Cost of Capital and Project Valuation


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1 Cost of Capital and Project Valuation 1 Background Firm organization There are four types: sole proprietorships partnerships limited liability companies corporations Each organizational form has different legal and tax implications. In this handout, we focus only on the corporation. Corporate ownership Corporations have many owners; each owner owns only a fraction of the corporation. The ownership stake is divided into shares known as stock. The collection of all outstanding shares of stock is referred to as the equity of the corporation. An owner of a share of stock is called a shareholder, stockholder or equityholder. Shareholders are entitled to dividend payments. Dividend payments are made at the discretion of the corporation to its equityholders. The dividend share to each stockholder is typically in proportion to their ownership stake. Ownership is distinct from control. 1
2 Stock market A public company is one whose shares trade on a stock market or stock exchange. In the US, three national stock exchanges are the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX) and the National Association of Security Dealers Automated Quotation (NASDAQ). Stock markets provide two useful features: They determine a market price for a company s shares. They provide liquidity. A stockholder can quickly sell a portion of his/her ownership stake and for a price very close to the price at which someone else can buy it. (The difference is called the bidask spread.) Corporate financing Corporations raise funds in two ways: Raise new equity by issuing new shares of stock and selling them to investors. The shares are sold on the primary market. Shares continue to trade in a secondary market between investors without involvement of the firm. Borrow funds from banks or by issuing debt (corporate bonds) via the financial markets. A firm s capital structure refers to its relative proportions of equity and debt. A firm with no debt is said to be unlevered. Its equity is referred to as unlevered. A firm with debt is said to be levered. Its equity is referred to as levered. 2
3 2 Valuation Definitions Firm value Defined to be the sum of its market value of equity and its market value of debt: V L := D + E. (1) Debt is net of any cash and shortterm investments and is referred to as net debt. V L represents the amount needed to acquire a firm to buy out the firm s shareholders and to pay off the firm s bondholders. An unlevered firm s value is denoted by the symbol V U. Here, V U = E as D = 0. Can be estimated as V L = Present Value (expected Free Cash Flows r W ACC (2) r W ACC = the firm s weighted average cost of capital (3) Free Cash Flow is the cash generated from a firm s business operations. It is the cash flow generated if the firm were unlevered. Equity value Can be estimated as E = Present Value (expected Free Cash Flows to Equity r E (4) r E = the firm s equity cost of capital (5) The equity cost of capital r E represents the riskadjusted required rate of return demanded by shareholders. For an unlevered firm, r E is denoted by r U, the firm s unlevered or asset cost of capital. For public companies, it equals the company s Market Capitalization (Market Cap). Market Cap is the product of the firm s share price and the number of the firm s outstanding shares of stock. 3
4 Debt value Can be estimated as (excluding the cash and shortterm investments) D = Present Value (expected Cash Flows to r D (6) r D = the firm s debt cost of capital (7) The debt cost of capital r D represents the riskadjusted required rate of return demanded by bondholders. Corporate debt Not risk free defaults can happen. If so, a portion of the debt is repaid. Agencies like Moody s and S&P rate corporate debt. Ratings indicate their assessment of the likelihood of default. Due to the possibility of default a bond s yield to maturity (IRR) does not equal its expected rate of return. Many types of corporate debt. Difficult to determine market value. Standard practice is to use the book value of debt. 4
5 3 Analysis of an Unlevered Firm Market and firm data: Market data: Riskfree rate r f = 2% Market premium R M r F = 5% ABC, Inc. data: Expected EBIT (Earnings Before Interest and Taxes) = 2,000 in perpetuity Capital Expenditures (CapExp) = Depreciation (Dep) each year Net Working Capital (NWC) = 0 Corporate tax rate = 40% Equity beta = 1.2 Number of outstanding shares = 1,000 5
