NPV CRITERION FOR CAPITAL EXPENDITURE ANALYSIS èDiscount incremental after-tax cash flows at the cost of capital èe.g., if initial investment = 100, cash.

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NPV CRITERION FOR CAPITAL EXPENDITURE ANALYSIS èDiscount incremental after-tax cash flows at the cost of capital èe.g., if initial investment = 100, cash flow in years 1 and 2 = 70, cost of capital = 10%, NPV = /(1.1) + 70/(1.1) 2 = èSince NPV > 0, project is worthwhile

NPV AND SHAREHOLDER WEALTH èFirm has no debt èExisting assets generate cash flows of 100 per year forever èDiscount rate = 10% èFirm has 20 mil shares currently selling at $50 per share

NPV AND S/H WEALTH (CONT.) èNow firm plans to invest $120 in new project èProject will generate $20 CF per year forever èFirm will issue  n new shares at price P* to finance project

NPV AND S/H WEALTH (CONT.) èEquating sides of post-project bal. sheet: 100/ /.10 = 20P* +  nP* èBut from original bal. Sheet: 100/.10 = 20x50 = nP èAnd since we need to raise 120 for project: 120 =  nP* èThus: 20x50 +20/.10 = 20P* + 120

NPV AND S/H WEALTH (CONT.) èRearranging: 20/ = 20 x (P* - 50) èOr: [20/ ]/20 = (P* - 50) èOr:     NPV per share = change in wealth for original shareholders    

COST OF CAPITAL What is it? èAppropriate discount rate èMinimum acceptable rate of return for investors èInvestors’ opportunity cost èRequired compensation for risk borne by investors

COST OF CAPITAL (all-equity financing) What rate of return will shareholders demand? Two possible answers from stock market: èCapital Asset Pricing Model r E = r f +  (r M - r f ) (shareholders demand compensation for systematic risk) èDividend Discount Model r E = D 1 /P 0 + g

COST OF CAPITAL (with debt and equity) E = equity mkt. value ATOCF = after-tax operating cash flow r D = cost of debt r E = cost of equity D = value of debt T = corporate tax rate

COST OF CAPITAL (debt and equity cont.) Cross-multiplying by V, we derive a discount rate for the company as a whole Note that debt ratio is measured at market value

COST OF CAPITAL FOR A PROJECT èFor a project, the cost of capital is project specific, not company-specific (Would a risky project be any less risky if undertaken by a currently safe company?) èCost of capital should reflect business risk of this project èCost of capital should reflect long-run financing mix for this project

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