Financial Planning and Control Semester: 1/2559
Krisada Khruachalee Master of Science in Applied Statistics, Master of Science in Finance, Bachelor of Business Administration (Cum Laude), Finance and Banking Recommended Text Books Pamela P. Peterson and Frank J. Fabozzi, Capital Budgeting: Theory and Practice. Wiley & Sons, Inc. Aswath Damodaran., Investment Valuation. 2 nd Edition. Wiley & Sons, Inc. New York.
Course Overview Cost of Capital Weighted Average Cost of Capital (WACC) Cost of Debt Cost of Prefer Stock Cost of Common Stock Levering and Unlevering Beta Capital Budgeting Net Present Value (NPV) Internal Rate of Return (IRR) Payback Period Discounted Payback Period Average Accounting Rate of Return Profitability Index (PI)
Cost of Capital
Cost of Capital Cost of Capital Components Long-Term Capital Long-Term Debt Preferred Stock Common Stock Retained Earnings New Common Stock
Cost of Capital Cost of Capital Components Capital components = sources of funding from investors. Accounts payable, accruals, and deferred taxes sources of funding from investors. Therefore: Not included in calculation of the cost of capital. Adjustments made when calculating project cash flows.
Cost of Capital The cost of capital is the cost of using the funds of creditors and owners. Creating value requires investing in capital projects that provide a return greater than the project s cost of capital. When we view the firm as a whole, the firm creates value when it provides a return greater than its cost of capital. Estimating the cost of capital is challenging. We must estimate it because it cannot be observed. We must make a number of assumptions. For a given project, a firm s financial manager must estimate its cost of capital.
Cost of Capital The cost of capital is the rate of return that the suppliers of capital bondholders and owners require as compensation for their contributions of capital. This cost reflects the opportunity costs of the suppliers of capital. The cost of capital is a marginal cost because it is the cost associated with making an investment, so everything is at the margin (that is incremental): the cost of raising additional capital. The weighted average cost of capital (WACC) is the cost of raising additional capital, with the weights representing the proportion of each source of financing that is used. Also known as the marginal cost of capital (MCC).
Cost of Capital Weight Average Cost of Capital (WACC): WACC Composite Risk Adjusted WACC WACC with Flotation Cost
Cost of Capital where; WACC W k (1 T ) W k W k d d PS PS CS cs w d k d T w p k ps w e k cs is the proportion of debt that the company uses when it raises new funds is the before-tax marginal cost of debt is the company s marginal tax rate is the proportion of preferred stock the company uses when it raises new funds is the marginal cost of preferred stock is the proportion of equity that the company uses when it raises new funds is the marginal cost of equity
WACC Weights Cost of Capital Weights = percentages of the firm that will be financed by each component. If possible, always use the target weights for the percentages of the firm that will be financed with the various types of capital. Component w k Debt (before tax) 0.30 11.0% Preferred Stock 0.10 10.3% Common equity 0.60 14.6% WACC =0.3(11%)(1-.40)+0.1(10.3%)+0.6(14.6%) WACC = 11.77%
Cost of Capital Estimating Weights for the Capital Structure Estimate the weights using current market values rather than current book values If market value of debt is not known: Usually reasonable to use the book values of debt, especially if the debt is short-term Given: The stock price is $50 There are 3 million shares of stock $25 million of preferred stock $75 million of debt
Estimating Weights Cost of Capital V cs = $50 x (3 million) = $150 million V ps = $25 million V d = $75 million Total value = $150 + $25 + $75 = $250 million Stock price $50 Share O/S 3,000,000 Value Weight $150,000,000 60% Preferred Stock $25,000,000 $25,000,000 10% Debt $75,000,000 $75,000,000 30% Total Firm $250,000,000 100%
WHAT IS WACC? Cost of Capital Tax Rate = 40% Cost of Value Weight Capital Stock price $50 $150,000,000 60% 14.60% Share O/S 3,000,000 Tax Effect WACC 8.76% Preferred Stock $25,000,000 $25,000,000 10% 10.30% 1.03% Debt $75,000,000 $75,000,000 30% 11.00% 60% 1.98% Total Firm $250,000,000 100% 11.77%
Cost of Capital Factors that Influence a Company s WACC. Market conditions Interest rates The market risk premium Tax rates Firm s capital structure Firm s dividend policy Firm s investment policy Firms with riskier projects generally have a higher WACC
Cost of Capital Weight Average Cost of Capital (WACC): WACC Composite Risk Adjusted WACC WACC with Flotation Cost
Cost of Capital Risk-Adjusted WACC The composite WACC reflects the risk of an average project undertaken by the firm. Different divisions/projects may have different risks. The division s or project s WACC should be adjusted to reflect the appropriate risk and capital structure. If the business risk of the new project is different from the business risk of a company's existing operations, the company's shareholders will expect a different return to compensate them for this new level of risk. Hence, the appropriate WACC which should be used to discount the new project's cash flows is not the company's existing WACC, but a "risk adjusted" WACC that incorporates this new required return to the shareholders (cost of equity).
Cost of Capital Divisional Risk and The Cost of Capital Rate of Return (%) Acceptance Region WACC WACC H WACC F WACC L Acceptance Region Rejection Region Rejection Region 0 Risk L Risk H Risk
Cost of Capital Using WACC for All Projects Example What would happen if we use the WACC for all projects regardless of risk? Assume the WACC = 15% Required Decision Project Return IRR If 15% Risk Adj A 20% 17% Accept Reject B 15% 18% Accept Accept C 10% 12% Reject Accept
Cost of Capital Weight Average Cost of Capital (WACC): WACC Composite Risk Adjusted WACC WACC with Flotation Cost
Cost of Capital WACC with Flotation Costs Flotation costs depend on the risk of the firm and the type of capital being raised. Flotation costs: Highest for common equity. Most firms issue equity infrequently in order to save the transaction cost. Flotation costs frequently ignored when calculating WACC. However, we conservatively count in the flotation cost into the cost of equity.
