Part 1 - AL-Tax

We can see that the second term in equation (2.19) is positive, showing that thefloor increases the present value of returns by cutting off the downside potential.Then:p0pɶ1γγp0E[ NPV ] .ρδπα γρδπα For the marginal investment, the return must just cover its cost, implying that α 0and p 0 p˜. It follows that:1 pE[ NPV] γ ɶ,γρδπ where the expected NPV is higher than the normal NPV because the presence ofrisk increases the cost of the irreversible investment. To be profitable, the investmentmust pay, in this case, the cost of capital incremented by the risk of the environment.In Pindyck (1991), this overcharge is associated with the value of an investmentoption. Delaying the investment is costly because it retards the realizationof profits, but it is beneficial since it allows the company to watch the evolution ofreturns in the industry. Observe that the standard deviation of the returns affects thenegative roots of the fundamental quadratic. Differentiating totally expression φ(ξ),∂φ∂ξ∂φ 0∂ξ∂σ ∂σand evaluating it at γ, ∂φ/∂ξ 0, ∂φ/∂σ 0, and therefore ∂ξ/∂σ 0 as σincreases, γ decreases and (1 γ)/γ increases. The greater the amount of uncertaintyover future values of p, the larger the excess return the firm will demandbefore it is willing to make the irreversible investment. Note also that when σ : 0,(1 γ)/γ : 1 and E[NPV] : NPV, and all other results will tend towards the deterministiccase presented earlier. Defining (1 γ)/γ Γ, the expected METR is now:Γpɶ rE[ METR ] ,ΓpɶChapter 2which is higher than the METR and increases with the level of risk. The intuitionbehind this is that when the uncertainty on the return of the investment goes up,the value of the waiting option also increases because it is likely that returns willbe smaller in the future, and the firm will only invest in a more profitable expectedproject. If a competitive firm enters when the returns are normal (p˜), it would justbreak even at the instant when entry takes place, and it would obtain lower returns27