lecture3

Lecture 3:CAPITAL BUDGETING UNDER UNCERTAINTY : 

Lecture 3:CAPITAL BUDGETING UNDER UNCERTAINTY CORPORATION FINANCE Krishnamurthy Subramanian IFM Vashi 2007

Risk : 

We know how time delays affect value of cash-flow C today: We now want to take into account the effect of risk on the market value of a project Consider following cash-flow: What is the market value of such a project? Risk $2M $0 .5 .5

Example: IPO : 

Example: IPO INTOX is a biotech start-up, fully owned by prof. X, with one project. In a week, results of clinical trial will determine whether Project is successful (prob .5) Project is a failure (prob .5) Prof X decides to do an IPO today. What is market value of INTOX? $2M $0 .5 .5

Pricing Risk : 

Pricing Risk First idea: take expected value of cash-flows (it means, weight by probabilities) Second idea: “discount” by risk premium to take aversion to risk into account. We prefer a dollar “for sure” than a dollar “in expectations”. p is the “risk premium”

Time+Risk : 

Time+Risk Now assume payoffs occur in one year: The expected return required by the market for this project is 1+Return=EC/V=1+r+p 2M 0 .5 .5 Value V Discount due to time delay Discount due to risk

NPV with Risk : 

NPV with Risk Take expected cash-Flows Discount using risk-premium ??we need a method to find the risk premium We are going to use the CAPM

Looking at the Data : 

Looking at the Data • Common stock have higher returns than government bonds. • Common stock have higher standard deviation of returns than government bonds. Assets with higher average risk tend to have higher expected return.

The risk-premium : 

The risk-premium Where does p come from? How big is it? It depends on nature of the risk (diversifiable or not): 2M 0 .5 .5 1 2 2M 0 .5 .5 1 2 4M 0 .25 .25 2M .5 Same expectation but less risky Another project INTOX Assuming projects are independent

Systematic vs. diversifiable risk : 

Systematic vs. diversifiable risk What happens with many independent projects? You would get 2M almost surely. ? The risk disappears by combining projects! Imagine there are on the market a lot of firms facing lotteries similar to INTOX and independent. Then the risk-premium should be zero P=0, Value=EC=1M Why? Because this risk can be eliminated by investors by investing only a little in each company: diversification eliminates the risk. Does it mean that risk doesn’t affect prices? NO! ??But only “systematic risk” affect prices, i.e. risk common to all firms.

Slide 10: 

2M 0 .5 .5 The risk-premium p should be : Zero if risk is independent from market return Bigger when the success of project is correlated with performance of market as a whole. Smaller if this project tends to be successful when market portfolio performs poorly. The CAPM captures this idea A fully diversified portfolio has expected return rM ?Only risk that still appears in the “market portfolio”, M, matters for the risk-premium of a project MARKET RETURN rM

The CAPM : 

The CAPM Only undiversifiable risk matters return on asset i return on market portfolio Risk free rate

Back to our problem:Evaluating a project : 

Back to our problem:Evaluating a project Question: Suppose your firm is contemplating a new project, using assets A. Should it use the firm’s expected return as the discount rate? No: it should discount with the return required by project. We are going to describe the method to find this return.

Computing a project’s discount rate : 

Computing a project’s discount rate Find discount rate from CAPM: rA = r + ?A (rM-r) rA is the return that is appropriate for the risk of the project’s cash flows. Expected return on an asset has 3 parts 1. Risk-free rate 2. Market price of risk = rM - r 3. asset's beta with the market.

Risk-free rate, r : 

Risk-free rate, r In principle, we should try to use the risk free rate that corresponds to the horizon of the cash flow. • For short term cashflows the risk free rate is the rate of return on T-bills. • For longer term cashflows, the risk free rate is the yield on a T- bond with the appropriate maturity. In practice, we often assume that the yield curve is (approximately) flat: using T-Bill is ok. If we use different rates for different horizons to account for yield curve, we also need to adjust the market risk premium – about 1 percent lower when we use long T-bonds.

Market risk premium, rM-r : 

Market risk premium, rM-r In principle, should use the expected risk premium for the value weighted entire universe of assets. We usually use the historic average of the difference between the return on the market index (value weighted NYSE/AMEX/NASDAQ, S&P 500) and the risk free rate taken over a long horizon (e.g. 1926-1993). This is about 8% over T-bills and about 7% over T-bonds.

ASSET BETA : 

ASSET BETA When we value a project, we focus on the cash flows produced by the project’s assets If we are using the CAPM to value cash flows, we care about the covariance of the returns produced by the asset with the market. This is the asset beta. Consider a firm about to undertake a project. The project's cash flows may have different risks from the firm's cash flows. Therefore, the project beta is not the asset beta of the firm. Moreover, the asset beta of a firm is not simply its equity beta, because of debt. (equity beta includes financial risk). How do we obtain a beta for a project we are just starting (which does not have same risk as company in total)?

