieverage unlevered firm is a firm without debt Numerical Example I Dyson s is a chain of gourmet food stores in a world where MampM s assumptions hold Dyson s is considering issuing 50 million of debt and using the proceeds to repurchase equity The firm s current capital structure and projected cash flows every year forever are as follows Before Restructuring shares millions 2 priceshare 50 market value of equity millions 100 market value of debt millions 0 State of Economy Slump Normal Boom Probability 20 60 20 Net cash flow millions 4 12 20 Debt cash flow millions 0 0 0 Equity cash flow millions 4 12 20 Cash flowshare 200 600 1000 Return on equity 4 12 20 The expected return on Dyson s equity is l 2TQ 42 l 60 1239f 4 392 Q 22quot039 12 I Numerical Example ll s mentioned Dyson s is considerin issuing 50 million of debt at an interest rate of 8 and buying back 1 million shares at 50share If Dyson s goes through with the debt issue and stock repurchase its capital structure and cash flows would be After Restructuring Shares millions 1 priceshare 50 market value of equity millions 50 market value of debt 33 millions 50 State of Economy Slump Normal Boom Probability 20 60 20 Net cash flow millions 4 12 20 Debt cash flow millions Equity cash flow mm Cash flowshare Return on equity The expected average return on Dyson s stock is now How has the expected return on equity changed How has the risk of equity changed Homemade Leverage Ill If Dyson s does NOT restructure an investor can do it herself Say the investor owns one share already She can buy a second share b borrowing 50 riskfree at an interest rate of 8 Her return is as follows Slump Probability 20 Net cash ow 55 millions 4 Debt cash ow 55 millions 0 Equity cash ow 55 millions 4 Cash owshare 200 Earnings on 2 shares 400 Less interest 8 on 50 400 Net earnings on investment 000 Return on 50 investment 0 Nor ml 60 12 0 12 600 1200 400 800 16 Boom 20 20 0 20 1000 2000 400 1600 32 Old calculations New calculations If Dyson s does not restructure investors can lever up on their own accounts to replicate the cash flows and returns that the restructuring would create The intuition behind Cash flows generated by the firm s operations do not change with its capital structure As a group holders of the firm s debt and equity own all these cash flows The overall risk and return of the firm s investors as a group do not change with the firm s capital structure The firm s cashflow pie is the same no matter how it s sliced Although the risk and return of debt and equity slices do change with capital structure investors can get the same slices riskreturn combinations on their own by adjusting their own portfolios What do we learn from the example Using homemade leverage investors can replicate returns on levered equity One crucial assumption is that investors can borrow at same rate as corporations In other words they get the same return by Investing in levered eguity and Borrowing and investing in unlevered eguity Therefore firm s choice of capital structure cannot create value for investors But how can that be Earlier we saw that if TO WACC de xRe DE DE Since ROI lt Re if you increase D and lower E shouldn t WACC decrease MM Proposition ll 1 NO because as we saw leverage increases risk to shareholders More volatile returns Debt increase EPSROE in good times ie shareholders can leverage debt to improve their returns however in bad times debt hurts In a world with perfect and complete capital markets the required return to eduitvholders ie Re increases with leverage As show on the next slide this follows from MM Proposition 1 which suggests that WACC does not change with leverage Understanding MM Proposition 2 Cost of equity Re Let Ru denote the WACC for an allequity firm ie an unlevered firm As per MM Proposition I WACC doesn t change with capital structure ie WACC RuI always Substituting Ru for WACC and rearranging equation we obtain D Re RuEXRuRd Understanding MM Proposition ll 3 Why doesn t WACC change in the MM world Rememberthe crucial assumption In the MM world there is no risk of bankruptcv As a result Rd doesn t change with leverage So as leverage increases Rd is unchanged Re increases but EV decreases Overall WACC is unchanged Note If risk of bankruptcy exists then Rd will also increase with the firm s leverage Why As a result WACC will increase We will study this in next class Cost of equity Re Understanding MM Proposition ll 4 The equation for R6 on the earlier slide implies that the cost of equity depends on the following factors Business risk or the risk arising from the nature of the firm s operating activities lt determines the firm s Ru adjustment for financial risk or the risk arising from debt in the financial structure This is the term DEgtltRu Rd Business amp financial risk in terms of Bs With no taxes u x d x e and36 u u we where Bu is the asset B unlevered B that reflects only the business risk of the firm s assets Note that 3 is unobserved Be measures risk of levered equity and 3d reflects the risk of firm s debt Leverage and 3 Since Be depends on financial risk changes in the firm s capital structure impact Be How do we compute the new Be after a change in capital structure Step 1 Unlever the 3 asset 3 Compute 3u implied by original capital structure Step 2 Relever the 3 Use the 3u from step 1 to compute the new Be Examplel A firm recently overhauled its capital structure by replacing debt with equity Before the overhaul it had 20 equity and 80 debt in its capital structure lts equity beta was 18 and its debt beta was 06 Afterthe overhaul it has 50 equity and 50 debt in its capital structure Assume zero taxes Questions What is the firm s equity beta after the change What will the firm s equity beta be if it gets rid of all its debt Answer Key to Example First compute Bu As per MM propositions in a perfect world Bu doesn t change with capital structure So we can use old capital structure to compute Bu 0 Bu So Be after change 3 DE X Bu Bd If firm gets rid of all debt Be Example ll Assume perfect world A firm has a DV ratio of 04 a cost of equity of 128 and a cost of debt of 4 Risk free rate is 4 and the market risk premium is 8 Suppose the firm s DV ratio rises to 06 firm is raising debt to repurchase stock What are the firm s old and new equity betas What is the firm s new cost of equity What are the old and new WACCs i Answer Key to Example Summary In the perfect world of MM capital structure is irrelevant ie it doesn t impact firm value Cost of debt doesn t change with leverage mainly because there is no risk of bankruptcy Cost of equity increases with leverage but WACC doesn t change because increase in cost of equity is offset by decrease in the weight attached to equity capital New concepts in this class homemade leverage distinction between levered and unlevered firms cost of equity and B
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