6 Analysis: 1. What is the cash flow to shareholders or Free Cash Flow to Equity (FCFE)? Profit before tax = 2,000 Tax = 0.40(2,000) = 800 Net income = 2, = 1,200 FCFE = Net income + Dep  CapExp + Increase in NWC = 1,200 ABC Inc. generates a cash flow to shareholders of 1,200 in perpetuity. Since there is no debt the FCFE equals the FCF. 2. What is the ABC Inc. s unlevered cost of capital? We use the Security Market Line (SML): 3. What is ABC, Inc. s market value? r U = r f + β( R M r f ) = (5) = 8%. (8) V U = E = Present Value (FCFE cash r U = 4. What is ABC, Inc. s share price? 1, = 15, 000. (9) Total firm value is 15,000. There are 1,000 shares, so each share is worth 15,000/1,000 = $15. 6
7 4 A Leverage Recapitalization ABC, Inc. is an unlevered firm. Suppose it decides to change its capital structure by taking on some debt. It announces it will undertake a leverage recapitalization. It will: Issue 7,500 of debt. The interest rate is 6%. The debt will be perpetual: Interest is repaid each year. No repayment of principal. Use proceeds to buy back shares of stock. 7
8 Cash flow analysis: 1. What is the new cash flow to shareholders or FCFE? Interest expense = 0.06(7,500) = 450 Profit before tax = 2, = 1,550 Tax = 0.40(1,550) = 620 Net income = 1, = 930 FCFE = Net income + Dep  CapExp + Increase in NWC = 930 ABC Inc. generates a cash flow to shareholders of 930 in perpetuity. 2. What is the cash flow to bondholders? Interest expense = What is the total cash flow or new Free Cash Flow (FCF) generated? FCF = = 1, How does this new FCF compare to the FCF when there was no debt? The old FCF = FCFE = 1,200 since there was no debt. The cash flow has increased by 1,3801,200 = Why did the FCF increase? Look at the taxes. Before debt, the firm paid 800; after the debt issue, the firm will pay only 620. Difference is 180. This is the interest tax shield. Notice that 180 = T C r D D = (0.40)(0.06)(7, 500). (10) 8
9 Market value analysis: 6. What is the market value of the interest tax shield? What is the value to the firm for generating an extra 180 in perpetuity? It depends on the choice of discount rate. One acceptable choice is the firm s unlevered cost of equity capital, 8%. With this choice the answer is 180/0.08 = 2,250. Notice that 7. What is the new value for ABC, Inc.? 2, 250 = T Cr D D r U. (11) When the announcement is made the market prices in the value of the interest tax shield. So, the new value is 15, ,250 = 17,250. Notice that 17, 250 = V L = V U + T Cr D D r U = 15, , 250. (12) 8. What is the market value of debt? Debt issue = 7,500. This is the market value of debt, D. 9. What is the new value of equity? V L = 17, 250 = D + E = 7, E = E = 9, What is the new share price? There are still 1,000 shares after the announcement but before the buyback. The new share price = 17,250/1,000 = $ How many shares will be repurchased and how many shares will be left? The total amount of the purchase is 7,500. At $17.25/share, 7, 500/17.25 = 435 shares will be repurchased. This leaves 1, = 565 shares. Note that at $17.25/share, E = 565(17.25) = 9, 750, which is the same answer as before. 9
10 Cost of capital analysis: 12. What is the new weighted average cost of capital? Firm value equals the present value of the FCF cash flow stream discounted at r W ACC. So, V L 1, 200 1, 200 = 17, 250 = = r W ACC = = 6.96%. (13) r W ACC 17, What is new levered cost of capital? Equity value equals the present value of the FCFE cash flow stream discounted at r E. So, It can be shown that in this setting E = 9, 750 = 930 = r E = 930 = 9.54%. (14) r E 9, 750 r E = r U + (r U r D ) D E (15) = 7, (8 6) = 9.54%. 9, 750 (16) 10
11 5 Cost of Levered Equity Capital ABC, Inc. s cost of unlevered equity is 8%. After leverage, however, the cost of levered equity increased to 8.86%. Since the equity cash flows are now riskier, equityholders should demand a higher expected rate of return to compensate for this risk. To drive home this point, we consider the following simple stylized example in which there is only one period and there are no corporate taxes. Before leverage: Market value of the firm is 1,000. At the end of the period the firm s free cash flow will either be 1,400 if the market is good, or 900 if the market is bad. Each market state is equally likely. The return on unlevered equity is 40% if the market is good, or 10% if the market is bad. The expected return on unlevered equity is 0.5(40) + 0.5( 10) = 15%. 11