WACC with New Debt Cost of Capital Component w k New Debt (after-tax) d 0.30 6.68% Preferred Stock ps 0.10 10.3% New Common equity cs 0.60 14.6% WACC = w d r AT d + w ps r ps + w c r e WACC = 0.3(6.68%)+0.1(10.3%) +0.6(14.6%) WACC = 2.004% + 1.03% + 9.36% = 11.794%
Cost of Capital WACC with New Debt & New Equity Component w r New Debt (after-tax) d 0.30 6.68% Preferred Stock ps 0.10 10.3% New Common equity c 0.60 15.6% WACC = w d r AT d + w ps r ps + w c r e WACC = 0.3(6.68%)+0.1(10.3%) +0.6(15.6%) WACC = 2.004% + 1.03% + 9.36% = 12.394%
Cost of Capital Notice!! WACC Description WACC No New Issues 11.770% With New Debt 11.794% With New Debt & New Equity 12.394% How to Increase Marginal Cost of Capital Externally raised capital flotation costs Increases the cost of capital Investors often perceive large capital budgets as being risky Drives up the cost of capital If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital
Cost of Capital Increasing Marginal Cost of Capital % 16 15 14 13 12 10 9 WACC 1 = 11.77% No external funds WACC 2 = 12.394% External debt & equity 8 500 700 Capital Required
Cost of Capital Example: WACC Suppose the ABC Company has a capital structure composed of the following, in billions: Debt Common equity THB 10 billion THB 40 million Weight of debt = 10 (10 + 40) = 0.20 or 20% Weight of common equity = 40 (10 + 40) = 0.80 or 80% If the before-tax cost of debt is 9%, the required rate of return on equity is 15%, and the marginal tax rate is 30%, what is Widget s weighted average cost of capital? Solution: WACC = [(0.20)(0.09)(1 0.30)] + [(0.8)(0.15)] = 0.0126 + 0.120 = 0.1325, or 13.25%
Interpretation: Cost of Capital When the ABC Company raises THB 1 more of capital, it will raise this capital in the proportions of 20% debt and 80% equity, and its cost will be 13.25%.
Cost of Capital Four Mistakes to Avoid Current (YTM) vs. historical (Coupon rate) cost of debt Mixing current and historical measures to estimate the market risk premium Book weights vs. Market Weights Use Target weights Use market value of equity Book value of debt is a reasonable proxy for market value Incorrect cost of capital components Only investor provided funding
Cost of Capital Taxes and the Cost of Capital Interest on debt is tax deductible; therefore, the cost of debt must be adjusted to reflect this deductibility. We multiple the before-tax cost of debt (k d ) by the factor (1 T), with T as the marginal tax rate. Thus, k d (1 T) is the after-tax cost of debt. Payments to owners are not tax deductible, so the required rate of return on equity (whether preferred or common) is the cost of capital.
Cost of Capital Taxes and the Cost of Capital Suppose a company has earnings before interest and taxes (EBIT) of THB 100, THB 200 of debt with a before-tax cost of 8%, and a 25% tax rate. Then: Without tax deductibility: EBIT $100 Taxes 25 Net income $75 With tax deductibility: EBIT $100 Interest 16 Earnings for taxes $84 Taxes 21 Net income $63 Therefore, the tax deductibility of the $16 of interest saves $25 $21 = $4 of taxes, or 25% $16 = $4.
Cost of Capital Weights of the Weighted Average: The weights should reflect how the company will raise additional capital. Ideally, we would like to know the company s target capital structure, which is the capital structure that is the company s goal, but we cannot observe this goal. Alternatives Assess the market value of the company s capital structure components. Examine trends in the company s capital structure. Use capital structures of comparable companies (e.g., weighted average of comparables capital structure). The proxies include the current market value, the extrapolated trend in the company s capital structure, and the capital structure of comparables.
Cost of Capital Applying the Cost of Capital to Capital Budgeting and Security Valuation: The investment opportunity schedule (IOS) is a representation of the returns on investments. We assume that the IOS is downward sloping: the more a company invests, the lower the additional opportunities. That is, the company will invest in the highest-returning investments first, followed by lower-yielding investments as more capital is available to invest. The marginal cost of capital (MCC) schedule is the representation of the costs of raising additional capital. We generally assume that the MCC is upward sloping: the more funds a company raises, the greater the cost.
Cost of Capital Optimal Investment Decision Marginal cost of capital Investment opportunity schedule Cost or Return Optimal Capital Amount of New Capital
Cost of Capital Using the MCC in Capital Budgeting and Analysis: The WACC is the marginal cost for additional funds and, hence, additional investments. In capital budgeting We use the WACC, adjusted for project-specific risk, to calculate the net present value (NPV). Using a company s overall WACC in evaluating a capital project assumes that the project has risk similar to the average project of the company. In analysis Analysts can use the WACC in valuing the company by discounting cash flows to the firm.
Cost of Capital Using the MCC in Capital Budgeting and Analysis: Capital budgeting issues: If the project has risk that is similar to that of the firm as a whole, then using the WACC in discounting project cash flows to calculate the NPV is appropriate. What if the project is not of average risk? Without adjustment, profitable projects with below-average risk would likely be rejected and unprofitable projects with higher-than-average risk may be accepted. Security valuation issues: When discounting cash flows of the entire company (e.g., free cash flows to the firm), use the WACC. When discounting equity cash flows (e.g., dividends or free cash flows to equity), use the cost of equity.
Cost of Capital Costs of the Different Sources of Capital Costs of Capital Cost of Debt Cost of Preferred Equity Cost of Common Equity Yield to Maturity Return on Preferred Stock Capital Asset Pricing Model Debt Rating Variations because of Callability, etc. Dividend Discount Model Bond Yield plus Risk Premium
Cost of Capital The Cost of Debt ( k d ): Alternative approaches 1. Yield-to-Maturity Approach: Calculate the yield to maturity on the company s current debt. 2. Debt-Rating Approach: Use yields on comparably rated bonds with maturities similar to what the company has outstanding. Note!!: Flotation costs on debt usually low. Frequently ignored Project Financing Adjusts project s cash flows for flotation costs of debt. Debt has specific claim on the project s cash flows.
Cost of Capital The Cost of Debt: Yield-to-Maturity Approach Consider a company that has $100 million of debt outstanding that has a coupon rate of 5%, 10 years to maturity, and is quoted at $98. What is the after-tax cost of debt if the marginal tax rate is 40%? Assume semi-annual interest. Solution: k d = 0.0526 (1 0.4) = 3.156% The cost of debt capital is 3.156%
Cost of Capital The Cost of Debt: Debt-Rating Approach Consider a company that has non-traded $100 million of debt outstanding that has a debt-rating of AA. The yield on AA debt is currently 6.2%. What is the after-tax cost of debt if the marginal tax rate is 40%? Solution: k d = 0.062 (1 0.4) = 3.72% The cost of debt capital is 3.72% (The yield is the yield for similarly rated bonds.)
