You have the opportunity to invest in a project which would require you to pay $50,000 now and another $100,000 in one year,with the promise of a return of $300,000 four years from now.You don't have the cash,but your rich uncle is willing to lend you the money,and would charge you interest at j₁ = 8% for the first 2 years and j₁ = 12% thereafter.What is your net present value (NPV)for this investment?

Question

Quizplus · Accepted Answer

To calculate the NPV, we need to discount all cash flows to the present value using the given interest rates. The cash outflows are $50,000 now and $100,000 in one year. The cash inflow is $300,000 in four years. The interest rate is 8% for the first two years and 12% thereafter.1. The present value (PV) of $50,000 paid now is simply $50,000.2. The PV of $100,000 paid in one year, discounted at 8%, is $100,000 / (1 + 0.08) = $92,592.59.3. The PV of $300,000 received in four years needs to be discounted back to the present. For the first two years, we use 8%, and for the next two years, we use 12%. So, the discount factor for the first two years is (1 + 0.08)^2 = 1.1664, and for the next two years at 12%, it is (1 + 0.12)^2 = 1.2544. The combined discount factor is 1.1664 * 1.2544 = 1.4631936. Thus, the PV of $300,000 is $300,000 / 1.4631936 = $205,052.63.The NPV is the sum of all present values of cash inflows minus the sum of all present values of cash outflows:NPV = $205,052.63 - ($50,000 + $92,592.59) = $205,052.63 - $142,592.59 = $62,460.04.The closest answer provided is $62,447, which accounts for slight variations in the calculation method or rounding.

You Have the Opportunity to Invest in a Project Which