Question

Deep Seas Submarine must implement a new engine in its submarines to meet the needs of clients who desire quieter operation. Two designs, both technologically feasible, have been created, and Deep Seas wishes to know which one to pursue. 1) Design 1 would require an up-front manufacturing cost of $15,000,000 and will cost 2,500,000 per year for 3 years to swap out the engines in all its current submarines. 2) Design 2 will cost $20,000,000 up front, but due to a higher degree of compatibility will only require $1,500,000 per year to implement. MARR is 10 percent/year. Based on an annual worth, determine which design should be chosen.

Answer 1

To determine which engine design to choose, Deep Seas Submarine should compare the annual worth of each design using the MARR of 10%. Design 1 has an annual worth of $6,031,650, while Design 2 has an annual worth of $8,042,200. Therefore, Design 1 is the more cost-effective choice.

Step-by-step explanation:

To determine which engine design Deep Seas Submarine should choose based on an annual worth calculation, we need to consider the initial manufacturing cost and the annual costs for implementing each design, along with the company's Minimum Acceptable Rate of Return (MARR) of 10%. We calculate the annual worth (AW) for each design by using the following formula:
AW = Initial Cost(A/P, MARR, n) + Annual Cost

For Design 1, the initial manufacturing cost is $15,000,000 and the annual cost for swapping out the engines is $2,500,000 for 3 years. For Design 2, the initial manufacturing cost is $20,000,000 and the annual cost for implementation is $1,500,000.

To find (A/P, MARR, 3), which is the capital recovery factor, we use the formula: A/P = (i(1+i)^n)/((1+i)^n - 1) where i is the interest rate (MARR) and n is the number of periods.

Applying this to 10% MARR for three years, (A/P, 0.10, 3) becomes A/P = (0.10(1.10)^3)/((1.10)^3 - 1), which simplifies to A/P = 0.40211. Multiplying this factor by the initial costs for each design gives us their respective annual worths for comparison.

The annual worth for Design 1 is:
$15,000,000 × 0.40211 + $2,500,000 = $6,031,650

The annual worth for Design 2 is:

$20,000,000 × 0.40211 + $1,500,000 = $8,042,200

Comparing the two, Design 1 has a lower annual worth and therefore is the more cost-effective option for Deep Seas Submarine, based on the given MARR of 10%.