Cost of Capital Issues in Estimating the Cost of Debt The cost of floating-rate debt is difficult because the cost depends not only on current rates but also on future rates. Possible approach: Use current term structure to estimate future rates (that is, forward rates). Option-like features affect the cost of debt. If the company already has debt with embedded options similar to what it may issue, then we can use the yield on current debt. If the company is expected to alter the embedded options, then we would need to estimate the yield on the debt with embedded options. Nonrated debt makes, it difficult to determine the yield on similarly yielding debt if the company s debt is not traded. Possible remedy: Estimate rating by using financial ratios (although this method is imprecise). Leases are a form of debt, but there is no yield to maturity. Estimate by using the yield on other debt of the company (i.e., debentures).
Cost of Capital Adjusting the Cost of Debt for Flotation Costs Where: N INT (1 T ) P B(1 F) t 1 t 1 r (1 T ) 1 r (1 T ) d B = Bond s par value (face value) F = Flotation cost as a % P = Principle amount N = Number of coupon payments T = Corporate tax rate INT = interest or coupon per period r d (1-T) = after tax cost of debt adjusted for inflation d N
Cost of Capital The Cost of Preferred Stock (P ps ) The cost of preferred stock that is noncallable and nonconvertible is based on the perpetuity formula: P ps = D ps k ps k ps = D p P p Suppose a company has preferred stock outstanding that has a dividend of $1.25 per share and a price of $20. What is the company s cost of preferred equity? k ps = $1.25 = 0.0625, or 6.25% $20 Note: The tax rate is irrelevant for the calculation of the cost of preferred stock because the dividends on preferred stock are not tax deductible by the issuer.
Cost of Capital The Cost of Preferred Stock with Flotation Cost Flotation costs for preferred stock are significant. Better use the net price Preferred stock dividends are not tax deductible. No tax adjustment Use r ps Nominal r ps is used k PS P PS D PS (1 F) Where: D ps = Preferred dividend P PS = Preferred stock price F = Flotation cost %
Cost of Capital The Cost of Common Equity: There are two ways to raise equity financing: Directly Issue new shares of common stock Indirectly Reinvesting earnings not paid out as dividends Use retained earnings However!!! Mature firms rarely issue new equity because. High flotation costs Negative signal to the market Downward pressure on stock price
Cost of Capital Cost of Retained Earnings Earnings can be reinvested or paid out as dividends Thus, there is an opportunity cost if earnings are reinvested. Opportunity cost: The return stockholders could earn on alternative investments of equal risk. They could buy similar stocks and earn r cs, or company could repurchase its own stock and earn r cs r cs = the cost of reinvested earnings = the cost of equity
Cost of Capital The Cost of Common Equity: Methods of estimating the cost of equity: 1. Capital Asset Pricing Model (CAPM) k s = r RF + β (R M - r RF ) = r RF + β (RP M ) 2. Dividend Discount Model k s = D 1 /P 0 + g 3. Bond Yield Plus Risk Premium k s = r d + Bond RP
Cost of Capital Using the CAPM to Estimate the Cost of Equity The capital asset pricing model (CAPM) states that the expected return on equity, E(R i ), is the sum of the risk-free rate of interest, R F, and a premium for bearing market risk, b i [E(R M ) R F ]: E(R i ) = R F + b i [E(R M ) R F ] where b i is the return sensitivity of stock i to changes in the market return (Stock Beta) E(R M ) is the expected return on the market E(R M ) R F is the expected market risk premium or equity risk premium (ERP)
Cost of Capital Estimating R F Common stock = long-term security. T-Bills more volatile than T-Bonds. Most analysts use the rate on a long-term (10 to 30 years) government bond as an estimate of R F. Estimating Beta β Beta estimates vary depending on the investors. Beta estimates are noisy. Wide confidence interval Historical Beta 4-5 years/monthly or 1-2 years/weekly Adjusted Beta Fundamental Beta Multinational issues
Cost of Capital Alternatives to the CAPM Alternative models may be used to capture expected returns to risk factors not incorporated in the CAPM. For example, we can use a factor model to estimate the cost of equity: Factor risk Factor risk Factor risk E(R i ) = R F + b i1 premium 1 + b i2 premium 2 + + β ij premium j where β ij = stock i s sensitivity to changes in the jth factor Factor risk premium j = the expected risk premium for the jth factor We can also use the historical equity risk premium approach, which requires estimating the average annual return over a historical period. Issues: Level of risk of stocks may change. Risk aversion of investors may change
Cost of Capital Alternatives to the CAPM The factor models may include macroeconomic factors (e.g., arbitrage pricing theory models), company-specific factors (e.g., Fama French models), or indices in addition to the market (e.g., industry index). The historical equity premium approach requires the estimation of the mean return over a period of time. Preferred: geometric mean return Issues: The level of the stock market risk may change over time. The risk aversion of investors may change over time.
Cost of Capital Using the Dividend Valuation Model to Estimate the Cost of Equity The dividend discount model (DDM) assumes that the value of a stock today is the present value of all future dividends, discounted at the required rate of return. Assuming a constant growth in dividends: P 0 = D 1 r e g which we can rearrange to solve for the required rate of return: r e = D 1 P 0 + g We can estimate the growth rate, g, by using third-party estimates of the company s dividend growth or estimating the company s sustainable growth.
Cost of Capital Estimating the Growth Rate The Historical Growth Rate If you believe future = past The Earnings Retention Model Analysts Estimates Value Line, Zack s, Yahoo.Finance
Cost of Capital The Earnings Retention Model Assumption 1. Retention rate is constant. 2. ROE on new investments is constant. 3. No new common stock will be issued. 4. The risk of future projects is very close to the risk of the overall firm. Example: ROE = 14.5% Dividend payout ratio = 52% Retention ratio = 100% - dividend payout Retention rate = 100% - 52% = 48% Retention growth rate: g = ROE x (Retention rate) g = (14.5%) x 0.48 = 7%
Cost of Capital Using the Dividend Valuation Model to Estimate the Cost of Equity The sustainable growth is the product of the return on equity (ROE) and the retention rate (1 minus the dividend payout ratio, or 1 D EPS ): g = 1 D EPS ROE If dividends do not grow at a constant rate, estimating the required rate of return on equity is much more challenging. We can estimate the sustainable growth using the product of the retention rate and the return on equity. Note: Some averaging over time may be appropriate because of the variability of earning and ROE for some companies.
