(c) 2001 Contemporary Engineering Economics1 Discount Rate to be Used in Project Analysis ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences

(c) 2001 Contemporary Engineering Economics2 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.

(c) 2001 Contemporary Engineering Economics 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

(c) 2001 Contemporary Engineering Economics 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 + +

(c) 2001 Contemporary Engineering Economics Debt Financing Bond Financing:  Incur floatation cost  Pay only interests at the end 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 +

(c) 2001 Contemporary Engineering Economics Cost of Capital Cost of Equity (i e ) – Opportunity cost associated with using shareholders’ capital Cost of Debt (i d ) – Cost associated with borrowing capital from creditors Cost of Capital (k) – Weighted average of i e and i d Cost of Equity Cost of Debt Cost of Capital

(c) 2001 Contemporary Engineering Economics 1. Calculating the after-tax Cost of Debt Interest payments on both bond and loan financing is tax deductible

(c) 2001 Contemporary Engineering Economics Practice Problem Alpha Corporation needs to raise $10 million and has decided to finance $4 million by securing a term loan and issuing 20 ‑ year $1,000 par bonds for the following condition. (The remaining funds would be raised through equity financing.) Alpha ’ s marginal tax rate is 38%, and it is expected to remain constant in the future. What is the after-tax cost of debt? SourceAmountFractionInterest rate Term Loan Bond $1.33M $2.67M % 10.74% i d =0.33*0.12*(1-0.38) *0.1074*(1-0.38)=6.92%

(c) 2001 Contemporary Engineering Economics 2. Calculating the Cost of Equity Cost of Retained Earnings (k r ) Cost of issuing New Common Stock(k e ) Cost of Preferred Stock (k p ) Cost of equity: weighted average of k r k e, and k p

(c) 2001 Contemporary Engineering Economics Method 1: Calculating Cost of Equity Based on Financing Sources Where C r = amount of equity financed from retained earnings, C c = amount of equity financed from issuing new stock, C p = amount of equity financed from issuing preferred stock, and C e = C r + C c + C p

(c) 2001 Contemporary Engineering Economics Determining the Cost of Equity SourceAmountInterest Rate Fraction of Total Equity Retained earnings $1 M20.50%0.167 New common stock $4 M22.27%0.666 Preferred stock $1 M10.08%0.167

(c) 2001 Contemporary Engineering Economics 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, (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.

(c) 2001 Contemporary Engineering Economics The following formula quantifies the cost of equity (i e ). where r f = risk free interest rate (commonly referenced to U.S. Treasury bond yield) r M = market rate of return (commonly referenced to average return on S&P 500 stock index funds)

(c) 2001 Contemporary Engineering Economics 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.

(c) 2001 Contemporary Engineering Economics Solution I e = *( )=18.60% This means if this company finances a project totally from equity funds, the project should at least earn 18.60%

(c) 2001 Contemporary Engineering Economics 3. Calculating the Weighted after-tax Cost of Capital C d = Total debt capital(such as bonds) in dollars, C e =Total equity capital in dollars, V = C d + C e, i e = Average equity interest rate per period considering all equity sources, i d = After-tax average borrowing interest rate per period considering all debt sources, and k = Tax-adjusted weighted-average cost of capital.

(c) 2001 Contemporary Engineering Economics Marginal Cost of Capital Given: C d = $4 million, C e = $6 million, V= $10 millions, i d = 6.92%, i e =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. Same formula can be used with interest on new equity and new debt

(c) 2001 Contemporary Engineering Economics Cost of Capital 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)

(c) 2001 Contemporary Engineering Economics Summary Identifying and estimating relevant project cash flows is perhaps the most challenging aspect of engineering economic analysis. All cash flows can be organized into one of the following three categories: 1. Operating activities. 2. Investing activities 3. Financing activities.

(c) 2001 Contemporary Engineering Economics Cash Items 1. New investment and disposal of existing assets 2. Salvage value (or net selling price) 3. Working capital 4. Working capital release 5. Cash revenues/savings 6. Manufacturing, operating, and maintenance costs. 7. Interest and loan payments 8. Taxes and tax credits

(c) 2001 Contemporary Engineering Economics Non-cash items 1. Depreciation expenses 2. Amortization expenses The income statement approach is typically used in organizing project cash flows. This approach groups cash flows according to whether they are operating, investing, or financing functions.

(c) 2001 Contemporary Engineering Economics Methods of financing: 1. Equity financing uses retained earnings or funds raised from an issuance of stock to finance a capital. 2. Debt financing uses money raised through loans or by an issuance of bonds to finance a capital investment. Companies do not simply borrow funds to finance projects. Well-managed firms usually establish a target capital structure and strive to maintain the debt ratio when individual projects are financed.

(c) 2001 Contemporary Engineering Economics The selection of an appropriate MARR depends generally upon the cost of capital— the rate the firm must pay to various sources for the use of capital. The cost of the capital formula is a composite index reflecting the cost of funds raised from different sources. The formula is

(c) 2001 Contemporary Engineering Economics 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.