12 After leverage: Firm issues debt of 5%. With no taxes there is no interest tax shield. Firm value remains at 1,000. E = 500 since V L = 1, 000 = D + E = E. At the end of the period, the shareholders have to pay back the principal plus interest = (1.05)500 = 525. At the end of the period, the cash flow to the shareholders or Free Cash Flow to Equity (FCFE) will either be 1, = 875 if the market is good, or = 375 if the market is bad. The return on levered equity is 875/5001 = 75% if the market is good, or 375/5001 = 25% if the market is bad. The expected return on the levered equity is 0.5(75) + 0.5( 25) = 25%. Due to leverage, the return distribution is more skewed (risky). Investors demand a higher riskadjusted rate of return to compensate. The levered cost of equity capital is now 25%. Conclusion: Taking on debt does, in fact, increase the expected return on equity. But this is as it should be: the equity is now riskier. That is, the increase is not for free. 12
13 6 Weighted Average Cost of Capital Formula The market value of a levered firm or project is the present value of a firm s free cash flow discounted at the r W ACC. This is very useful as it allows a project manager to focus on forecasting the project s cash flows, letting the Chief Financial Officer (CFO) worry about how the firm will finance the project. It can be shown that the weighted average cost of capital is given by this formula: Observations: r W ACC := ( ) E r E + D + E ( ) D [(1 T C )r D ]. (17) D + E r E denotes the firm s cost of equity capital given the firm s leverage or capital structure. Do not use the firm s unlevered cost of equity capital, r U, in this formula. If the firm is unlevered, then D = 0, and so r W ACC = r U. Alternate formula: It can be shown that in this setting r W ACC = r U T C r D (D/V L ). (18) To use this formula you must use the unlevered cost of equity capital. Note that r U = r W ACC when T C = 0. 13
14 Example 1 XYZ, Inc. has 5 million shares outstanding at $10 per share. The market value of its debt is $25 million. The cost of equity capital (given the riskiness of the company s cash flow) is 12%. Its cost of debt is 7.5%. The company s tax rate is 40%. Given this data: Market value of the firm s equity is 5($10) = $50 million. Aftertax cost of debt is (1 0.4)(7.5) = 4.5%. The company s weighted average cost of capital is r W ACC = ( ) 50 12% ( ) % = 9.5%. (19) The company s cost of unlevered equity capital can be obtained from the formula r E = r U + (r U r D )( D E ) (20) 12 = r U + (r U 7.5)( ) (21) = 1.5r U 3.75 = r U = 10.5%. (22) The company s weighted average cost of capital can also be computed as r W ACC = r U T C r D (D/V L )) (23) = (7.5)(25/75) = 9.5%. (24) Alert! To use this formula for r W ACC you have to use the unlevered cost of equity capital. If the company is levered, you will obtain the levered cost of equity capital. From this quantity, you must unlever it to obtain r U. 14
15 Example 2 Let s return to ABC, Inc. s leverage recapitalization. Recall that V L = 17, 250 D = 7, 500 E = 9, 750 r D = 6% T C = 40% r E = 9.54% The new weighted average cost of capital is r W ACC = ( ) 9, % + 17, 250 ( ) 7, 500 [(1 0.40)6%] = 6.96%. (25) 17, 250 This matches our earlier calculation using the market definition of r W ACC. Alert! When calculating r W ACC under leverage you must use the new levered cost of equity capital. A common mistake is to use the unlevered cost of equity capital in the formula, as in: ( ) ( ) 9, 750 7, 500 r W ACC = 8% + [(1 0.40)6%] = 6.09%. (26) 17, , 250 Of course, 6.09% 6.96%. Given an unlevered cost of equity capital, the weighted average cost of capital can also be computed as r W ACC = r U T C r D (D/V L ) (27) = (6)(7, 500/17, 250) = 6.96%. (28) 15
