Flow-to-Equity Approach Calculate Free Cash Flow to Equity Compute their NPV using r E as a discount rate.

Expected Free Cash Flows to Equity from Avcos RFX Project (continuing last lecture example))

Alternative way to compute FCFE: The same NPV as with WACC and APV!

Project-Based Cost of Capital What if the project changes either the leverage of the firm or its risk or both?

Taking into account the projects risk We need to compute Assume r D is known. Then we need to compute r E But how to compute r U ? But how to compute r U ? Pure-play technique. Find firms in the market (comparables) whose whole business is similar to your project, and take their r U

These firms may be levered, then you have to find their r U first Example: Comparable 1: r E =12%, r D =6%, D/(E+D)=40% r U =9.6% Comparable 1: r E =12%, r D =6%, D/(E+D)=40% r U =9.6% Comparable 2: r E =10.7%, r D =5.5%, D/(E+D)=25% r U =9.4% Comparable 2: r E =10.7%, r D =5.5%, D/(E+D)=25% r U =9.4% Average r U =9.5% Average r U =9.5%

Assume the leverage of the firm before the project was 1, and its cost of debt was = 6% (see last lecture). If we assume that both things stay the same, we obtain Instead we could directly use (from the two formulas above) where d is D/(E+D) – the projects debt-to-value ratio

Note: sometimes you dont know r E and r D of the comparable firms, but know (or can estimate) their β E and β D. Then you simply use CAPM to find r E and r D, or you can directly compute And then use CAPM to determine r U. In general, your project may have D/(E+D) different from the rest of your firm. Then in the formulas in the previous slide you need to use the projects D/(E+D). See example (next two slides)

Example: Computing Divisional Costs of Capital

Determining a projects D/(D+E) (incremental leverage of a project) Let d p =D p /(D p +E p ) is the debt-to-value ratio you want for your project Compute the projects PV using WACC (assuming you know the projects risk, i.e. r U, and r D, you can always find its r E ) Then E p = PV p – D p, and d p =D p /PV p you can find D p such that you achieve your desired d p If you need to achieve certain target D/(D+E) for your firm, then you need to solve simultaneously: (D old +D p )/(D old +D p +E old +E p ) = D/(D+E) (D old +D p )/(D old +D p +E old +E p ) = D/(D+E) D p +E p PV p = dicounted FCF using WACC D p +E p PV p = dicounted FCF using WACC WACC is determined by d p =D p /(D p +E p ) WACC is determined by d p =D p /(D p +E p )

Real Options Approach to Capital Budgeting Managers are always faced with various options (start a project or not, expand the business or not, terminate or not, etc…) the costs and benefits of which may change in time depending on the realization of some uncertainty Thus managers should not stick to a certain strategy once and for all. Rather they should change it according to the circumstances How to account for this flexibility?

Failure of traditional capital budgeting Option to defer investment: The manager has an option to defer building a plant for a year. If he chooses to defer, after a year he either may or may not find it profitable to build a plant What is the value of this flexibility?

Setup At t = 0 investment outlay (required inv-t) I 0 = 104 At t = 1: If the market moves up (prob. q) the plant generates V + = 180 If the market moves up (prob. q) the plant generates V + = 180 If the market moves down (prob. 1-q) the plant generates V – = 60 If the market moves down (prob. 1-q) the plant generates V – = 60 The manager has a choice: To invest at t = 0 and get 180 with prob. q and 60 with prob 1-q, or To invest at t = 0 and get 180 with prob. q and 60 with prob 1-q, or To wait until t = 1 and build a plant only in the good state of nature (i.e. if the market has moved up). But then the required investment is I 1 = Thus, then he gets To wait until t = 1 and build a plant only in the good state of nature (i.e. if the market has moved up). But then the required investment is I 1 = Thus, then he gets E + = 180 – I 1 = in the good state E + = 0 in the bad state.

Assume q = 1/2 Risk free rate: r = 8% There exist a risky security (twin security), which payoffs are perfectly correlated with the payoffs of the project: S + = 0.2*V + = 36, S – = 0.2*V – = 12 which payoffs are perfectly correlated with the payoffs of the project: S + = 0.2*V + = 36, S – = 0.2*V – = 12 which price S = 20 which price S = 20 rate of return k = (½* S + + ½* S – )/S = 20% rate of return k = (½* S + + ½* S – )/S = 20% How much a manager would pay for this investment opportunity (what is the NPV of the project)? Setup (cont-d)

No flexibility case: Assume theres no option to defer Assume theres no option to defer The traditional DCF technique yields: The traditional DCF technique yields: V 0 = (qV + + (1-q)V - )/(1+k) = (0.5* *160)/(1+ 0.2) = 100 NPV passive = V 0 - I 0 = 100 – 104 = - 4 Reject the project! Reject the project! V=100, S=20 I 0 =104 V + =180, E + =67.68 S + =36 q= V - =60, E - =0 S - =12 I 1 =112.32

Using probabilities q and the rate of return on the twin security k = 20% we can discount cash flows, assuming we wait until t=1: E 0 = (qE + + (1-q)E - )/(1+k) = > 0 Apparently we should wait instead of rejecting the project right away. This strategy yields NPV > 0! But is this a correct estimation? In the risk- neutral world, where k would be the risk-neutral rate – yes. Otherwise – no! Now lets account for flexibility

Correct Way to Value This Opportunity The opportunity to delay is a call option on the plant with an exercise price I 1 So we can use the same technique as with financial options to value it: replicating portfolio (risk neutral valuation)

Consider a strategy: Buying N shares of the twin security S, partly financed by borrowing of amount B at the riskless rate r = 8% We can always pick such N and B that: E + = NS + - (1+r)B E - = NS - - (1+r)B Thus, we can replicate the payoffs from the project with this portfolio the arbitrage argument tells us that the project value must be the same as the price of the portfolio: E 0 = NS - B

N = (E + - E - )/(S + - S - ) B = (NS - – E - )/(1+r) We obtain the risk-neutral valuation: E 0 = NS – B = (pE + + (1-p)E - )/(1+r) where p = ((1 + r)S – S - )/(S + - S - )= (1 + r – d)/(u - d) Notice: q does not enter the expression for E 0 Why? Because q is already incorporated in the price of the twin security S. pE + + (1-p)E - can be viewed as Certainty Equivalent of the random payoff at t = 1.

For our project: p = 0.4, E 0 = The value of the option to delay investment: E 0 – NPV passive = – (-4) = If you consider that without flexibility you would not actually invest then the value of the option would be E 0 = – this is how much you would agree pay to have the flexibility Notice that when we used the actual probabilities q and the rate of return on the twin security k = 20% to discount cash flows we got E 0 = (qE + + (1-q)E - )/(1+k) = > – it was an overestimation