The Maritime Cannery Company is considering a new machine that costs $100,000. It will last three years and management feels there are two possible cash flow possibilities each year, depending on whether the country is in recession or not. Year 1: 70% chance of $40,000 and 30% chance of $20,000; Year 2: 60% chance of $50,000 and 40% chance of $30,000; Year 3: 80% chance of $60,000 and 20% chance of $20,000. What is the expected net present value of the new machine if the company's discount rate is 6%?

Question

Quizplus · Accepted Answer

To calculate the expected net present value (NPV), first, we find the expected cash flows for each year by multiplying each cash flow by its probability and then summing these products. Next, we discount these expected cash flows back to their present value using the discount rate of 6%. Finally, we subtract the initial investment of $100,000 to find the NPV.Year 1 expected cash flow: (0.7 * $40,000) + (0.3 * $20,000) = $28,000 + $6,000 = $34,000Year 2 expected cash flow: (0.6 * $50,000) + (0.4 * $30,000) = $30,000 + $12,000 = $42,000Year 3 expected cash flow: (0.8 * $60,000) + (0.2 * $20,000) = $48,000 + $4,000 = $52,000Present value of Year 1 cash flow: $34,000 / (1 + 0.06)^1 = $32,075.47Present value of Year 2 cash flow: $42,000 / (1 + 0.06)^2 = $37,358.49Present value of Year 3 cash flow: $52,000 / (1 + 0.06)^3 = $43,681.82Total present value of cash flows = $32,075.47 + $37,358.49 + $43,681.82 = $113,115.78NPV = Total present value of cash flows - Initial investment = $113,115.78 - $100,000 = $13,115.78Rounded to the nearest dollar, the NPV is approximately $13,116, making the correct answer D.

The Maritime Cannery Company Is Considering a New Machine That