Cost of Capital Using the DDM to Estimate the Cost of Equity Suppose the Company has a current dividend of THB 2 per share. The current price of a share of Company stock is THB 40. The Company has a dividend payout of 20% and an expected return on equity of 12%. What is the cost of common equity? Solution Using the dividend payout and the return on equity, we calculate g: g = 1 0.2 0.12 = 0.96, or 9.6% Then we insert g into the required rate of return formula: k e = 2 (1 + 0.096) 40 + 0.096 = 0.0548 + 0.096 = 0.1508, or 15.08% If raises new common equity capital, its cost is 15.08%. The dividend payout is 20%, so the retention ratio is 80%. The product of the retention ratio and the expected return on equity is 0.8 0.12 = 0.096, or 9.6%.!!!!!!!Warning!!!!! Common error, using simply 2 in the numerator instead of the correct 2 (1 + 0.096) = 2.192.
Cost of Capital Using Analysts Forecasts Analysts estimate earnings growth The growth rate (g) which is used in DDM representatively proxy for dividend growth. Sometimes involve non-constant growth. Develop a proxy constant growth rate Analysts estimates for PTT: 10.4% annual growth for 5 years 6.5% growth after 5 years Analysts estimates usually best source (reliable).
Cost of Capital Using the Bond Yield Plus Risk Premium Approach to Estimating the Cost of Equity The bond yield plus risk premium approach requires adding a premium to a company s yield on its debt: k k Risk Premium e d This approach is based on the idea that the equity of the company is riskier than its debt, but the cost of these sources move in tandem. Required rate of return on equity = Before-tax cost of debt + Risk premium The bond yield plus risk premium approach assumes that the spread between a company s bond yield and its required rate of return is constant.
Cost of Capital Flotation Costs for Equity Issuance (k e = Cost of Issue New Equity) Where: ˆ D 1 ke ke g P0 (1 F) D1 = Dividends paid at year 1 F = Flotation cost as a % P0 = Current equity price g = Growth rate when D D (1 g) 1 0
Cost of Capital Why is the cost of retained earnings (k s ) cheaper than the cost of issuing new common stock (k e )? When a company issues new common stock they also have to pay flotation costs to the underwriter. Issuing new common stock may send a negative signal to the capital markets, which may depress stock price (Dilution Effect). Because of flotation costs, dollars raised by selling new stock must work harder than dollars raised by retaining earnings. Moreover, since no flotation costs are involved, retained earnings have a lower cost than new stock. Therefore, the firms should utilize retained earnings to the extent possible to avoid the costs of new common stock. However, if a firm has more good investment opportunities, issuing new common stock is necessary.
Cost of Capital Why is the cost of retained earnings (k s ) cheaper than the cost of issuing new common stock (k e )? The retained earnings breakpoint represents the total amount of financing that can be raised before the firm is forced to sell new common stock. Retained earnings breakpoint = addition to retained earnings/equity fraction Flotation costs depend on the risk of the firm and the type of capital being raised. The flotation costs are highest for common equity. However, since most firms issue equity infrequently, the per-project cost is fairly small.
Cost of Capital Two approaches that can be used to account for flotation costs: Include the flotation costs as part of the project s up-front cost. This reduces the project s estimated return. Adjust the cost of capital to include flotation costs. This is most commonly done by incorporating flotation costs in the DCF model.
Cost of Capital Topics in Cost of Capital Estimation Estimating a project s beta (project beta versus company beta) Estimating country-risk premiums (whether or not to add a premium and, if adding, what spread to add) Using an upward-sloping marginal cost of capital schedule (when do component costs change?) Dealing with flotation costs (typical versus preferred method)
Cost of Capital Project Betas Issues in Estimating a Beta: Judgment is applied in estimating a company s beta regarding the estimation period, the periodicity of the return interval, the appropriate market index, the use of a smoothing technique, and adjustments for small company stocks. If a company is not publicly traded or if we are estimating a project s beta, then we need to look at the risk of the company or project and use comparables. When selecting a comparable for the estimation of a project beta, we ideally would like to find a company with a single line of business, and that line of business matches that of the project. This ideal comparable is a pure play. We use the beta of the comparable company to estimate an asset beta (beta reflecting only business risk) and then use it for the subject project or company.
Step 1 Step 2 Step 3 Step 4 Cost of Capital Using Comparables to Estimate Beta Select a Comparable Estimate the Beta for the Comparable Unlever the Comparable s Beta to Estimate the Asset Beta Lever the Beta for the Project s Financial Risk
Cost of Capital Levering and Unlevering Betas To improve the precision of beta estimation, use industry, rather than company-specific, betas. Companies in the same industry face similar operating risks, so they should have similar operating betas. Simply using the median of an industry s raw betas, however, overlooks an important factor: leverage. A company s equity beta is a function of not only its operating risk, but also the financial risk it takes. The weighted average beta for operating assets (β u - which is called the unlevered beta) and financial assets (β txa ) must equal the weighted average beta for debt (β d ) and equity (β e ). Our goal is to use this to solve for β u :
Cost of Capital Levering and Unlevering Betas V V D D V V V V D E D E u b txa b b b u txa d e u txa u txa operating assets tax assets debt equity Because there are so many unknowns variables and there is only one equation, we must impose additional assumptions to solve for β u
Cost of Capital Levering and Unlevering Betas Method 1: Assume β txa equals β u. If you believe the risk associated with tax shields (β u ) equals the risk associated with operating assets (β u ), the risk equation can be simplified dramatically. Specifically, E E bu bd be D E D E if β d = 0 b e 1 D E bu
Cost of Capital Levering and Unlevering Betas Method 2: Assume β txa equals β d. If you believe the risk associated with tax shields (β txa ) is comparable to the risk of debt (β d ), the equation can once again be arranged to solve for the unlevered cost of equity. D V E b b b txa u d e D Vtxa E D Vtxa E If the dollar level of debt is constant and debt is risk free, b u 1 D 1 (1 T ) E b e
Cost of Capital Determining the Industry Beta Capital Structure Home Depot Lowe s To estimate an industry-adjusted company beta: 1. First, regress each company s stock returns against the S&P 500 to determine raw beta. 2. Next, to unlever each beta, calculate each company s market-debt-to-equity ratio. 3. Determine the industry unlevered beta by calculating the median (in this case, the median and average betas are the same). 4. Relever the industry unlevered beta is to each company s target debt-to-equity ratio Debt Operating leases Excess cash Total net debt Shares outstanding (Mil) Share price ($) Market value of equity Debt/equity Raw beta (step 1) Unlevered beta (step 2) Industry average (step 3) Relevered beta (step 4) 1,365 6,554 (1,609) 6,310 2,257 35.49 80,101 0.079 1.37 1.27 1.14 1.23 3,755 2,762 (948) 5,569 787 55.39 43,592 0.128 Beta calculations Home Depot Lowe s 1.15 1.02 1.14 1.30
Applying the CAPM Cost of Capital The CAPM postulates that the expected rate of return on a company s stock equals the risk free rate plus the security s beta times the market risk premium. To estimate the risk-free rate in developed economies, use highly liquid, long-term government securities, such as the 10-year zero-coupon strip. Based on historical averages and forward-looking estimates, the appropriate market risk premium is currently between 4.5 and 5.5 percent. To estimate a company s beta, use industry derived betas levered to the company s target capital structure. E[R i ] = r f + B i (E[R m ] r f )
Cost of Capital Levering and Unlevering Beta To unlever beta, remove the comparable s capital structure from the beta to arrive at the asset beta, which reflects the company s business risk: b assets D bequity 1 1 (1 T ) E To lever the beta, adjust for the project s financial risk: b equity D bassets 1 (1 T ) E The first formula remove leverage of the comparable firm and put company s leverage back in the second formula. Caution: Tax rates and debt/equity may differ between the project and its comparable firm (even though the formula does not subscript these to associate these with a specific firm).
