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 equity- holders. ∗ The dividend share to each stockholder is typically in proportion to their own- ership stake. { Ownership is distinct from control. 1 • 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 bid-ask 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 in- volvement 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 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 short-term investments and is referred to as net debt. { V L represents the amount needed to acquire a firm | to buy out the firm’s share- holders 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 L V = Present Value (expected Free Cash Flows (FCF)) @ rW ACC (2) rW 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 (FCFE)) @ rE (4) rE = the firm's equity cost of capital (5) The equity cost of capital rE represents the risk-adjusted required rate of return demanded by shareholders. { For an unlevered firm, rE is denoted by rU , 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 • Debt value { Can be estimated as (excluding the cash and short-term investments) D = Present Value (expected Cash Flows to Bondholders) @ rD (6) rD = the firm's debt cost of capital (7) The debt cost of capital rD represents the risk-adjusted required rate of return de- manded 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 3 Analysis of an Unlevered Firm Market and firm data: Market data: • Risk-free rate rf = 2% • Market premium R¯M − rF = 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 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 = 2,000 - 800 = 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): rU = rf + β(R¯M − rf ) = 2 + 1:2(5) = 8%: (8) 3. What is ABC, Inc.'s market value? 1; 200 V U = E = Present Value (FCFE cash flows) @ r = = 15; 000: (9) U 0:08 4. What is ABC, Inc.'s share price? Total firm value is 15,000. There are 1,000 shares, so each share is worth 15,000/1,000 = $15. 6 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 Cash flow analysis: 1. What is the new cash flow to shareholders or FCFE? • Interest expense = 0.06(7,500) = 450 • Profit before tax = 2,000 - 450 = 1,550 • Tax = 0.40(1,550) = 620 • Net income = 1,550 - 620 = 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 = 450. 3. What is the total cash flow or new Free Cash Flow (FCF) generated? FCF = 930 + 450 = 1,380. 4. 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 1,380 - 1,200 = 180. 5. 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 = TC rDD = (0:40)(0:06)(7; 500): (10) 8 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 cost of debt capital, 6%. With this choice the answer is 180/0.06 = 3,000. Notice that TC rDD 3; 000 = = TC D = (0:40)(7; 500): (11) rD 7. What is the new value for ABC, Inc.? When the announcement is made the market prices in the value of the interest tax shield. So, the new value is 15,000 + 3,000 = 18,000. Notice that L U 18; 000 = V = V + TC D = 15; 000 + 3; 000: (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 = 18; 000 = D + E = 7; 500 + E =) E = 10; 500. 10. What is the new share price? There are still 1,000 shares after the announcement but before the buyback. The new share price = 18,000/1,000 = $18. 11. How many shares will be repurchased and how many shares will be left? The total amount of the purchase is 7,500. At $18/share, 7; 500=18 = 416:6¯ shares will be repurchased. This leaves 1; 000 − 416:6¯ = 583:3¯ shares. Note that at $18/share, E = 583:3(18)¯ = 10; 500, which is the same answer as before. 9 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 rW ACC . So, L 1; 200 1; 200 V = 18; 000 = =) rW ACC = = 6:6%¯ : (13) rW ACC 18; 000 13. What is new levered cost of capital? Equity value equals the present value of the FCFE cash flow stream discounted at rE. So, 930 930 E = 10; 500 = =) rE = = 8:86%: (14) rE 10; 500 It can be shown that in this setting D r = r + (r − r )(1 − T ) (15) E U U D C E 7; 500 = 8 + (8 − 6)(1 − 0:40) = 8:86%: (16) 10; 500 10 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.