Selecting a Minimum Attractive Rate of Return Chapter 15 Mechanical Engineering 431 Engineering Economics

Term 2MECH 431 — Engineering Economics15-2 Chapter 15 …  Identifies various sources of capital and the costs of those sources to the firm.  Determines a firm’s MARR for the purpose of analyzing investments.  Adjusts the firm’s MARR to recognize risk.  Selects the optimal set of investment projects when capital is limited using capital rationing.

Term 2MECH 431 — Engineering Economics15-3 Sources of capital  Internal — money generated from the firm’s operations: retained profits, i.e. not paid out as dividends.  External — money raised from sources outside the firm: Short term debt: banks; generally unsecured. Long term debt: bondholders, banks, insurance companies, pension funds, mortgages; generally secured. Permanent equity: holders of common or preferred shares.  The mix of externally provided funds is the capital structure. It depends on the needs of the firm and the decisions of its managers.

Term 2MECH 431 — Engineering Economics15-4 Cost of funds — debt  The cost of debt is the rate of return the debt market requires.  It is determined by matching the market value of the debt to its future cash flows (interest payments plus repayment of debt principal).  The cost of debt is usually approximately equal to the rate of interest the firm is paying on the debt.

Term 2MECH 431 — Engineering Economics15-5  The cost of equity is the rate of return that investors require on the shares of a firm.  It is determined by matching the market value of the shares to their future cash flows (dividend payments plus possible sale of the shares at a future date).  The shares of a firm should have the same cost of equity as the shares of all other firms that have the same level of risk. Cost of funds — equity

Term 2MECH 431 — Engineering Economics15-6 Cost of funds — risk & rate of return  Risk is measured by the uncertainty of the firm’s cash flows.  A firm’s overall cost of capital is the weighted average of the rates of return required by the providers of all funds (after-tax for debt). The weights are the market values of the various forms of funds in the firm: debt, common equity, and preferred equity.

Term 2MECH 431 — Engineering Economics15-7 Cost of funds …  Example: A firm with a marginal tax rate of 30% has raised funds from these sources: Bonds: 45,000 issued, price = $ each, yield rate = 4.65% Preferred shares: 100,000 outstanding, price = $68.75 each, rate of return = 8.35%. Common shares: 950,000 outstanding, price = $42.35 each, rate of return = 10.70%. Find the weighted average (overall) cost of capital of the firm.

Term 2MECH 431 — Engineering Economics15-8 Opportunity cost of capital  A firm has many investment opportunities but there is a limited amount of capital available.  The opportunity cost of capital is the rate of return of the best opportunity that is foregone or not accepted.  On the whole, the opportunity cost of capital tends to be the same among all firms that operate at the same level of risk.

Term 2MECH 431 — Engineering Economics15-9 Opportunity cost of capital …

Term 2MECH 431 — Engineering Economics15-10 Selecting MARR/adjusting for risk  The appropriate MARR that a firm should use to analyze its investment projects is generally the maximum of: the cost of borrowing funds, the weighted average cost of capital, and the opportunity cost of capital.  For each project, use a MARR that is appropriately risk- adjusted.  Assess projects using techniques other than economic analysis.

Term 2MECH 431 — Engineering Economics15-11 Capital rationing  Firms have access to limited funds to invest in projects.  As a guide to selecting projects, rank them based on the profitability index (similar to the benefit-cost ratio): Profitability index (PI) = NPV / initial investment.  With capital rationing, a firm selects the projects for which they have adequate resources and that together give the highest overall NPV.

Term 2MECH 431 — Engineering Economics15-12 Capital rationing …  Example: a firm has the following project opportunities and $10 million in investment capital. Recommend which projects to undertake if the cost of capital is 12%. ProjectCostCF 1 CF 2 CF 3 NPV A$3.0m$1.5m$2.5m$1.5m$1.400m B$7.5m$3.5m$5.0m$4.0m$2.458m C$4.0m$2.0m$2.5m$2.0m$1.202m D$5.5m$2.5m$4.0m$3.0m$2.056m E$3.0m$2.0m$1.5m$1.0m$0.693m

Term 2MECH 431 — Engineering Economics15-13 Suggested problems — Chapter 15  15-4 (tax rate = 30%), 15-5 (tax rate = 30%), 15-13,