Question

problem:the following costs are estimated for two equal-service tomato-peeling machines in a food-canning plant:if the minimum required rate of return is 15% per year, which machine should be selected?

Explanation:

Step1: Define Annual Worth (AW) formula

For each machine, $AW = -First\ Cost \times (A/P, i, n) - Annual\ Costs + Salvage\ Value \times (A/F, i, n)$
Where $(A/P, i, n) = \frac{i(1+i)^n}{(1+i)^n - 1}$, $(A/F, i, n) = \frac{i}{(1+i)^n - 1}$, $i=0.15$

Step2: Calculate factors for Machine A

$n=6$, $(A/P, 0.15, 6) = \frac{0.15(1.15)^6}{(1.15)^6 - 1} \approx 0.2636$
$(A/F, 0.15, 6) = \frac{0.15}{(1.15)^6 - 1} \approx 0.1136$
Annual total cost = $800 + 11000 = 11800$

Step3: Compute AW for Machine A

$AW_A = -26000 \times 0.2636 - 11800 + 2000 \times 0.1136$
$AW_A = -6853.6 - 11800 + 227.2 = -18426.4$

Step4: Calculate factors for Machine B

$n=10$, $(A/P, 0.15, 10) = \frac{0.15(1.15)^{10}}{(1.15)^{10} - 1} \approx 0.1993$
$(A/F, 0.15, 10) = \frac{0.15}{(1.15)^{10} - 1} \approx 0.0493$
Annual total cost = $300 + 7000 + 2600 = 9900$

Step5: Compute AW for Machine B

$AW_B = -36000 \times 0.1993 - 9900 + 3000 \times 0.0493$
$AW_B = -7174.8 - 9900 + 147.9 = -16926.9$

Step6: Compare AW values

Select machine with higher (less negative) AW.
$AW_B (-16926.9) > AW_A (-18426.4)$

Answer:

Machine B should be selected.