Final answer:
The Net Present Value (NPV) of the project is -$1,670.35, indicating that it is not financially viable. The Benefit-Cost Ratio (BCR) is 0.977, meaning the benefits do not outweigh the costs. If the inflation rate is expected to be 4% in each of the next four years, the adjusted NPV of the project is -$5,074.08.
Step-by-step explanation:
To calculate the Net Present Value (NPV) of the project, we need to discount the cash flows using the required rate of return. In this case, the required rate of return is 20%. Using the formula:
NPV = (Cash Flow1 / (1 + r)^1) + (Cash Flow2 / (1 + r)^2) + (Cash Flow3 / (1 + r)^3) + (Cash Flow4 / (1 + r)^4) - Initial Cost
Plugging in the values, we have:
NPV = ($20,000 / (1 + 0.20)^1) + ($25,000 / (1 + 0.20)^2) + ($30,000 / (1 + 0.20)^3) + ($50,000 / (1 + 0.20)^4) - $75,000
Simplifying the equation, we get:
NPV = $16,666.67 + $17,361.11 + $15,586.42 + $23,715.45 - $75,000
NPV = $-1,670.35
The NPV of the project is -$1,670.35, which means it is not financially viable.
The benefit-cost ratio (BCR) for the project can be calculated by dividing the present value of the future cash flows by the initial cost. In this case:
BCR = ($16,666.67 + $17,361.11 + $15,586.42 + $23,715.45) / $75,000
BCR = $73,329.65 / $75,000
BCR = 0.977
The benefit-cost ratio for the project is 0.977, which means the benefits do not outweigh the costs.
f the inflation rate is expected to be 4% in each of the next four years, we need to adjust the cash flows for inflation before calculating the NPV. To do this, we divide each cash flow by (1 + inflation rate)^n, where n is the number of years in the future. Plugging in the values, we have:
New Cash Flow1 = $20,000 / (1 + 0.04)^1
= $19,230.77
New Cash Flow2 = $25,000 / (1 + 0.04)^2
= $22,727.27
New Cash Flow3 = $30,000 / (1 + 0.04)^3
= $25,694.44
New Cash Flow4 = $50,000 / (1 + 0.04)^4
= $42,525.61
Plugging in the new cash flows into the NPV formula, we get:
NPV = ($19,230.77 / (1 + 0.20)^1) + ($22,727.27 / (1 + 0.20)^2) + ($25,694.44 / (1 + 0.20)^3) + ($42,525.61 / (1 + 0.20)^4) - $75,000
Simplifying the equation, we get:
NPV = $15,942.98 + $16,749.16 + $15,010.61 + $22,223.17 - $75,000
NPV = $-5,074.08
The NPV of the project, adjusted for inflation, is -$5,074.08, which means it is still not financially viable.