selecting a minimum attractive rate of return chapter 15 mechanical engineering 431 engineering...

Selecting a Minimum Attractive Rate of Return

Chapter 15

Mechanical Engineering 431

Engineering Economics

2009-2010 Term 2 MECH 431 — Engineering Economics 15-2

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.


Sources of capitalInternal — 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.


Cost of funds — debtThe 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.


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


Cost of funds — risk & rate of returnRisk 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.


Cost of funds …Example: A firm with a marginal tax rate of 30% has

raised funds from these sources: Bonds: 45,000 issued, price = $1007.25 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.


Opportunity cost of capitalA 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.


Opportunity cost of capital …$1,250

Project Number Cost

Estimated ROR

Select Project

Total Capital Invested

Rejected Project's ROR

2 $50 35% Yes $504 $100 30% Yes $1503 $50 29% Yes $2005 $200 25% Yes $4001 $150 22% Yes $5506 $100 18% Yes $6508 $250 16% Yes $9009 $300 15% Yes $1,2007 $200 13% No $1,200 13%11 $400 12% No $1,200 12%10 $300 10% No $1,200 10%12 $1,200 8% No $1,200 8%

13%Opportunity cost

Capital available:


Selecting MARR/adjusting for riskThe 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.


Capital rationingFirms 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.


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%.

Project Cost CF1 CF2 CF3 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


Suggested problems — Chapter 1515-4 (tax rate = 30%), 15-5 (tax rate = 30%), 15-13, 15-

16

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