Question

The Bursar at Tain came up with new library project that requires an initial investment of $100 and has the following cash flow estimates (ignore taxes):

Pessimistic Most Likely Optimistic

Revenues $15 $20 $25

Costs 8 8 8

Suppose the cash flows will last forever and the opportunity cost of capital is 10%. Conduct a sensitivity analysis of the project’s NPV to variations in revenues. What is the NPV in the pessimistic scenario?

Answer 1

In the pessimistic scenario, the NPV of the project is $6.36 million.

Step-by-step explanation:

The Net Present Value (NPV) of a project is a measure of its profitability, and it helps determine whether the project is worth undertaking. To conduct a sensitivity analysis of the project's NPV to variations in revenues, we need to calculate the NPV for different revenue scenarios. In the pessimistic scenario, the revenues are $15. The formula to calculate NPV is:

NPV = (Revenues - Costs) / (1 + Opportunity cost of capital)

Substituting the values, we have:

NPV = (15 - 8) / (1 + 0.10) = 7 / 1.10 = $6.36 million.

Therefore, the NPV in the pessimistic scenario is $6.36 million.

Answer 2

The NPV in the pessimistic scenario for the new library project is negative $30, calculated by subtracting the initial investment from the present value of perpetuity cash flows.

Step-by-step explanation:

To calculate the Net Present Value (NPV) in the pessimistic scenario for the new library project, we start by finding the net cash flow: subtract the costs from the revenues in the pessimistic case, which are $15 and $8 respectively, to get a net cash flow of $7. Since the cash flows are expected to last forever, we can use the perpetuity formula to calculate the present value of these cash flows. The perpetuity formula is PV = C / r, where C is the cash flow, and r is the opportunity cost of capital. In this case, C = $7 and r = 0.10 (10%). Therefore, the NPV of the project in the pessimistic scenario is $7/0.10, or $70. We must then subtract the initial investment of $100 to find the NPV: $70 - $100, which gives us a NPV of -$30. Thus, the NPV in the pessimistic scenario is negative $30.