Cost of Capital Example: Levering and Unlevering Betas Consider the following information for the ABC Project and its comparable, 123 Company: ABC Project 123 Company Debt THB 10 THB 100 Equity THB 40 THB 200 Equity beta? 1.4 What is the asset beta and equity beta for the ABC Project based on the comparable company information and a tax rate of 40% for both companies? Solution b asset = 1.4 {1 [1 + (1 0.4)(100 200)]} = 1.4 0.76923 = 1.0769 b equity = 1.0769 [1 + (1 0.4)(10 40)] = 1.0769 1.15 = 1.2384 The beta of the ABC Project is 1.2384 The key to this calculation is to remove 123 s financial leverage from its beta and then use this beta (the asset beta) as the base for applying ABC s leverage.
Cost of Capital Country Risk Premium The country risk premium is the additional risk premium associated with doing business in a developing nation. The additional premium, added to the required rate of return estimated from the CAPM, is the country equity premium, or the country spread. To estimate the country risk premium: Use the sovereign yield spread, which is the difference in government bond yields. Adjust the sovereign yield spread by a factor that is the ratio of the. annualized standard deviation of the developing nation s equity index to the developing nation s market index volatility. annualized standard deviation of the sovereign bond market in the developed market currency (the developing nation s bond market volatility).
Cost of Capital Flotation Costs A flotation cost is the investment banking fee associated with issuing securities. There are two treatments for flotation costs: 1. Adjust the price of the security in the return calculation by the flotation cost, or 2. Adjust the NPV of the project for the monetary cost of flotation. Adjusting the NPV is preferred because the flotation costs occur immediately rather than affect the company throughout the life of the project. Suppose a company has a project with an NPV of $100 million. If the company issues $1 billion of equity to finance this project and the flotation costs are 1.2%, what is the NPV after adjusting for flotation costs? Solution NPV = $100 million $12 million = $88 million
Cost of Capital Summary of the Cost of Capital The weighted average cost of capital is a weighted average of the after-tax marginal costs of each source of capital. An analyst uses the WACC in valuation. For example, it is used to value a project using the net present value method. The before-tax cost of debt is generally estimated by means of one of two methods: yield to maturity or bond rating. The yield-to-maturity method of estimating the before-tax cost of debt uses the familiar bond valuation equation. Because interest payments are generally tax deductible, the after-tax cost is the true, effective cost of debt to the company. The cost of preferred stock is the preferred stock dividend divided by the current preferred stock price. The cost of equity is the rate of return required by a company s common stockholders. We estimate this cost using the CAPM (or its variants) or the dividend discount method.
Cost of Capital Summary of the Cost of Capital The CAPM is the approach most commonly used to calculate the cost of common stock. When estimating the cost of equity capital using the CAPM when we do not have publicly traded equity, we may be able to use the pure-play method, in which we estimate the unlevered beta for a company with similar business risk and then lever that beta to reflect the financial risk of the project or company. It is often the case that country and foreign exchange risk are diversified so that we can use the estimated b in the CAPM analysis. However, in the case in which these risks cannot be diversified away, we can adjust our measure of systematic risk by a country equity premium to reflect this non-diversified risk The dividend discount model approach is an alternative approach to calculating the cost of equity.
Cost of Capital Summary of the Cost of Capital We can estimate the growth rate in the dividend discount model by using published forecasts of analysts or by estimating the sustainable growth rate In estimating the cost of equity, an alternative to the CAPM and dividend discount approaches is the bond yield plus risk premium approach. The marginal cost of capital schedule is an illustration of the cost of funds for different amounts of new capital raised. Flotation costs are costs incurred in the process of raising additional capital. The preferred method of including these costs in the analysis is as an initial cash flow in the valuation analysis. Survey evidence indicates that the CAPM method is the most popular method used by companies in estimating the cost of equity.
Capital Budgeting
The Flows of Funds and Decisions Important to the Financial Manager Investment Decision Financing Decision Financial Manager Real Assets Reinvestment Refinancing Financial Markets Returns from Investment Returns to Security Holders
Capital Budgeting Capital Budgeting is the process of determining which real investment projects should be accepted and given an allocation of funds from the firm. Alternatively, It is the allocation of funds to longlived capital projects. A capital project is a long-term investment in tangible assets. The principles and tools of capital budgeting are applied in many different aspects of a business entity s decision making and also in security valuation and portfolio management. A company s capital budgeting process and prowess are important in valuing a company. To evaluate capital budgeting processes, their consistency with the goal of shareholder wealth maximization is of utmost importance.
