Problem 8-4 A company that produces pleasure boats has decided to expand one of
ID: 355202 • Letter: P
Question
Problem 8-4 A company that produces pleasure boats has decided to expand one of its lines. Current facilities are insufficient to handle the increased workload, so the company is considering three alternatives, A (new location), B (subcontract), and C (expand existing facilities) Alternative A would involve substantial fixed costs but relatively low variable costs: fixed costs would be $295,000 per year, and variable costs would be $580 per boat. Subcontracting would involve a cost per boat of $2,550, and expansion would require an annual fixed cost of $53,000 and a variable cost of $1,030 per boat. a. Find the range of output for each alternative that would yield the lowest total cost (Leave no cells blank-be certain to enter"0" wherever required. Round your answers to the nearest whole number.) or to to more b. Which alternative would yield the lowest total cost for an expected annual volume of 320 boats? O A ??Explanation / Answer
Given values:
Fixed costs = F and Variable costs = V
For Alternative A (New location): F = $295,000 per year, V = $580 per boat
For Alternative B (Subcontract): V = $2,550 per boat
For Alternative C (Expansion): F = $53,000 per year, V = $1,030 per boat
Solution:
(a) Let the number of boats be represented by letter B, therefore, the given values can be written in mathematical equation as;
Total Cost for Alternative A = $295,000 + $580 B
Total Cost for Alternative B = $2,550 B
Total Cost for Alternative C = $53,000 + $1,030 B
The number of boats at which alternative A and alternative B will incur same costs is calculated as;
$295,000 + $580 B = $2,550 B
1970 B = 295000
B = 149.75
B = 150 boats
At 150 boats, alternative A and alternative B will incur same total costs.
The number of boats at which alternative B and alternative C will incur same costs is calculated as;
$2,550 B = $53,000 + $1,030 B
1520 B = 53000
B = 34.86 or 35 boats
At 35 boats, alternative B and alternative C will incur same total costs.
The number of boats at which alternative A and alternative C will incur same costs is calculated as;
$295,000 + $580 B = $53,000 + $1,030 B
450 B = 242000
B = 537.78 or 538 boats
At 538 boats, alternative A and alternative C will incur same total costs.
The range of output for which each alternative would yield the lowest total cost is:
A = 538 boats or more
B = 1 to 35 boats
C = 35 to 538 boats
(b) Total cost for an expected annual volume of 320 boats:
Alternative A = $295,000 + ($580 x 320) = $480,600
Alternative B = $2,550 x 320 = $816,000
Alternative C = $53,000 + ($1,030 x 320) = $382,600
At 320 boats, Alternative C (Expansion) yields the lowest cost.