454. A company is evaluating two manufacturing processes for producing a new product. Process A has an initial cost of \$500,000 and generates a return of \$200,000 annually for 4 years. Process B has an initial cost of \$300,000 but generates a return of \$150,000 annually for 3 years. The company requires a rate of return of 10\% per annum. Which process should the company choose based on net present value (NPV)?
Key Concept: Evaluating Alternatives
c) Process A because its NPV is higher.
[Solution Description]
To evaluate the alternatives, we calculate the NPV for both processes using the formula: $NPV = \sum_{t=1}^{n} \frac{R_t}{(1 + r)^t} - C_0$, where $R_t$ is the annual return, $r$ is the rate of return, and $C_0$ is the initial cost.
For Process A:
$NPV_A = \frac{200,000}{1.10} + \frac{200,000}{(1.10)^2} + \frac{200,000}{(1.10)^3} + \frac{200,000}{(1.10)^4} - 500,000$
Calculating each term:
$NPV_A = 181,818.18 + 165,289.26 + 150,262.96 + 136,602.69 - 500,000 = 633,973.09 - 500,000 = 133,973.09$
For Process B:
$NPV_B = \frac{150,000}{1.10} + \frac{150,000}{(1.10)^2} + \frac{150,000}{(1.10)^3} - 300,000$
Calculating each term:
$NPV_B = 136,363.64 + 123,966.94 + 112,697.22 - 300,000 = 373,027.80 - 300,000 = 73,027.80$
Since $NPV_A > NPV_B$, the company should choose Process A.
Your Answer is correct.
c) Process A because its NPV is higher.
[Solution Description]
To evaluate the alternatives, we calculate the NPV for both processes using the formula: $NPV = \sum_{t=1}^{n} \frac{R_t}{(1 + r)^t} - C_0$, where $R_t$ is the annual return, $r$ is the rate of return, and $C_0$ is the initial cost.
For Process A:
$NPV_A = \frac{200,000}{1.10} + \frac{200,000}{(1.10)^2} + \frac{200,000}{(1.10)^3} + \frac{200,000}{(1.10)^4} - 500,000$
Calculating each term:
$NPV_A = 181,818.18 + 165,289.26 + 150,262.96 + 136,602.69 - 500,000 = 633,973.09 - 500,000 = 133,973.09$
For Process B:
$NPV_B = \frac{150,000}{1.10} + \frac{150,000}{(1.10)^2} + \frac{150,000}{(1.10)^3} - 300,000$
Calculating each term:
$NPV_B = 136,363.64 + 123,966.94 + 112,697.22 - 300,000 = 373,027.80 - 300,000 = 73,027.80$
Since $NPV_A > NPV_B$, the company should choose Process A.