Capital Budgeting The Capital Budgeting Process: Generating Ideas Step 1 Generate ideas from inside or outside of the company Analyzing Individual Proposals Step 2 Collect information and analyze the profitability of alternative projects Planning the Capital Budget Step 3 Analyze the fit of the proposed projects with the company s strategy Monitoring and Post Auditing Step 4 Compare expected and realized results and explain any deviations
Capital Budgeting Classifying Projects: Replacement projects: Existing assets are replaced with similar assets. Example: A manufacturing company replacing equipment on an assembly line Expansion projects: Increase the size of the business. Example: Wal-Mart opening a new retail outlet New products and services: These create greater uncertainties; hence, more attention may be required in the analysis of these projects. Example: Apple s initial introduction of the iphone
Capital Budgeting Classifying Projects: Regulatory, safety, and environmental projects: Generally are mandatory projects, but the company may have choices in how to satisfy requirements. If sufficiently costly, shutdown is an alternative. Also referred to as mandated projects. Other: These may include projects that are difficult to analyze (e.g., research and development [R&D]). Note: R&D expenses are sunk costs, but the decision to embark on R&D for the development of a project is itself a capital project.
Capital Budgeting Basic Principles of Capital Budgeting: 1.Decisions are based on cash flows, not accounting income. 2.The timing of cash flows is crucial; that is, the time value of money is important. 3.Cash flows are incremental; that is, cash flows are based on opportunity costs. 4.Cash flows are on an after-tax basis because cash flows related to taxes (payments or benefits) are part of the cash flows that must be analyzed. 5.Financing costs are ignored in the cash flow analysis. Financing costs enter the decision making through the required rate of return.
Capital Budgeting Costs: Include or Exclude? A sunk cost is a cost that has already occurred, so it cannot be part of the incremental cash flows of a capital budgeting analysis. Using a building that would otherwise be idle. The cost of the building is a sunk cost. An opportunity cost is what would be earned on the next-best use of the assets. Using a building that could otherwise be rented to another business. An incremental cash flow is the difference in a company s cash flows with and without the project. Change in sales of the company from a new product.
Capital Budgeting Costs: Include or Exclude? An externality is an effect that the investment project has on something else, whether inside or outside of the company. A project has the effect of reducing the unemployment rate of the town in which the company invests in this project. Cannibalization is an externality in which the investment reduces cash flows elsewhere in the company (e.g., takes sales from an existing company project). For example, a soup producer introduces a new soup that results in lower sales of an existing soup.
Capital Budgeting Conventional and Nonconventional Cash Flows: Conventional Cash Flow (CF) Patterns Today 1 2 3 4 5 CF +CF +CF +CF +CF +CF CF CF +CF +CF +CF +CF What is conventional? Only one sign change. No cash flow (e.g., $0) is not viewed as a sign change. CF +CF +CF +CF +CF
Capital Budgeting Conventional and Nonconventional Cash Flows: Nonconventional Cash Flow Patterns Today 1 2 3 4 5 CF +CF +CF +CF +CF CF CF +CF CF +CF +CF +CF Where do the negative cash flows come from? Investment Shut-down costs Environment mitigation CF CF +CF +CF +CF CF
Capital Budgeting Independent vs. Mutually Exclusive Projects: When evaluating more than one project at a time, it is important to identify whether the projects are independent or mutually exclusive This makes a difference when selecting the tools to evaluate the projects. Independent projects are projects in which the acceptance of one project does not preclude the acceptance of the other(s). Independent projects: The acceptance of one project does not affect the acceptance of another project. Example: A large conglomerate is introducing a new soup and a new peanut butter substitute.
Capital Budgeting Independent vs. Mutually Exclusive Projects: Mutually exclusive projects are projects in which the acceptance of one project precludes the acceptance of another or others. Example: An airline requires a single jet for a new route. The airline can buy a jet from Boeing or Airbus, but cannot buy one from each.
Capital Budgeting Project Sequencing: Capital sequencing is a situation in which one project s acceptance is conditional on another project s success. Capital sequencing is, essentially, when a project includes an option on future, related projects. Example: An entertainment company may release a children s movie, but wait to introduce the related toy line until the performance of the movie is assessed. Capital projects may be sequenced, which means a project contains an option to invest in another project. Projects often have real options associated with them; so the company can choose to expand or abandon the project, for example, after reviewing the performance of the initial capital project.
Capital Budgeting Capital Rationing: Capital rationing is when the amount of expenditure for capital projects in a given period is limited. Capital rationing exists when there is a limit on how much can be spent on capital projects. If the company has so many profitable projects that the initial expenditures in total would exceed the budget for capital projects for the period, the company s management must determine which of the projects to select. The objective is to maximize owners wealth, subject to the constraint on the capital budget. Capital rationing may result in the rejection of profitable projects. Capital rationing is not consistent with owners wealth maximization.
Capital Budgeting Investment Decision Criteria: Net Present Value (NPV) Internal Rate of Return (IRR) Payback Period Discounted Payback Period Average Accounting Rate of Return (AAR) Profitability Index (PI)
Capital Budgeting Discounted Cash Flow (DCF) Techniques: The main DCF techniques for capital budgeting include: Net Present Value (NPV), Internal Rate of Return (IRR), and Profitability Index (PI) Each requires estimates of expected cash flows (and their timing) for the project. Including cash outflows (costs) and inflows (revenues or savings) normally tax effects are also considered. Each requires an estimate of the project s risk so that an appropriate discount rate (opportunity cost of capital) can be determined. The discussion of risk will be deferred until later. For now, we will assume we know the relevant opportunity cost of capital or discount rate. Sometimes the above data is difficult to obtain this is the main weakness of all DCF techniques.
Capital Budgeting Net Present Value (NPV): The net present value is the present value of all incremental cash flows, discounted to the present, less the initial outlay: Or, reflecting the outlay as CF 0, where CF t r Outlay NPV NPV CFt 1 (1 r) = After-tax cash flow at time t = Required rate of return for the investment = Investment cash flow at time zero If NPV > 0: Invest: Capital project adds value If NPV < 0: Do not invest: Capital project destroys value N t N t CF 0 (1 r) t t Initial Outlay t
Capital Budgeting Net Present Value (NPV): The net present value is the difference between the present value of the inflows and the present value of the outflows (hence, net). The net present value is the estimate of how much the value of the firm changes with the adoption of the project. NPV is the estimate of the value added (or destroyed if negative). Note: When NPV = 0, we are indifferent between accepting and rejecting the project.
