The required investment is $1 million, and anticipated year-end cash flows are as follows:
Year 1 2 3 4
Cash flow $300,000 $400,000 $500,000 $200,000
Compute the net present value rate of return using a 10 percent required return. What should be decision rule in this example.
To compute the net present value (NPV) rate of return for this investment, you will need to discount each year's cash flow to determine the present value. The formula to calculate NPV is:
NPV = (Cash Flow Year 1 / (1 + r)^t1) + (Cash Flow Year 2 / (1 + r)^t2) + (Cash Flow Year 3 / (1 + r)^t3) + (Cash Flow Year 4 / (1 + r)^t4) - Initial Investment
Where:
- Cash Flow Year X represents the cash flow expected at the end of year X
- r represents the required return rate (10% in this case)
- tX represents the number of years from the present to year X
Let's calculate the NPV for this example:
NPV = ($300,000 / (1 + 0.10)^1) + ($400,000 / (1 + 0.10)^2) + ($500,000 / (1 + 0.10)^3) + ($200,000 / (1 + 0.10)^4) - $1,000,000
Simplifying the expression:
NPV = $300,000 / (1.10) + $400,000 / (1.10)^2 + $500,000 / (1.10)^3 + $200,000 / (1.10)^4 - $1,000,000
NPV = $272,727.27 + $330,578.51 + $373,899.58 + $132,231.40 - $1,000,000
NPV ≈ $109,436.76
Now, to determine the decision rule based on NPV, compare the calculated NPV to zero:
- If NPV > 0: The investment project is considered good as it generates more cash inflow than its initial investment. Therefore, you should undertake the investment.
- If NPV = 0: The investment project's cash inflows exactly match its initial investment. In this case, the decision is subjective and may depend on other qualitative factors.
- If NPV < 0: The investment project is considered unfavorable as it generates less cash inflow than its initial investment. Therefore, you should reject the investment.
So, the decision rule in this example is to undertake the investment since the calculated NPV of $109,436.76 is greater than zero.