# Choice of Discount Rate

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1 Choice of Discount Rate Discussion Plan Basic Theory and Practice A common practical approach: WACC = Weighted Average Cost of Capital Look ahead: CAPM = Capital Asset Pricing Model Massachusetts Institute of Technology Choice of Discount Rate Slide 1 of 32 Choice of Discount Rate: Basic Theory The Principle Consequences Practice Application to Government Inflation Is Critical! Massachusetts Institute of Technology Choice of Discount Rate Slide 2 of 32 Page 1

2 Choice of DR: Principle DR should reflect rate at which money can increase in productive investments = productivity of capital An empirical definition -- answer depends on circumstances Are there good opportunities? What are they? If on desert island, no investments possible, DR = 0 Test: What is rate at which current investments are producing, at margin? Massachusetts Institute of Technology Choice of Discount Rate Slide 3 of 32 Example of Application (1 -- Opportunities) A person could invest up to \$ 3,000 in an enterprise to get 12% \$ 10,000 in saving account at 6% This person also has loans, and can repay up to: \$ 500 at store 18% \$ 5,000 for tuition 9% What are investment opportunities? Important to recognize that paying off a debt is a form of investment -- it leads to a similar increase in cash flow compared to new investment WHY IS THIS CORRECT??? Massachusetts Institute of Technology Choice of Discount Rate Slide 4 of 32 Page 2

3 Example of Application (2 -- Calculation) Investment Return % Projects Cumulative Investment Opportunities Cumulative Amount Invested What is the DR if person only has 400? 6500? Answer: (a) 18% (b) = alternative return of \$6500 = ( )/6500 = ~11% Massachusetts Institute of Technology Choice of Discount Rate Slide 5 of 32 Rate of Return Consequences of Principle DR peculiar to situation of decision-making unit depends on opportunities DR not a precise measure except in classroom examples, exact return difficult to obtain precisely; ± 1 or 2% quite acceptable DR interest rate paid repaying debt always one possible investment, so DR at least equals interest actually you borrow because: value of money > interest Since DR = minimum acceptable profitability, NPV > 0 indicates a good project (may not be best) Massachusetts Institute of Technology Choice of Discount Rate Slide 6 of 32 Page 3

4 DR Used in Practice A nice round number, generally recognition of imprecision in measurement For example see values US Government is using in 2007, at most 2 significant figures (See next slide and historical tables in Engineering Economy lecture) Where rate must be defended legally, as to regulatory groups - by precise formula not subjective illusory precision -- not accurate Research, industry reports indicate real profitability, with no inflation 10 to 15%/year worldwide Massachusetts Institute of Technology Choice of Discount Rate Slide 7 of 32 Discount rates by OMB Circ. A-94, Appendix C [Ref: Nominal Discount Rates. A forecast of nominal or market interest rates for 2007 based on the economic assumptions from the 2008 Budget are presented below. These nominal rates are to be used for discounting nominal flows, which are often encountered in lease-purchase analysis. Nominal Interest Rates on Treasury Notes and Bonds of Specified Maturities (in percent) 3-Year Year Year Year Year Year 5.1 Real Discount Rates. A forecast of real interest rates from which the inflation premium has been removed and based on the economic assumptions from the 2008 Budget is presented below. These real rates are to be used for discounting real (constant-dollar) flows, as is often required in cost-effectiveness analysis. Real Interest Rates on Treasury Notes and Bonds of Specified Maturities (in percent) 3-Year Year Year Year Year Year 3.0 Massachusetts Institute of Technology Choice of Discount Rate Slide 8 of 32 Page 4

5 Example of Corporate thinking B&W seeks an after tax return on assets of 25% if return on net assets was less than 15%, we would go into a fix or exit mode a rule that any new product had to meet a hurdle rate an internal rate of return (IRR) of 30% It s not going to come as any surprise that any new product was better than 30%. The problem is that managers knew which levers to tweak to project the required returns Source: /pg_4 CFO: Magazine for Senior Financial Executive, May 1998 Massachusetts Institute of Technology Choice of Discount Rate Slide 9 of 32 Application to Government Where does Government Money come from? Taxes: One of Government s possible investments is to reduce taxes Thus, from national perspective, Government DR should equal that of private sector (thus around 10% to 15%) Recall, DR to be used for economic investments. Many government actions not measured in money (e.g.: defense, justice,...) DR not appropriate to decide if schools should be built at all; is appropriate for choice of design Massachusetts Institute of Technology Choice of Discount Rate Slide 10 of 32 Page 5