Slide 17: 

A C B We want to value A: Biotech project Big Pharma company OUR PROBLEM The equity beta of the pharma company is not the right benchmark (it’s mostly not biotech)

Identical Twin Method: : 

Identical Twin Method: Find firms traded in the market that are in same line of business as the project. They should not be involved in any other type of business (“pure plays”). The asset beta of a pure play is the same as the asset beta of the project you are considering. Now, our job is: Getting assets beta of the pure plays: You can find the betas for these companies by looking them up in Value Line, Merrill Lynch Beta Book, BARRA, etc, or by running a regression for these companies to find beta. Problem: These reported betas are usually betas for the equity of the company. We need to translate from equity beta to asset beta (this process is called unlevering the beta)

How do we find ßA? : 

How do we find ßA? A’ C’ B’ Find the “twins” (firms running exclusively projects similar to A). Find their equity beta. Get their assets beta by “unlevering” equity betas Take an average of these asset betas A C B We want to value A: Biotech project Pharma company Look at Biotech companies

Asset returns vs. Equity Returns : 

Asset returns vs. Equity Returns Rate of return demanded by market to invest in the company assets, rA. This rate reflects the riskiness of the cash flows generated by existing operating assets. Since cash-flows serve both debt and equity, rA is different from the expected return of equity. rD (expected return on debt) rE (expected return on equity) rA (expected return on assets)

Relation among rA, rD, rE: : 

Relation among rA, rD, rE: Suppose you buy a portfolio of all the equity and debt of the firm. ?expected return is: rA reflects business risk only rE reflects both business and financial risk ?Same result with betas: ?to get the beta of firm’s assets, you have to “unlever” the beta of equity, to eliminate financial risk

Slide 22: 

To calculate asset beta we need the value of debt and equity, and the debt and equity betas. E = Price per share * # of shares. (common stock) D = Market value of outstanding debt. Often we will use book value of debt as an estimate of the market value. In practice, we will usually group together different kinds of debt, along with other debt-like liabilities such as preferred stock. ?E is obtained from a “beta” book or is calculated directly from regression analysis ?D is more difficult to get…

Getting ?D: 2 ways : 

Getting ?D: 2 ways Estimate it from past returns: If we have time series for rD we can regress the return on debt on the market and get an estimate of ?D. Problem: very imprecise measurement; multiple classes, infrequent trading, illiquid. 2) Use beta obtained from similar rated debt or use the following crude approximations: For short-term debt in a company with investment grade (BBB or higher) rating, ?D = 0 For short-term, non-investment grade debt, ?D is 0.20 – 0.25 For long-term, investment grade debt, ?D is 0.20 – 0.25 For long-term, non-investment grade debt, ?D is 0.40 – 0.45 Ratings can be estimated (if not directly available) by comparing interest coverage, debt to capitalization, return on invested capital, growth rate, and other ratios with the ratios of rated fi

EXAMPLE : 

EXAMPLE It is 1982. General Conglomerates wants to evaluate an oil exploration project proposed by the manager of its aviation division. What rate of return should it use to evaluate the project? Cannot use General Conglomerates' beta or the beta of aviation firms. Get beta for oil exploration firms. Assume zero debt beta for these firms. For which companies is the assumption of a zero debt beta probably incorrect?

EXAMPLE (cont.) : 

EXAMPLE (cont.) In 1982, r= 8%. Using rM-r = 8%, the appropriate discount rate for an oil exploration project is: rA = 8% + 1.28 (8%) = 18.24%.

Robustness Checks : 

Robustness Checks Sensitivity analysis What is the impact of small changes in discount rate? Run best-case/worst-case for cash-flows and discount rate: it gives you an “optimistic” and a “conservative” valuation. Calibration: use info in market prices. Using beta is looking backward. Instead, you can look forward. Take analysts forcasts of CF of companies in same industry. Then you can do reverse ingeneering: Given the market value of these companies, what is the discount rate implied by these forcasts? How does it compare to what CAPM gave you? Valuation by Multiples multiply estimated earnings of project by price earning ratio of a comparable firm.

Summary : 

Summary Lesson from asset pricing: if investors are diversified (an assumption of the CAPM), only systematic risk is priced A project’s cost of capital is not necessarily the cost of capital of the company undertaking the investment To get the asset beta of a company, you have to “unlever” its equity beta. To estimate the asset beta of a project, average the asset beta of its “identical twins” (firms traded in the market that are in the same line of business as the project). Despite the evidence on inefficient markets, the CAPM is still a good model to use for capital budgeting