- The Net Present Value (NPV) is calculated for both projects by discounting future cash flows to the present value and subtracting the initial investment.
- Project A's NPV is \(\boxed{271.51}\) and Project B's NPV is \(\boxed{304.24}\).
- Since both projects have positive NPVs (\(>0\)), they are both financially viable.
- Therefore, the correct decision is to pursue \(\boxed{Both}\) projects.
Explanation
- Analysis of the NPV Problem
The net present value (NPV) is a financial metric used to determine the profitability of an investment. It is calculated by taking the sum of the present values of all future cash flows and subtracting the initial investment cost. The formula for NPV is given by:
\[NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}\]
where \(C_t\) is the cash flow at time \(t\), and \(r\) is the discount rate (the opportunity cost of capital). In this problem, we have two independent projects, A and B, both with an initial investment cost of \(\$380\) at \(t=0\) and a discount rate \(r=0.11\). We need to calculate the NPV for both and decide which to pursue.
- Calculating NPV for Project A
For Project A, the cash inflow is \(\$210\) at the end of each year for 4 years. The NPV calculation is:
\[NPV_A = -380 + \frac{210}{(1+0.11)^1} + \frac{210}{(1+0.11)^2} + \frac{210}{(1+0.11)^3} + \frac{210}{(1+0.11)^4}\]
Calculating each term:
\(\frac{210}{1.11} \approx 189.1892\)
\(\frac{210}{1.11^2} \approx 170.4407\)
\(\frac{210}{1.11^3} \approx 153.5499\)
\(\frac{210}{1.11^4} \approx 138.3333\)
Summing these gives: \(-380 + 189.1892 + 170.4407 + 153.5499 + 138.3333 = 271.5131\).
Rounding to two decimal places, we find \(NPV_A \approx \boxed{271.51}\).
- Calculating NPV for Project B
For Project B, the cash inflow is \(\$280\) at the end of each year for 3 years. The NPV calculation is:
\[NPV_B = -380 + \frac{280}{(1+0.11)^1} + \frac{280}{(1+0.11)^2} + \frac{280}{(1+0.11)^3}\]
Calculating each term:
\(\frac{280}{1.11} \approx 252.2523\)
\(\frac{280}{1.11^2} \approx 227.2543\)
\(\frac{280}{1.11^3} \approx 204.7336\)
Summing these gives: \(-380 + 252.2523 + 227.2543 + 204.7336 = 304.2402\).
Rounding to two decimal places, we find \(NPV_B \approx \boxed{304.24}\).
- Project Decision Rule
The decision rule for independent projects is that any project with an NPV greater than zero is worth pursuing, as it adds value to the firm.
- \(NPV_A \approx 271.51 > 0\)
- \(NPV_B \approx 304.24 > 0\)
Since both projects have a positive NPV, both projects are worth pursuing. Therefore, the correct choice is "Both".
Examples
Net Present Value (NPV) is a cornerstone of corporate finance, helping businesses decide whether to invest in long-term projects like building a new factory or developing a software product. By converting all future earnings back into today's dollars, management can accurately compare the benefits of projects that pay off over different time frames, ensuring capital is allocated to investments that create the most value for shareholders.