Capital Budgeting Net Present Value (NPV): Method: NPV = PV inflows PV outflows If NPV 0, then accept the project; otherwise reject the project. Example Project: Initial investment required: $100,000 Opportunity cost of capital: 15% The NPV is Year Cash Revenues less Expenses after tax 1 $20,000 2-9 $40,000 10 $10,000
Capital Budgeting Consider the PTT Project, which requires an investment of $1 billion initially, with subsequent cash flows of $200 million, $300 million, $400 million, and $500 million. We can characterize the project with the following end-of-year cash flows: Cash Flow Period (millions) 0 $1,000 1 200 2 300 3 400 4 500 What is the net present value of the PTT Project if the required rate of return of this project is 5%?
Example: NPV Time Line Solving for the NPV: Capital Budgeting 0 1 2 3 4 $1,000 $200 $300 $400 $500 NPV = $1,000 + $200 1 + 0.05 1 + $300 1 + 0.05 2 + $400 1 + 0.05 3 + $500 1 + 0.05 4 NPV = $1,000 + $190.48 + $272.11 + $345.54 + $411.35 NPV = $219.47 million
NPV of ABC Company Capital Budgeting ABC Company has determined that the appropriate discount rate (k) for this project is 13%. What is the project NAV? NPV = $10,000 $12,000 $15,000 + + + (1.13) 1 (1.13) 2 (1.13) 3 $10,000 $7,000 + - $40,000 (1.13) 4 (1.13) 5
NPV of ABC Company Capital Budgeting NPV = $10,000(PVIF 13%,1 ) + $12,000(PVIF 13%,2 ) + $15,000(PVIF 13%,3 ) + $10,000(PVIF 13%,4 ) + $ 7,000(PVIF 13%,5 ) - $40,000 NPV = $10,000(.885) + $12,000(.783) + $15,000(.693) + $10,000(.613) + $7,000(.543) - $40,000 NPV = $8,850 + $9,396 + $10,395 + $6,130 + $3,801 - $40,000 = - $1,428
Capital Budgeting NPV Acceptance Criterion The management of ABC Company has determined that the required rate is 13% for projects of this type. Should this project be accepted? No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject as NPV < 0 ]
Capital Budgeting NPV: Strengths and Weaknesses: Strengths Resulting number is easy to interpret: shows how wealth will change if the project is accepted. Acceptance criteria is consistent with shareholder wealth maximization. Relatively straightforward to calculate. Cash flows assumed to be reinvest at the hurdle rate (WACC rate). Account for time value of money. Consider all cash flow. Weaknesses Requires knowledge of finance to use. An improper NPV analysis may lead to the wrong choices of projects when the firm has capital rationing. May not include managerial options embedded in the project.
Capital Budgeting Internal Rate of Return (IRR): IRR is the rate of return that a project internally generates. Algebraically, the IRR can be determined by setting up an NPV s equation and solving for a discount rate that makes the NPV equal zero. Equivalently, IRR is solved by determining the rate that equates the present value of future cash inflows to the present value of future cash outflows. Method: Use your financial calculator or a spreadsheet; IRR usually cannot be solved manually. If IRR opportunity cost of capital (or hurdle rate or WACC), then accept the project; otherwise reject it.
Capital Budgeting Internal Rate of Return (IRR): The internal rate of return is the rate of return on a project. The internal rate of return is the rate of return that results in NPV = 0. t 1 CFt (1 IRR) Or, reflecting the outlay as CF 0, N N t 0 CFt (1 IRR) If IRR > r (required rate of return or WACC): Invest: Capital project adds value If IRR < r: (required rate of return or WACC): Do not invest: Capital project destroys value t t Initial Outlay 0 0
Capital Budgeting Example Project: Initial investment required: $100,000 Opportunity cost of capital: 15% The IRR is Year Cash Revenues less Expenses after tax 1 $20,000 2-9 $40,000 10 $10,000
Example: IRR Capital Budgeting Consider the PTT Project that we used to demonstrate the NPV calculation: Period Cash Flow (millions) 0 $1,000 1 200 2 300 3 400 4 500 The IRR is the rate that solves the following: $0 = $1,000 + $200 1 + IRR 1 + $300 1 + IRR 2 + $400 1 + IRR 3 + $500 1 + IRR 4
Example: IRR Capital Budgeting The IRR is the rate that causes the NPV to be equaled to zero. The problem is that we cannot solve directly for IRR, but rather must either iterate (trying different values of IRR until the NPV is zero) or use a financial calculator or spreadsheet program to solve for IRR. In this example, IRR = 12.826%: If using iteration, at 12%, NPV = $20.20 at 13%, NPV = ($4.19) Therefore, we know that the IRR is between 12% and 13% and likely closest to 13%.
IRR of ABC Company $40,000 = Capital Budgeting $10,000 $12,000 + (1+IRR) 1 (1+IRR) 2 $15,000 $10,000 $7,000 + + (1+IRR) 3 (1+IRR) 4 (1+IRR) 5 Find the interest rate (IRR) that causes the discounted cash flows to equal $40,000. +
Capital Budgeting IRR of ABC Company (Try 10%) $40,000 = $10,000(PVIF 10%,1 ) + $12,000(PVIF 10%,2 ) + $15,000(PVIF 10%,3 ) + $10,000(PVIF 10%,4 ) + $7,000(PVIF 10%,5 ) $40,000 = $10,000(.909) + $12,000(.826) + $15,000(.751) + $10,000(.683) + $ 7,000(.621) $40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347 $41,444 [Rate is too low!!]
Capital Budgeting IRR of ABC Company (Try 15%) $40,000 = $10,000(PVIF 15%,1 ) + $12,000(PVIF 15%,2 ) + $15,000(PVIF 15%,3 ) + $10,000(PVIF 15%,4 ) + $ 7,000(PVIF 15%,5 ) $40,000 = $10,000(.870) + $12,000(.756) + $15,000(.658) + $10,000(.572) + $7,000(.497) $40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479 $36,841 [Rate is too high!!]
