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Lectures in Engineering Economy

Lectures in Engineering Economy. Prof. Corrado lo Storto DIEG, Dept. of Economics and Engineering Management School of Engineering, University of Naples Federico II email: corrado.lostorto@unina.it phone: 081-768.2932. Major issues. What is MARR? What is the cost of capital?

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Lectures in Engineering Economy

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  1. Lectures in Engineering Economy Prof. Corrado lo Storto DIEG, Dept. of Economics and Engineering Management School of Engineering, University of Naples Federico II email: corrado.lostorto@unina.it phone: 081-768.2932

  2. Major issues • What is MARR? • What is the cost of capital? • What is the relation between cost of capital and financing funds? • How can we measure the cost of capital? • MARR, IRR and the cost of capital Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  3. Minimum requirements of acceptability (MARR) The interest rate or discount rate that should be used to estimate cash flows for several competing alternatives is the minimum attractive/acceptable rate of return (MARR). MARR is also called the cost of capital. The determination of MARR is generally controversial and difficult. An easy method to compute for determining what is alleged to be the minimum rate of return is to determine the rate of cost of each source of funds and to weight these by the proportion that each sources constitutes of the total. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  4. MARR: example If 1/3 of the capital of a firm is borrowed at 6% and the remainder of its capital is equity earning 12%, then the alleged minimum rate of return is Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  5. MARR and capital budgeting MARR determination is a task of capital budgeting. Capital budgeting is a critical function that takes place at the highest level of management. It can be defined as: “The series of decisions by individual economic units as to how much and where resources will be obtained and expended for future use, particularly in the production of future goods and services”. However, many decisions at the lower level in the management hierarchy affect those proposals competing in the overall capital budget. For example, before a major project is considered in top management capital budgeting process, usually many sub-alternatives of design and technical specifications are considered and the related decisions have been made. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  6. The scope of Capital Budgeting The scope of capital budgeting addresses • how the money is acquired and from what sources • how individual capital project opportunities (and combination of opportunities) are identified and evaluated • how minimum requirements of acceptability are set • how final project selections are made, and • how post-mortem reviews are conducted Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  7. MARR calculation There are different school of thought relatively to how MARR can be calculated. • if particular projects are to be undertaken using borrowed funds, then the minimum rate of return should be based on the rate of cost of those borrowed funds alone; • the minimum rate of return should be based on the cost of equity funds alone, on the grounds that a firm tends to adjust its capitalization structure to the point at which the real costs of new debt and new equity capital are equal (see E. Solomon “The management of corporate capital, The Free Press, NY); • Modigliani and Miller developed a theory that asserts that the average cost of capital to any firm is completely independent of its capital structure and is strictly the capitalization rate of future equity earnings; • another way to determine the minimum rate of return is to consider it as an opportunity cost in the “capital rationing” perspective. Capital rationing describes what is necessary when there is a limitation of funds relative to prospective proposals to use the funds. This limitation may be either internally or externally imposed. Its parameter is often expressed as a fixed sum of capital, but when the prospective returns from the investment proposals together with the fixed sum of capital available to invest are known, then the parameter can be expressed as a minimum acceptable rate of return, or cut-off rate. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  8. MARR calculation Ideally, the cost of capital by the opportunity cost principle can be determined by ranking prospective projects according to a ladder of profitability and then establishing a cut-off point where the capital is used on the better projects. The rate of return earned by the last project before the cut-off point is the cost of capital or minimum rate of return by the opportunity cost principle. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  9. 45 40 35 30 25 20 15 10 5 0 1 2 3 4 5 MARR calculation Prospective rate of return Amount of money invested Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  10. MARR standards It is not uncommon for firms to set two or more MARR levels according to risk categories. • High risk (MARR=40%) • New products, new business, acquisitions, joint venture • Moderate risk (MARR=25%) • Capacity increase to meet forecasted sales • Low risk (MARR=15%) • Cost improvements, make versus buy, capacity increase to meet existing order Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  11. MARR standard determination To determine MARR standards, the firm could rank prospective projects in each risk category according to the prospective rates of returns and investment amounts. After tentatively deciding how much investment capital should be allocated to each risk category, the firm could then determine the MARR for each risk category for a single category. In theory, it would be desirable that a firm invest additional capital as long as the return from the capital were greater than the cost of obtaining that capital. In such a case, the opportunity cost would be equal to the marginal cost of the last capital used. In practice, the amount of capital actually invested is more limited due to risk and conservative money policies. Hence, the opportunity cost is higher than the marginal cost of the capital. