Question

Birkenstock is considering an investment in a nylon-knitting machine. The machine requires an initial investment of $27,000, has a 5-year life, and has no residual value at the end of the 5 years. The company’s cost of capital is 10.87%. Known with less certainty are the actual after-tax cash inflows for each of the 5 years. The company has estimated expected cash inflows for three scenarios: pessimistic, most likely, and optimistic. These expected cash inflows are listed in the following table. Calculate the range for the NPV given each scenario.

Expected cash inflows Year Pessimistic Most likely Optimistic
A) $6,750 $ 9,250 $11,750
B)7,250 10,250 13,250
C)8,750 11,750 15,750
D)7,750 10,750 12,750
E)5,750 7,750 8,750

Answer 1

The range of NPV for Birkenstock's investment is the difference between the highest and lowest NPV values obtained by discounting the expected cash inflows for each scenario (pessimistic, most likely, optimistic) at the company's cost of capital and then subtracting the initial investment of $27,000.

Step-by-step explanation:

To calculate the range of the Net Present Value (NPV) for Birkenstock's investment in a nylon-knitting machine given the different scenarios of cash flows, we need to evaluate each scenario separately. The NPV is calculated by discounting the future cash flows back to the present value at the company's cost of capital and then subtracting the initial investment. In this case, the cost of capital is 10.87% and the initial investment is $27,000.

For each scenario, the NPV can be calculated using the formula:

NPV = (Cash Flow in Year 1 / (1 + r)) + (Cash Flow in Year 2 / (1 + r)^2) + ... + (Cash Flow in Year 5 / (1 + r)^5) - Initial Investment,

where r is the cost of capital.

Once we have the NPV for the pessimistic, most likely, and optimistic scenarios, the range of NPV can be determined by the difference between the highest and lowest NPV value obtained from the scenarios.