MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 11.011 Project EvaluationChoosing a Discount RateCarl D. MartlandRate of Return on an InvestmentMinimally Acceptable Rate of ReturnCapital Markets - Risk vs. ReturnWeighted Average Cost of CapitalLeveragingA Basic QuestionFor any arbitrary sequence of cash flows and for any interest rate i, we can find an equivalent cash flow that is much easier to work with when evaluating projects:Present worthFuture worth, at any time tAn annuity for N periods begining at time 0An annuity for N periods beginning at any future timeBut - how do we choose i? Opportunity Cost of CapitalWhat else could we do with our money?Give it awaySpend it on food, Red Sox games, movies, or clothesPut it in the bankBuy government bonds or corporateBuy blue chip stocksBuy growth stocksBuy emerging markets mutual fundsThe opportunity cost depends upon what other options are available to us given our own situation and current market conditionsReturn on Investment = A/I(where A is the annual income from the investment over a long time horizon)Time020040060080010001200InvestmentTime020040060080010001200Equivalent Annual Income From InvestmentI = InvestmentA = Equivalent Annual ReturnMinimum Attractive Rate of ReturnThe MARR is the lowest return that you would be willing to accept given:The risks associated with this projectThe other opportunities for investmentIn general, we can look at the capital markets to find out what kinds of return are available for different kinds of investmentInterest rates for bondsHistorical rates or return (i.e. growth rates) for stocks (assuming that stocks are priced today such that they will offer new owners similar rates of return in the future)Cost of CapitalA company has various potential sources of funds in addition to using its own funds and losing opportunities to invest those funds elsewhere)Debt: borrow money from a bank or issue bonds (pay a defined payment of principal plus interest rate per period, but retain complete ownership of the company) Sell stock (raise money without committing to interest payments, but also give up ownership of the company)MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 2What is an Appropriate Discount Rate?Risk vs. Expected ReturnGov. BondAAA BondsB BondsBlue ChipsGrowth StocksEmerg. Markets00.050.10.150.20.250.3Debt Financing Increases the Expected Return of the Project if the Interest Rate is lower than the ROI0510152025Income Debt Payment ROI-10010203040Borrow half the cost, payonly 25% of income for iLeveraging"Leveraging" is borrowing money to increase the expected ROI for the projectIf base ROI is greater than the interest rate, then leveraging increases the return: ROI = Net income/Net Investment = (Income - i*Debt)/(Invest - Debt) = (ROI*Invest - i*Debt)/(Invest - Debt)Debt Financing Increases Risks of a Projects, Because Principal & Interest Must be Paid When DueTime01020304050607080Annual IncomeTime-60-40-20020406080Annual Income or PaymentIncomeDebt PaymentNet IncomeLimits on LeveragingBanks may limit debt to a percentage of the total project costs (typically 80% for a real estate project)Banks may increase interest rates for highly leveraged companiesInvestors may shun stock of highly leverage companies Owners may limit debt in highly volatile industries to limit risk of bankruptcyCost of Capital for Debt FinancingInterest rates will be determined by the capital markets and the credit of the company (NOT the quality of the project)Rates will be higher if:Interest rates in general move higher (as happens in times of inflation)If company is perceived as a credit riskIf company relies too much on debt financingRisk bankruptcy by having high levels of interest paymentsIf company is in a risky industry If company operates within a risky polical environmentMIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 3Cost of Capital for Equity FinancingTo sell stock, you must persuade investors that the value of the company will grow fast enough to provide investors with a suitable returnIn principal, investors can value the company at some future time, select an appropriate discount rate, and determine the maximum price that they would be willing to pay today In practice, investors often look at the ratio of price to current earnings in comparison to P/E ratios for other companies with similar anticipated growth rates (Note: if earnings are stable, the P/E is the inverse of the return on investment) Cost of Capital for Equity FinancingTo sell stock, you must persuade investors that the value of the company will grow fast enough to provide investors with a suitable returnIn principal, investors can value the company at some future time, select an appropriate discount rate, and determine the maximum price that they would be willing to pay today In practice, investors often look at the ratio of price to current earnings in comparison to P/E ratios for other companies with similar anticipated growth rates (Note: if earnings are stable, the P/E is the inverse of the return on investment) Public Sector FinancingThe public can raise money by issuing bonds guaranteed by the government and backed up by the power of the government to raise taxes if necessary to meet its obligationsThe government may make income on some government bonds tax-freeBUT - the government also is raising money from individuals and the private sector by taxation - the opportunity cost is what they could do with the moneuySO - there is pressure on government not to use discount rates that are too low (or too high)Choosing a Discount RateThe discount rate (i.e. the interest rate that you use in finding equivalent values) should begreater than or equal to your average cost of capital (not necessarily your cost of capital for a particular project)at least as high as your other investment opportunities (adjusted for risk)The discount rate therefore will equal equal your "minimum acceptable rate of return"Choosing A Discount RateThe discount rate reflects the opportunity cost for the person or organization that will receive the cash flows (e.g. the federal government specifies a rate to be used)The analysis can be done with real or nominal discount ratesReal rates are used in constant-dollar analysesNominal rates reflect expected inflation (market interest rates are therefore "nominal" interest rates)The
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