Use the discount factor to find the NPV of both projects using the following table.Project/Year 0 1 2 3Project A Cash Flow -100 50 40 30Project B Cash Flow -100 30 45 50Discount factor (10%)Discounted Cash Flow of ADiscounted Cash Flow of BNPV of A (10%) =NPV of B (10%) =
Question
Use the discount factor to find the NPV of both projects using the following table.Project/Year 0 1 2 3Project A Cash Flow -100 50 40 30Project B Cash Flow -100 30 45 50Discount factor (10%)Discounted Cash Flow of ADiscounted Cash Flow of BNPV of A (10%) =NPV of B (10%) =
Solution
The Net Present Value (NPV) is calculated by summing the present values of the individual cash flows. The present value of each cash flow is calculated by multiplying the cash flow by the discount factor for that time period. The discount factor is calculated as 1 / (1 + r)^n, where r is the discount rate and n is the number of periods.
The discount factor for a 10% rate is as follows:
- Year 0: 1 / (1 + 0.10)^0 = 1.000
- Year 1: 1 / (1 + 0.10)^1 = 0.909
- Year 2: 1 / (1 + 0.10)^2 = 0.826
- Year 3: 1 / (1 + 0.10)^3 = 0.751
Now, we can calculate the discounted cash flows for each project:
Project A:
- Year 0: -100 * 1.000 = -100
- Year 1: 50 * 0.909 = 45.45
- Year 2: 40 * 0.826 = 33.04
- Year 3: 30 * 0.751 = 22.53
Project B:
- Year 0: -100 * 1.000 = -100
- Year 1: 30 * 0.909 = 27.27
- Year 2: 45 * 0.826 = 37.17
- Year 3: 50 * 0.751 = 37.55
Finally, we sum these values to find the NPV for each project:
NPV of Project A (10%) = -100 + 45.45 + 33.04 + 22.53 = 1.02 NPV of Project B (10%) = -100 + 27.27 + 37.17 + 37.55 = 1.99
So, the NPV of Project A at a 10% discount rate is 1.02 and the NPV of Project B at a 10% discount rate is 1.99.
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