6 US Govt base position on Discount rate (OMB Circular A-94, 1992 revised annually) 1. Base-Case Analysis. Constant-dollar benefit-cost analyses of proposed investments and regulations should report net present value determined using a real discount rate of 7 percent. This rate approximates the marginal pretax rate of return on an average investment in the private sector in recent years. [R de N note: statement about average return is not universally held] 2. Other Discount Rates. Analyses should show the sensitivity of the discounted net present value and other outcomes to variations in the discount rate. The importance of these alternative calculations will depend on the specific economic characteristics of the program under analysis. For example, in analyzing a regulatory proposal whose main cost is to reduce business investment, net present value should also be calculated using a higher discount rate than 7 percent. NOTE: This is pre 2000 version. Later ones indicate DR around 5%, as shown. Massachusetts Institute of Technology Choice of Discount Rate Slide 11 of 32 Discount Rate and Inflation Issue is Comparability the idea is to place all B, C on current basis of value Two factors Productivity, p % / year Change in purchasing power, i % / year Inflation, same item costs more each period Deflation, same item costs less each period Procedure depends on whether B, C stated in constant or changing purchasing power If constant: r = p this is real return If varying: r = p + i this is nominal return Massachusetts Institute of Technology Choice of Discount Rate Slide 12 of 32 Page 6

7 Examples: Which DR? p or (p + i)? 1) Build Bridge, Tolls \$1/car r = p + i Tolls unlikely to adjust with inflation Revenues are in nominal terms. If inflation were taken into account, they would be decreasing by i %/year in real terms 2) Build Hospital, Fee \$1000/bed/day r = p Rates here (in US) do adjust with inflation, therefore you get \$ equal to current \$. You do analysis using real revenues, that you expect will be adjusted upward according to inflation. Massachusetts Institute of Technology Choice of Discount Rate Slide 13 of 32 Examples: Which DR? p or (p + i)? 3) Buy New Furnace, Save 2000 gallons fuel / year r = p So long as fuel costs vary with inflation Same rationale as above. You do the analysis in real terms, and use the real DR. If you had tried to account for inflation in your estimates of future savings (thus looking at nominal returns), you would want to use a nominal DR. Note that US Government publishes DR for both real and nominal cases (In OMB Circular A-94, mentioned earlier). Massachusetts Institute of Technology Choice of Discount Rate Slide 14 of 32 Page 7

8 US Government Guidance on Inflation 7. Treatment of Inflation. Future inflation is highly uncertain. Analysts should avoid having to make an assumption about the general rate of inflation whenever possible. a. Real or Nominal Values. Economic analyses are often most readily accomplished using real or constant-dollar values, i.e., by measuring benefits and costs in units of stabl purchasing power. (Such estimates may reflect expected future changes in relative prices however, where there is a reasonable basis for estimating such changes.) Where future benefits and costs are given in nominal terms, i.e., in terms of the future purchasing powe of the dollar, the analysis should use these values rather than convert them to constant dollars as, for example, in the case of lease-purchase analysis. Nominal and real values must not be combined in the same analysis. Logical consistency requires that analysis be conducted either in constant dollars or in terms of nominal values. This may require converting some nominal values to real values, or vice versa. Massachusetts Institute of Technology Choice of Discount Rate Slide 15 of 32 Choice of DR Critical DR indicates if any investment is minimally acceptable Ranking of investments changes with DR which are: less capital intensive shorter lives (example: VW vs. Mercedes) Choice of DR very political. Low rates favored by project enthusiasts ; believers in government control DR difficult to define accurately! Massachusetts Institute of Technology Choice of Discount Rate Slide 16 of 32 Page 8

9 Part 2 : A Common Practical Method Weighted Average Cost of Capital (WACC) Massachusetts Institute of Technology Choice of Discount Rate Slide 17 of 32 How do Companies Estimate Cost of Money? Weighted Average Cost of Capital (WACC) is a common starting point. WACC is based on average cost of money an aggregate measure, estimated returns expected by investors, NOW BUT, limitations on use as Discount Rate May represent a minimum rate Does not reflect Opportunity Cost Does not account for RISK of project Massachusetts Institute of Technology Choice of Discount Rate Slide 18 of 32 Page 9

10 Issues to Address Now How do companies raise money? What do investors expect? Mechanics of Calculations for WACC Uses and Mis-uses of WACC Treatment of risk comes later Massachusetts Institute of Technology Choice of Discount Rate Slide 19 of 32 How do Companies Raise Money? Debt -- they borrow money General bank loans and bond issues Company uses immediate proceeds, and repays over time with interest Equity -- they sell shares in the company Company uses proceeds Shareholders gain ownership in the company Shareholders expect future earnings and growth Note: Most trades of stock occur in secondary market, company gets money only once Massachusetts Institute of Technology Choice of Discount Rate Slide 20 of 32 Page 10

