I am trying to figure out how to do this problem:
scenarios (projected $90,000 annual cash inflow vs. projected $70,000 annual cash inflow). Note, 5 years of $90,000 per year equals $450,000 of total cash received over the duration of the project ($350,000 for 2nd project). But, due to the time value of money (i.e. inflation) that $450,000 cash received is not worth that amount in today's dollars.
You first need to determine what the PV of the cash inflows are for each of the two projects. Then, you need to determine the Net Present Value of that project (PV Cash Inflows - Cost of Investment). Once you have the NPV of the two projects AND what actually occurred, then use the bonus structure of the company to calculate the manager's bonus for each of the two projects: (NPV Actual - NPV Project #1) * 10%.
To solve this problem, you need to follow these steps:
1. Calculate the Present Value (PV) of the cash inflows for each project:
- PV is a financial concept that takes into account the time value of money, meaning that money received in the future is worth less than the same amount received today.
- To calculate the PV, you need to discount the future cash inflows using an appropriate discount rate. The discount rate can be determined based on factors such as the projected rate of inflation or the cost of capital.
- Let's assume a discount rate of 5% for this example. You would discount each cash inflow by 5% using a formula like: (Cash Inflow / (1 + Discount Rate)^Number of Years).
2. Determine the Net Present Value (NPV) of each project:
- NPV is a measure of the profitability of an investment, taking into account both the cash inflows and the initial investment cost.
- To calculate the NPV, subtract the initial investment cost from the sum of the PV of the cash inflows.
- Let's say the initial investment cost for both projects is $300,000. Calculate the NPV for Project #1 by subtracting $300,000 from the sum of the PV of the cash inflows. Repeat the same process for Project #2.
3. Compare the NPV of the two projects with the actual outcome:
- You mentioned that one project had a projected cash inflow of $90,000 per year and the other had a projected inflow of $70,000. Let's assume the actual cash inflows for Project #1 were $80,000 per year and for Project #2, they were $60,000 per year.
- Calculate the NPV using the actual cash inflows for each project in the same way as in step 2.
4. Calculate the manager's bonus for each project:
- To determine the manager's bonus, subtract the NPV of Project #1 from the actual NPV and multiply the result by 10%.
- Repeat the same process for Project #2.
By following these steps, you can determine the PV, NPV, and manager's bonus for each project based on the projected and actual cash inflows.