16 7 Estimating the Weighed Average Cost of Capital We illustrate one approach to estimating r W ACC. The example firm is The Home Depot, Inc. Data was obtained from Yahoo! Finance on October 10, Data: Key Statistics page. Market Cap = E = 54.22B. beta = Balance Sheet Quarterly Data page. Short/Current Long Term Debt + Long Term Debt = 0.044B B = B (July 31, 2011). Cash and Cash Equivalents = 2.551B (July 31, 2011). Short/Current Long Term Debt + Long Term Debt = 0.043B B = B (May 1, 2011). Income Statement Quarterly Data page. Income Before Tax = 2.148B (July 31, 2011). Income Tax Expense = 0.785B (July 31, 2011). Interest Expense = 0.149B (July 31, 2011). Bonds Center page. US Treasury 2yr bond rate yield = 0.30%. US Treasury 5yr bond rate yield = 1.16%. US Treasury 10yr bond rate yield = 2.21%. US Treasury 30yr bond rate yield = 3.19%. Assumptions: Market risk premium = 5.1%. Reference: Market Risk Premium used in 2010 by Analysts and Companies: a survey with 2,400 answers. P. Fernandez and J. del Campo. Working paper, May Riskfree rate = 2.21%. 16
17 Calculations: E = 54.22B. D = 10.78B 2.55B = 8.23B. This is the net debt. r E = (5.1) = 6.39%. Average debt over the current quarter = (10.775B B)/2 = B. For the current quarter, r D = 0.149B/10.769B = %. Annual debt cost of capital r D = ( ) 4 1 = 5.65%. T C = 0.785B/2.148B = 36.5%. Aftertax cost of debt = ( )(5.65) = 3.64%. An estimate of the weighted average cost of capital is ( ) ( 54.22B r W ACC = B B 8.23B 54.22B B ) 3.64 = 6.03%. (29) Remarks: Estimating beta is a nontrivial exercise. Several companies provide estimates (e.g. Bloomberg, Value Line, S&P). Highest quality corporate bond rates are sometimes used in lieu of treasury rates. Estimate of the cost of debt capital here uses the observed interest expense. Expected return on corporate debt is lower due to the possibility of default. An alternative approach is to estimate a firm s debt beta and then use the SML. Estimate of corporate tax here uses the effective tax rate. An alternative approach is to use the marginal tax rate. In principle, estimates should be forward looking. 17
18 8 Estimating Project Cost of Capital Example 3 A firm is considering investing in a constructionrelated business whose business risk is similar to that of The Home Depot, Inc. The firm s equity is valued at 30M and its debt is valued at 20M. Its debt cost of capital is 6% and its corporate tax rate is 30%. What is a good estimate of a weighted average cost of capital to be used for valuation of projects within this business? Home Depot, Inc. s r W ACC = 6.03%. Calculate The Home Depot, Inc. s r U from its r W ACC : r W ACC = 6.03% (30) = r U T C r D (D/V L ) (31) = r U 0.365(5.65)(8.23/62.45) = r U = 6.30%. (32) Calculate the firm s r W ACC from r U : r W ACC = (6)(20/50)) = 5.58%. (33) 18
19 Example 4 Let s go back to midyear A firm has decided to start a new division that will specialize in general retail goods such as can be found in large department stores. It wishes to estimate a suitable weighted average cost of capital it can use to valuing projects within this division. Data and Assumptions: Security Market Line will be used to estimate the cost of equity and debt. A market premium of 5.1% and a riskfree rate of 2.21% will be used. Firm s tax rate is 36%. Firm s target debttovalue ratio D/V L = Firm s debt is rated BBB. Data from seven department stores has been collected see Tables?? and??. Table 1: Data for US Department Stores, mid Reference: Example 12.7, p. 394 in Corporate Finance by Berk and DeMarzo. Company Ticker Equity Beta D/V Debt Rating Dillard s DDS B J.C. Penney Company JCP BB Kohl s KSS BBB Macy s M BB Nordstrom JWN BBB Saks SKS CCC Sears Holding SHLD BB Table 2: Average Debt Betas by Rating and Maturity. Reference: Table 12.3, p. 389 in Corporate Finance by Berk and DeMarzo. By Rating A and above BBB BB B CCC Avg. Beta < By Maturity (BBB and above) 15 year 510 year year > 15 year Avg. Beta
