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| Question: 6 |
A not-for-profit social agency provides home health care assistance to as many patients as possible. Its budgeted appropriation (X) for next year must cover fixed costs of $5 million, and the annual per-patient cost (Y) of its services. However, the agency is preparing for a possible 10% reduction in its appropriation that will lower the number of patients served from 5,000 to 4,000. The reduced appropriation and the annual per-patient cost equal |
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Answer (D) is correct.
This question applies CVP analysis in a not-for-profit context in which the agency wishes to assist as many people as possible. Thus, a breakeven point must be calculated. Total revenue (the appropriation) equals fixed cost plus the product of unit variable cost (per-patient annual cost) and the number of patients who can be assisted given the available resources. The following are simultaneous equations stated in the two unknowns:
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X – 5,000Y = $5,000,000
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.9X – 4,000Y = $5,000,000
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Because X must equal 5,000Y + $5,000,000, the second equation may be solved as follows for the per-patient annual cost (Y):
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.9(5,000Y + $5,000,000) – 4,000Y
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=
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$5,000,000
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4,500Y + $4,500,000 – 4,000Y
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=
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$5,000,000
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500Y
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=
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$500,000
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Y
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=
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$1,000
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Accordingly, the budgeted appropriation (X) must be $10,000,000 [(5,000 × $1,000) VC + $5,000,000 FC], and the reduced appropriation must be $9,000,000 ($10,000,000 × 90%). |
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