Fee Collection, Discounts and the 85 Per Cent Target
A self-financing B.Ed college has 180 sanctioned seats and 135 students actually enrolled for the year. The annual fee is fixed at Rs 24,000 per student and the college does not charge anything extra. Three concessions operate together. First, six toppers get a full fee waiver. Second, twelve students from low-income families get a 50 per cent waiver. The remaining 117 students pay full fee unless they pay before 10 July, in which case they get a 15 per cent early-payment discount; 96 of those 117 paid before the deadline. The eighteen waiver students are excluded from the early-payment scheme, so no student receives two concessions. At the governing-body meeting the accountant reports that the college 'collected roughly 78 per cent of gross fee income' and recommends that the shortfall be closed by converting the half-waivers into full-fee admissions, since 'twelve full-fee students will more than cover the gap'.
1. Calculate the actual collection and the collection as a percentage of gross potential fee income. Check the accountant's 78 per cent figure.
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Gross potential income (all 135 students at full fee): 135 x 24,000 = Rs 32,40,000
Concessions given:
- Early-payment discount: 96 x (15% of 24,000 = 3,600) = Rs 3,45,600
- Full waivers: 6 x 24,000 = Rs 1,44,000
- Half waivers: 12 x 12,000 = Rs 1,44,000
- Total concession = 3,45,600 + 1,44,000 + 1,44,000 = Rs 6,33,600
Collection: 32,40,000 - 6,33,600 = Rs 26,06,400
Percentage: 26,06,400 / 32,40,000 = 0.80444... = 80.4 per cent.
The accountant understates the collection by about 2.4 percentage points, i.e. roughly Rs 78,000. The likely slip is treating the 96 early payers as if the discount applied to all 117, or double-counting the waiver group inside the paying pool. Either way the reported figure is not conservative - it is simply wrong, and a governing body should not act on it.
2. The management decides to convert the six full waivers into 50 per cent waivers instead. Recompute the collection and the percentage, and state what this single change does and does not achieve.
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What changes: each of the six students now pays 12,000 instead of 0, adding 6 x 12,000 = Rs 72,000.
New collection: 26,06,400 + 72,000 = Rs 26,78,400 New percentage: 26,78,400 / 32,40,000 = 0.82666... = 82.7 per cent
What it achieves: a 2.3 percentage-point improvement with no change in fee level and no effect on the early-payment pool, because the waiver group is excluded from that scheme.
What it does not achieve: it still leaves about Rs 2,76,000 uncollected against the gross figure, and it does not touch the largest single concession - the early-payment discount of Rs 3,45,600, which is more than five times the sum recovered here. It also converts a merit award into a partial one, which is a policy cost, not merely an accounting one: the six toppers were presumably promised a full waiver, so the change may need to be phased in for the next admitted batch rather than applied retrospectively.
3. Management wants collection at 85 per cent of gross and proposes converting all twelve half-waivers into full-fee admissions. Test the proposal numerically and state what else must change.
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Target: 0.85 x 32,40,000 = Rs 27,54,000
Maximum effect of the proposal: converting all twelve half-waivers adds 12 x 12,000 = Rs 1,44,000, giving 26,06,400 + 1,44,000 = Rs 27,50,400.
Resulting percentage: 27,50,400 / 32,40,000 = 0.84889... = 84.9 per cent - short of the target.
Size of the miss: 27,54,000 - 27,50,400 = Rs 3,600. The shortfall is exactly the value of one early-payment discount (15 per cent of 24,000).
Interpretation, not just arithmetic: twelve conversions would each be worth Rs 12,000, so reaching the target would need Rs 1,47,600, i.e. 12.3 conversions - thirteen students, but only twelve exist. The proposal is therefore exhausted before the target is met, and it also spends the entire equity budget. The realistic alternatives are (a) reduce the early-payment discount from 15 per cent to about 14.9 per cent, which alone recovers Rs 3,600, or (b) collect the small outstanding dues already on the books. A single uncollected Rs 3,600 from one student closes the gap without touching any waiver.