Assume a business is deciding whether to invest in a new project that is projected to generate profits of $90,000 each year for the next three years. The project start-up costs are $225,000. a. If the business nominally earns 11 percent on its investments, should the business invest? b. If the business normally earns 5 percent on its investments, should the business invest?
Answered on
To determine whether the business should invest in the project, we can use the Net Present Value (NPV) method. NPV helps assess the profitability of an investment by comparing the present value of cash inflows (profits) to the initial investment (cost).
The formula for NPV is:
NPV = ∑ Cash Flow / (1+r) t - Initial Investment
Where:
Cash Flow = Profits generated each year = $90,000
Initial Investment = Start-up costs = $225,000
r = Discount rate or cost of capital
Let's calculate the NPV for both scenarios:
a. If the business nominally earns 11 percent on its investments:
Using the formula:
NPV= 90,000 / (1+0.11) 1 + 90,000 / (1+0.11) 2 + 90,000 / (1+0.11) 3 - 2,25,000
Calculating this gives:
NPV= 90,000 / (1+0.11) 1 + 90,000 / (1+0.11) 2 + 90,000 / (1+0.11) 3 - 2,25,0000
NPV = 81090.09 - 225,000
NPV = −143909.91
The NPV at 11 percent nominal return is negative, suggesting that at this rate of return, the project's returns are not sufficient to cover the initial investment. Therefore, the business should not invest at a nominal return of 11 percent.
b. If the business normally earns 5 percent on its investments:
Using the formula:
NPV = 90,000 / (1+0.05) 1 + 90,000 / (1+0.05) 2 + 90,000 / (1+0.05) 3 - 2,25,000
NPV = 80972.38−225,000
NPV = −144027.62
The NPV at 5 percent nominal return is also negative, suggesting that even at a lower nominal return of 5 percent, the project's returns are not sufficient to cover the initial investment. Therefore, the business should not invest at a nominal return of 5 percent either.
In both scenarios, with different nominal returns, the NPV remains negative, indicating that the project's returns are not enough to justify the initial investment. Hence, the business should likely reconsider investing in this project.