20 Analysis: Table?? shows the analysis. Corporate tax rates were obtained from the 2010 annual reports. The cost of unlevered equity in the last column can be inferred from the weighted average cost of capital or the equity cost of capital: r W ACC = r U T C r D (D/V L ) or r E = r U + (r E r U )(D/E). (34) Calculating r U from r E does not require knowledge of each company s corporate tax rate. r D = (5.1) = 2.72%. r W ACC = (2.72)(0.40)) = 7.75%. Table 3: Cost of Capital for US Department Stores, mid Company r E r D D/V L T C r W ACC r U Dillard s 14.35% 3.54% % 7.97% J.C. Penney Company 10.37% 3.08% % 9.13% Kohl s 9.20% 2.72% % 8.68% Macy s 13.23% 3.08% % 6.93% Nordstrom 12.10% 2.72% % 8.82% Saks 11.65% 3.79% % 7.72% Sears Holding 9.15% 3.08% % 7.75% Average 8.14% Remark: Define a firm s asset beta as β U = E V L β E + D V L β D. (35) It can be shown that in this setting r U = r f + β U ( R M r f ). (36) To obtain an average unlevered cost of capital, r avg U, proceed, as follows: Calculate the asset beta for each department store, β i U. Take the average of these asset betas to obtain β avg U. Use this average beta in the Security Market Line to obtain r avg U. You will obtain the same answer as above! 20
21 Example 5 Let s revisit the previous example with current data see Table??. Analysis is shown in Table??. Table 4: Data for US Department Stores, Oct Company Ticker Equity Beta D/V L Debt Rating Dillard s DDS BB J.C. Penney Company JCP BB+ Kohl s KSS BBB+ Macy s M BBB Nordstrom JWN A Saks SKS BB Sears Holding SHLD B+ Table 5: Cost of Capital for US Department Stores, Oct Company r E r D D/V L T C r W ACC r U Dillard s 16.08% 3.08% % 13.09% J.C. Penney Company 12.10% 3.08% % 10.39% Kohl s 6.49% 2.72% % 5.89% Macy s 11.34% 2.72% % 8.67% Nordstrom 11.54% 2.47% % 10.27% Saks 16.29% 3.08% % 14.70% Sears Holding 12.00% 3.54% % 9.55% Average 10.37% New r W ACC = (2.72)(0.40)) = 9.97%. 21
22 9 Project Valuation The Weighted Average Cost of Capital (WACC) method: Most common approach. Estimate the project s free cash flows. (Ignore financing.) Estimate the project s r W ACC : Find comparable firm s whose business risk is similar. Estimate the unlevered cost of equity capital, r U. Calculate r W ACC from r U using a target or estimated D/V L ratio. Use firm s r W ACC if project risk is similar to firm s overall risk. Not an exact science! Estimate project value by discounting free cash r W ACC. Perform sensitivity analysis! The Adjusted Present Value (APV) method: Most useful when Firm does not maintain a constant D/V L ratio. When debt is tied to project (e.g. real estate). It has been argued that a firm s or project s levered value is V L = V U + P V (interest tax shield). (37) Estimate the project s free cash flows. (Ignore financing.) Estimate the project s r U : Find comparable firm s whose business risk is similar. Not an exact science! Estimate project s unlevered value V U by discounting free cash r U. Estimate PV(interest tax shield) using unlevered cost of equity capital. Estimate project value by adding PV(interest tax shield) to V U. Perform sensitivity analysis! 22
23 10 Remarks Costs of leverage. Benefit of debt is the value of the interest tax shield. But there are costs to financing. Banks that provide the loan or underwrite the sale of the securities charge fees. Higher debt levels increase the likelihood of financial distress, which can lower the free cash flow of the firm. Potential loss of customers, suppliers, employees. Fire sales of assets to generate cash. Loss of receivables. Personal taxes were ignored. This effect will lower the benefits of the interest tax shield. For these reasons some argue the costs offset the benefits. Firms do issue debt. It is typically easier to raise capital via debt than equity. Interest tax shield valuation. Most debt is not perpetual. One can still calculate the PV(interest tax shield). If the company issues permanent debt, then the debt cost of capital is an appropriate discount rate to value the interest tax shield. Assuming perpetual debt, using r D to discount the interest tax shield cash flow stream will generate somewhat different formulae, as follows: Hurdle rates. V L = V U + T C D (38) r E = r U + (r U r D )(1 T C )(D/E) (39) ) r W ACC = r U (1 T C (D/V L ) (40) ( ) ( ) E D = r E + [(1 T C )r D ] as before (41) D + E D + E A firm s target rateofreturn Higher than the theoretical riskadjusted rate of return (cost of capital). Applicable in capital budgeting: Capital constraints impose limitations on funds. Implicitly values option to invest in future possibly more profitable projects. 23
24 11 Key Formulae V L = V U + T Cr D D r U. r E = r U + (r U r D )(D/E). ( ) ( ) r W ACC = E D+E r E + D D+E [(1 T C )r D ]. r W ACC = r U T C r D (D/V L )). r i = r f + β i ( R M r f ), i = E, U and D. 24
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