11 What do Investors Expect? Holders of Debt and Equity expect to make money Explicit for Debt: Equals interest rate Implicit for Equity: Investors anticipate combination of growth and earnings, realized as dividends or higher stock prices To Company, these expectations represent cost of money Either repay loan with interest Or give up part of future earnings and stock growth Massachusetts Institute of Technology Choice of Discount Rate Slide 21 of 32 What Affects Cost of Money? Confidence in Company Either interest company pays to borrow Or value of Shares in company Factors that Affect Confidence Start-up vs. Well-established company Risky vs. Safe Industries or Regions of World Weak vs. Strong company (financially or strategically) Other? Massachusetts Institute of Technology Choice of Discount Rate Slide 22 of 32 Page 11

12 Calculating WACC (1) Basic Idea: Average Expected Return First-order formula: WACC = R for equity (Equity %) + R on Bonds (Bond %) Return on Equity difficult to estimate Estimate future growth and earnings, based on track record (if any) and prospects Examine historical returns for similar companies in similar situations More sophisticated formulas take into account local tax issues, not relevant to current presentation of principle Massachusetts Institute of Technology Choice of Discount Rate Slide 23 of 32 Simple Example: Start-up Company Hypothetical case First money raising effort No outstanding debts Equity: Will sell \$10 million worth of shares; estimated return = 25% Debt: Will issue \$5 million in debt, will pay 10% interest a year Note: Bonds cheaper than stock -- WHY? Total money raised = debt + equity = \$15 million WACC =? = 25% (2/3) + 10% (1/3) = 20 % Massachusetts Institute of Technology Choice of Discount Rate Slide 24 of 32 Page 12

13 Calculating WACC (2) For Established Companies Procedure similar in concept, more difficult to do because of variety of securities Estimated debt and equity returns estimated from current MARKET prices of securities A \$1000 bond paying 10% on face value may, for example, be selling at \$1200 so that its actual return = (10%) 1000/1200 = 8.33% Total value of Equity = market capitalization = (share price)(number of shares outstanding)l Massachusetts Institute of Technology Choice of Discount Rate Slide 25 of 32 Calculating WACC (3) WACC = r equity (E/V) + r debt (D/V) D, E = current market value of debt and equity V = D + E = sum of debt and equity value r debt = current rate of borrowing r equity = current expected rate of return on stock Again, return on equity includes earnings and growth Massachusetts Institute of Technology Choice of Discount Rate Slide 26 of 32 Page 13

14 Simple Example: Established Company Company has a proven record Current market value of its securities Debt = 50 million; Annual payments = 4 million Stock = 100 million; expected return = 20% WACC = Equity R (Equity %) + Bond R (Bond %) =??? = 20% (2/3) + 8% (1/3) = 16% Represents Current Average: Investor expectations (if stock safer => lower return) Cost of capital company could expect Massachusetts Institute of Technology Choice of Discount Rate Slide 27 of 32 Potential Use and Mis-Use of WACC as DR Uses as a Metric Performance: cost of money over time Comparison: within and between companies in industry Use as a reasonable discount rate if project is an average investment for company example: the 10,000th McDonald store Often, WACC is an inappropriate discount rate Many projects not average (some more risky than others) WACC is cost of money, not necessarily opportunity cost Will explore these issues more deeply later on Massachusetts Institute of Technology Choice of Discount Rate Slide 28 of 32 Page 14

15 WACC Summary WACC is an average cost of raising money; proportional average of investor expectations Useful metric for some activities A starting point for project analyses HOWEVER, use WACC as DR with caution Is the investment typical for the organization? If not, WACC is probably not applicable Massachusetts Institute of Technology Choice of Discount Rate Slide 29 of 32 Part 3 Look Ahead Capital Asset Pricing Model (CAPM) Massachusetts Institute of Technology Choice of Discount Rate Slide 30 of 32 Page 15

16 CAPM Overview CAPM adjusts discount rate for risk. Basic idea: More risk => more return Riskfree rate, r f Risk measure Rate= r f + c (risk measure) Will be covered when we get to Uncertainty Massachusetts Institute of Technology Choice of Discount Rate Slide 31 of 32 Summary for today Choice of DR rate not obvious Principle is clear but application not easy Difficult to calculate precisely Easy to manipulate Motivation to manipulate great WACC is a common approximation But not fully satisfactory And we also need to incorporate risk! Massachusetts Institute of Technology Choice of Discount Rate Slide 32 of 32 Page 16

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