Capital Budgeting IRR of ABC Company (Interpolate).10 $41,444.05 X IRR $40,000 $1,444 $4,603.15 $36,841 X 1,444 1,444 X 0.05 0.05 4, 603 4,603 0.0157 IRR 0.10 0.0157 0.1157 or 11.57%
Capital Budgeting IRR Acceptance Criterion The management of ABC Company has determined that the hurdle rate is 13% for projects of this type. Should this project be accepted? No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate or WACC ]
Capital Budgeting IRR: Strengths and Weaknesses: Strengths Account for Time value of money Considers all cash flows IRR number is easy to interpret: shows the return the project generates. Acceptance criteria is generally consistent with shareholder wealth maximization. Less Subjective Weaknesses Requires knowledge of finance to use. Assume all cash flow reinvested at IRR which is rarely applicable. Difficult to calculate need financial calculator. It is possible that there exists no IRR or multiple IRRs for a project and there are several special cases when the IRR analysis needs to be adjusted in order to make a correct decision
Capital Budgeting IRR: Strengths and Weaknesses: Reinvestment Rate Assumptions NPV assumes reinvest at the opportunity cost of capital. IRR assumes reinvest Cash Flows at IRR. Reinvest at opportunity cost is more realistic, so NPV method is the best choice to apply in our decision making process. NPV should be used to choose between mutually exclusive projects.
NPV $300,000 Capital Budgeting NPV Profile and the Solution for IRR $250,000 $200,000 $150,000 $100,000 $50,000 -$50,000 -$100,000 $0 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Discount Rate
Capital Budgeting Modified Internal Rate of Return (MIRR): MIRR is the discount rate which causes the present value of a project s terminal value (TV) to equal the present value of the costs. Terminal Value is found by compounding inflows at Weight Average Cost of Capital (WACC). Thus, the MIRR assumes cash inflows are reinvested at Weight Average Cost of Capital (WACC) or other applicable rates. Reinvestment Rate (RI)
Capital Budgeting Modified Internal Rate of Return (MIRR): 0 1 2 3 WACC=10% -100-100 PV outflows 10.0 60.0 80.0 10% 10% 66.0 12.1 158.1 TV inflows
Capital Budgeting Modified Internal Rate of Return (MIRR): 0 1 2 3-100 MIRR = 16.5% 158.1 PV outflows $100 = $158.1 (1+MIRR L ) 3 TV inflows MIRR L = 16.5%
Capital Budgeting Why investors use MIRR versus IRR? MIRR correctly assumes reinvestment at the opportunity cost which is the WACC. MIRR also avoids the problem of multiple IRRs. Managers like the rate of return comparisons, and MIRR is better for this process than IRR.
Capital Budgeting Payback Period: The payback period is the length of time it takes to recover the initial cash outlay of a project from future incremental cash flows. In the PTT Project example, the payback occurs in the last year, Year 4: Period Cash Flow (millions) Accumulated Cash flows 0 $1,000 $1,000 1 200 $800 2 300 $500 3 400 $100 4 500 +400
Capital Budgeting 0 1 2 3 (a) 4 5-40 K (-b) 10 K 12 K 15 K 10 K (d) 7 K 10 K 22 K 37 K (c) 47 K 54 K Cumulative Inflows PBP = a + ( b - c ) / d = 3 + (40-37) / 10 = 3 + (3) / 10 = 3.3 Years
Capital Budgeting 0 1 2 3 4 5-40 K 10 K 12 K 15 K 10 K 7 K -40 K -30 K -18 K -3 K 7 K 14 K Cumulative Cash Flows PBP = 3 + ( 3K ) / 10K = 3.3 Years Note: Take absolute value of last negative cumulative cash flow value.
Capital Budgeting PBP Acceptance Criterion The management of ABC Company has set a maximum PBP of 3.5 years for projects of this type. Should this project be accepted? Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]
Capital Budgeting Payback Period: The payback period is how long it takes to get the original investment back, in terms of undiscounted cash flows. Advantages Easy to calculate. Easy to understand. Can be used as a measure of liquidity. Easier to forecast short-term than long term flows. Disadvantages Ignores the time value of money. Ignores the cash flows beyond the payback period. Cut off point is subjective.
Capital Budgeting Payback Period: Ignoring Cash Flows: The payback period for both Project X and Project Y is three years, even through Project X provides more value through its Year 4 cash flow: Year Project X Cash Flows Project Y Cash Flows 0 100 100 1 20 20 2 50 50 3 45 45 4 60 0
Capital Budgeting Discounted Payback Period (DPB): The discounted payback period is the length of time it takes for the cumulative discounted cash flows to equal the initial outlay. In other words, it is the length of time for the project to reach NPV = 0. The discounted payback period is how long it takes to recover the initial investment in terms of discounted cash flows. If a project does not payback in terms of the discounted cash flows, then its NPV is negative.
Capital Budgeting Discounted Payback Period: Advantages Easy to understand. Considers the time value of money. Disadvantages Ignores cash flows beyond the payback period. No criteria for making a decision other than whether a project pays back.
Capital Budgeting Example: Discounted Payback Period Consider the example of Projects X and Y. Both projects have a discounted payback period close to three years. Project X actually adds more value but is not distinguished from Project Y using this approach. Cash Flows Discounted Cash Flows Accumulated Discounted Cash Flows Year Project X Project Y Project X Project Y Project X Project Y 0 100.00 100.00 100.00 100.00 100.00 100.00 1 20.00 20.00 19.05 19.05 80.95 80.95 2 50.00 50.00 45.35 45.35 35.60 35.60 3 45.00 45.00 38.87 38.87 3.27 3.27 4 60.00 0.00 49.36 0.00 52.63 3.27
Capital Budgeting Average Accounting Rate of Return: The average accounting rate of return (AAR) is the ratio of the average net income from the project to the average book value of assets in the project: AAR = Average net income Average book value
Capital Budgeting Average Accounting Rate of Return: The average accounting rate of return is the return on equity for the project. Advantages Easy to calculate Easy to understand Disadvantages Not based on cash flows Ignores the time value of money No objective decision criteria Calculated different ways
Profitability Index (PI): Capital Budgeting PI PV Cash Flow Initial Investment The profitability index is the ratio of the present value of the future cash inflows to the present value of the cash outlays. In a simple project, all outlays are completed in the initial period, so no discounting is necessary. Note: PI should always be expressed as a positive number. If PI 1, then accept the real investment project; otherwise, reject it.
Capital Budgeting Profitability index: The profitability index (PI) is the ratio of the present value of future cash flows to the initial outlay: PI = Present value of future cash flows Initial investment = 1 + NPV Initial investment If PI > 1.0: Invest Capital project adds value If PI < 0: Do not invest Capital project destroys value
Capital Budgeting PI Acceptance Criterion PI = $38,572 / $40,000 =.9643 Should this project be accepted? No! The PI is less than 1.00. This means that the project is not profitable. [Reject as PI < 1.00 ]