Question

cash flows per assessed outcomes cash flows. Taxes are not considered as this is assumed to be a not-for-profit business entity.

Pessimistic Most Likely Optimistic

Investment 80 80 80

Revenues 40 40 40

Costs 20 15 10

The revenues and costs occur in perpetuity. The cost of capital (WACC) for your project is 8 percent. Conduct a sensitivity analysis of the project's NPV to variations in costs base on the 3 outcomes above, that is Pessimistic, Most Likely, and Optimistic.

Answer 1

NPV for a time period of n can be calculated using the formula: -C0+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n; where C is the initial investment, C1 to Cn are cash inflows and r is the required rate of return.

Given that cashflows are C for perpetuity. Present value of a cashflow of C till perpetuity with a discount rate of r is C/r.

So, NPV formula will become: NPV= -C0+ C/r.

Let us consider each scenario and calculate NPV for each one of them.

Pessimistic:

In Pessimistic Scenario, annual cashflows will be $40-$20= $20.

So, NPV= -80+ (20/8%)= -80+250= $170.

Most Likely:

In Most likely scenario, annual cashflows will be $40-$15= $25.

So, NPV= -80+ (25/8%)= -80+312.5= $232.50

Optimistic:

In Optimistic scenario, annual cashflows will be $40-$10= $30.

So, NPV= -80+ (30/8%)= -80+375= $295.

From the calculations, NPV is very sensitive to cost base. As expected cost decreases, NPV increases rapidly.