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  12. MARR standard determination Since managers cannot truly know the opportunity cost for capital in any given period (such as a budget year), it is useful to proceed as if the MARR for the upcoming period were the same as in the previous period. In addition to the normal difficulty of projecting the profitability of future projects and acceptability to permit the approval of favored, even if economically undesirable, projects or classes of projects. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  13. Minimum Acceptable Rate of Return • Lower limit for investment acceptability • Criterion set by organization • Before-tax calculations • Depends on the cost-of-capital (expense for acquiring funds) • Determined by: • Organization circumstances and goals • Project risk(high-risk requires higher return rate) Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  14. Cost of Capital – What is it? Cost of capital is the risk-adjusted discount rate (k) to be used in computing a project’s NPV. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  15. Methods of Financing • Equity Financing – Capital is coming from either retained earnings or funds raised from an issuance of stock • Debt Financing – Money raised through loans or by an issuance of bonds • Capital Structure – Well managed firms establish a target capital structure and strive to maintain the debt ratio Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  16. Equity Financing • Flotation (discount) Costs: the expenses associated with issuing stock • Types of Equity Financing: • Retained earnings • Common stock • Preferred stock Retained earnings + Preferred stock + Common stock Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  17. Debt Financing • Bond Financing: • Incur floatation cost • Pay only interests at the end of each period (usually semi-annually) • Pay the entire principal (face value) in a lump sum when the bond matures • Term Loan: • Involve an equal repayment arrangement. • May incur origination fee • Allow terms to be negotiated directly between the borrowing company and a financial institution Bond Financing + Term Loans Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  18. Cost of capital Cost of Capital • Cost of Equity (ie) – Opportunity cost associated with using shareholders’ capital • Cost of Debt (id) – Cost associated with borrowing capital from creditors • Cost of Capital (k) – Weighted average of ie and id Cost of Debt Cost of Equity Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  19. Calculating the Cost of Equity • Cost of Retained Earnings (kr) • Cost of issuing New Common Stock(ke) • Cost of Preferred Stock (kp) • Cost of equity: weighted average of krke, and kp Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  20. Method 1: Calculating Cost of Equity Based on Financing Sources Where Cr = amount of equity financed from retained earnings, Cc= amount of equity financed from issuing new stock, Cp = amount of equity financed from issuing preferred stock, and Ce = Cr + Cc + Cp Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  21. Example: Determining the Cost of Equity Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  22. Method 2: Calculating Cost of Equity based on CAPM • The cost of equity is the risk-free cost of debt (20 year U.S. Treasury Bills around 7%) plus a premium for taking a risk as to whether a return will be received. • The premium is the average return on the market, S&P 500, (i.e., 12.5%) less the risk-free cost of debt. This premium is multiplied by beta, a measure of stock price volatility. • Beta quantifies risk and is an approximate measure of stock price volatility. It measures one firm’s stock price compared (relative) to the market stock prices as a whole. • A number greater than one means that the stock is more volatile than the market on average; a number less than one means that the stock is less volatile than the market on average. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  23. Method 2: Calculating Cost of Equity based on CAPM The following formula quantifies the cost of equity (ie). where rf = risk free interest rate (commonly referenced to U.S. Treasury bond yield) rM = market rate of return (commonly referenced to average return on S&P 500 stock index funds) Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  24. Terminology relative to Common Stock Common Stock: Ownership shares in a publicly held corporation Secondary Market: Market in which already issued securities are traded by investors Dividend: Periodic cash distribution from the firm to the shareholders Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  25. Valuing Common Stocks • Key concept: expected return rate • Expected Return Rate: The percentage yield that an investor forecasts from a specific investment over a set period of time • “Market Capitalization Rate” Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  26. Market Capitalization Rate • DIVt: dividend during year t • Pt: stock price at end of year t • Using a single-period model: • DIV1/P0: Dividend yield • P1-P0: Capital gain • (P1-P0)/P0: Capital appreciation Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  27. Valuing Common Stocks Example: Company X stock is selling at $100 a share. Expected dividends over the next year $5. Expected price in a year $110. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  28. Valuing Common Stocks Example: Company X stock. Expected dividends over the next year $5. Expected price in a year $110. Given that equally risky investments have a capitalization rate of r=15%, what is the price of the stock today? Equilibrium condition of capital markets: All securities in the same risk class are priced to offer the same expected rate of return Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  29. Dividends vs. Capital Gains • Beginning of 1st yr: investor buys at P0 based on • dividends for 1st yr, and • sell price at end of 1st yr • End of 1st yr: another investor is willing to buy at P2 • Combining the two: Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  30. Dividends vs. Capital Gains Question: Which of the following is the value of a stock is equal to? • The discounted PV of the sum of next period’s dividend plus next period’s stock price, or • The discounted PV of all future dividends Answer: Both Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  31. Dividend Discount Model • Criticism against model: “shortsighted investors do not care about long-run stream of dividends” • But: an investor who wants to cash out early must find another investor who is willing to buy • Dividend-discount model holds even if investors have short-term horizons • Finite horizon of H periods: • Infinite horizon: Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  32. Valuation of Different Types of Stocks Comment: • “Growth” typically refers to EPS (earnings per share) • The examples assume that DIV grow at the same rate as EPS 1. Zero Growth [Perpetuity Formula] 2. Constant Growth (rate g) [Growing Perpetuity Formula] Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  33. Dividend Discount Model Where does g (growth rate) come from? Where does r (return rate) come from? Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  34. Where Does g Come From? • Growth: earnings next year are higher than this year • Net investment necessary for growth • Part of this year’s earnings are retained (not paid out as dividends) and reinvested • Payout Ratio: fraction of earnings paid out as dividends • Plowback or Retention Ratio: fraction of earnings retained by the firm • Growth rate Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  35. Formula for Firm’s Growth Rate • DIV: dividends per share • EPS: earnings per share • ROE: return on equity Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  36. Where Does r Come From? • Two methods: • Risk analysis • Dividend discount model • Dividend Discount Model: • Assume constant growth • DIV, P0: publicly available information • g: estimate Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  37. Example: Estimating Growth and Return Rates Example: Krueger Enterprises has 1 million shares outstanding. Firm just reported earnings of $2 million. It plans to retain 40% of earnings. Historical ROE has been 16%, a figure that is expected to continue in the future. The stock is selling at $10. What is the rate of return? • Growth rate • Earnings a year from now • Dividends • Dividends per share • Return rate Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  38. Estimating Growth and Return Rates • Assumptions/Approximations: • Return on retained earnings equal to historical ROE • Plowback ratio remains the same • Constant growth • Extreme Cases: • No-dividend firm • g close to r : infinite-growth firm • Suggestions: • Estimate r for an entire industry – averaging reduces estimation error • A high estimate of the growth rate (g close to r): • might be correct for the next few years • cannot be sustained forever Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  39. Example: Dividends vs. Growth Opportunities Example: Krueger Enterprises forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, the firm decides to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision? • No Growth: • With Growth: Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  40. Practice Problem – Cost of Equity Alpha Corporation needs to raise $10 million for plant modernization. Alpha’s target capital structure calls for a debt ratio of 0.4, indicating that $6 million has to be financed from equity. Alpha is planning to raise $6 million from the financial market Alpha’s Beta is known to be 1.8, which is greater than 1, indicating the firm’s stock is perceived more riskier than market average. The risk free interest rate is 6%, and the average market return is 13%. Determine the cost of equity to finance the plant modernization. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  41. Solution ? Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  42. Calculating the Weighted (after-tax) Cost of Capital Cd= Total debt capital(such as bonds) in dollars, Ce=Total equity capital in dollars, V = Cd+ Ce, ie= Average equity interest rate per period considering all equity sources, id = After-tax average borrowing interest rate per period considering all debt sources, and k = Tax-adjusted weighted-average cost of capital. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  43. Example: calculation of the Cost of Capital • Given: Cd = $4 million, Ce = $6 million, V= $10 millions, • id= 6.92%, ie=19.96% • Find: k Comments: This 14.74% would be the (marginal) cost of capital that a company with this financial structure would expect to pay to raise $10 million. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  44. The marginal cost of capital The marginal cost of capital is defined as the cost of obtaining another dollar of new capital. The marginal cost rises as more and more capital is raised during a given period. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  45. The CAPM approach The CAPM approach involves the following steps: • Estimate the risk free rate rf (i.e., the Treasury Bill rate) • Estimate the stock’s beta coefficient, b, which is an index of systematic (or nondiversifiable) market risk • Estimate the rate of return on the market portfolio (such as the Standard & Poor’s 500 Stock Composite Index or Dow Jones 30 Industrials) • Estimate the required rate of return on the firm’s stock using the CAPM equation Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  46. The CAPM approach: example Assuming that rf is 7%, b is 1.5, and rm is 13%, then This 16% cost of common stock can be viewed as consisting of a 7% risk free rate plus a 9% risk premium which reflects that the firm stock price is 1.5 times more volatile than the market portfolio due to factors affecting nondiversifiable or systematic risk. Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  47. Calculating Cost of Capital using CAPM • Cost of Debt • Cost of Equity Cost of Capital = (cost of debt) x (% of capital from debt) + (cost of equity) x (% of capital from equity) Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  48. Return Rates Minimum Acceptable Rate of Return (MARR)Lowest level of return that makes an investment acceptable Internal Rate of Return (IRR)Discount rate that makes PW of an investment zero External Rate of Return (ERR)Return Rate that can be obtained for an investment under current economic conditions Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  49. Internal Rate of Return Caution! IRR calculation Interpretation of IRR for evaluation of mutually exclusive projects Internal (or discounted cash flow) Rate of Return: Interest rate at which the PW of the cash flow generated by the project is zero Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

  50. Calculation of the IRR (Single Project) • Cn: receipt (positive), disbursement (negative), or net benefit (receipt minus disbursement) at period n • C0: initial cost • Find discount rate i, such that the PW of the cash flow is equal to zero • Polynomial equation on i • Existence of multiple solutions i* Engineering Economy/cost of capital and MARR/ 2005 /prof. corrado lo storto

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