When does a commission plan reward a discount that loses money?
A revenue commission tells a representative to discount far sooner than the company’s own arithmetic would, and raising or lowering the rate does not move the point at which it does.
A 4,000 discount on a 92,000 instrument pays the representative who grants it as soon as it wins 4.55 extra units for every hundred budgeted. It pays the company, counted over the whole life of what it places, only from 11.40. Between the two, the commission plan pays for discounts that lose the company money on its own conservative reading, and the gap is set entirely by what the commission is a rate on. The 1.20 per cent itself cancels out of the comparison.
The quarter that paid everyone
The instruments segment budgeted 1,200 units at 92,000 in the third quarter and sold 1,380 at 88,000. The realised discount was 4,000 a unit, 4.35 per cent of the budget price, and it bought 180 more units than the budget, 15 for every hundred. Revenue from instruments rose from 110,400,000 to 121,440,000. Gross profit on them, with the standard unit cost held at 62,560 throughout, fell from 35,328,000 to 35,107,200: 180 more units and 220,800 less money.
The 84 representatives are paid 1.20 per cent of instrument revenue, so their commission followed revenue and not profit.
Line
Budget
Actual
Actual less budget
Instrument revenue
110,400,000
121,440,000
+11,040,000
Instrument gross profit
35,328,000
35,107,200
−220,800
Commission at 1.20 per cent of revenue
1,324,800
1,457,280
+132,480
The same pool at 3.75 per cent of gross profit
1,324,800
1,316,520
−8,280
Price_Volume_and_Mix.xlsx, Bridge rows 6 to 19 and Commission rows 4 to 22. 3.75 per cent is the rate on gross profit that pays exactly the same pool at budget.
Under the plan in force the sales force was paid 132,480 more for a quarter in which the segment earned 220,800 less. The swing between the two, 353,280, is 15.28 per cent of the 2,312,000 the instruments segment is budgeted to contribute in the whole year. Under a gross profit plan at the neutral rate the same quarter would have paid 1,316,520, which is 140,760 less than the revenue plan paid and 8,280 below budget.
The exchange rate at the desk
Look at one unit. At the budget price the representative earns 1,104 on it; at the realised price, 1,056. Granting the discount costs the representative 48 and the company 4,000, an exchange rate of 83.33 to one. On a gross profit plan at 3.75 per cent the representative gives up 150 on the same unit, and the rate is 26.67 to one.
The 83.33 is nothing more than the reciprocal of the commission rate: one divided by 0.012. Every commission plan on revenue asks the company to pay 1/rate for each unit of the representative’s sacrifice, whatever the product and whatever the price. That is true and it is also the less useful half of the story, because a representative does not grant a discount in order to sell the same unit for less. The discount is granted to sell more units, and the question that matters is how many.
How many extra units each party needs
For the representative on a revenue plan, a hundred units at 92,000 pay the same commission as 100 + x units at 88,000 when (100 + x) × 88,000 = 100 × 92,000, which gives x = 100 × 4,000 / 88,000 = 4.55. The commission rate multiplies both sides and drops out. On a gross profit plan the same equation runs on the unit margin, 29,440 at budget and 25,440 after the discount, and gives 100 × 4,000 / 25,440 = 15.72. Again the rate drops out.
For the company the answer depends on how an extra unit is valued, and the book’s figures support four readings. Each credits the extra unit with its own sale after its own discount, as Chapter 4’s bridge does, and adds what it earns downstream: 6,951.67 a year of consumables and service contribution per installed instrument on the conservative reading, 10,076.67 of gross profit on the marginal one. Over the life, the unit retires at the base’s own 8 per cent a year and is discounted at the 10 per cent the book uses to illustrate, so a year of downstream earnings is worth 5.56 years in present value.
Who is asking
Extra units needed per hundred
Representative, revenue plan
4.55
Company, marginal, over the life
4.91
Company, marginal, one year
11.26
Company, conservative, over the life
11.40
Representative, gross profit plan at 3.75 per cent
15.72
Company, conservative, one year
116.50
A 4,000 discount on a 92,000 price. Case_3_Should_We_Discount_Again.xlsx, sheet 1. The rule, cells D26 to D29, C46 and C47.
The revenue plan’s bar sits below every one of the company’s four. The nearest is the most generous reading the book allows, where every extra unit earns its full gross margin and its full downstream gross profit for life, and even that asks for 4.91. On the conservative reading over the life, which is the one the approval route should apply, the representative is better off from 4.55 and the company from 11.40.
What the gap looks like in money
Per hundred budgeted units, the table below sets the change in the representative’s commission beside the value to the company, at a range of uplifts. The company column is conservative and over the life: each extra unit is worth 35,102.04 after its own discount (481.67 of contribution on the placement, less the 4,000, plus 6,951.67 a year for 5.56 years), and the discount costs 4,000 on each of the hundred units that would have been sold anyway.
Extra units per hundred
Commission, revenue plan
Commission, gross profit plan
Value to the company
0
−4,800
−15,000
−400,000
4.55
0
−10,664
−240,445
8
+3,648
−7,368
−119,184
11.40
+7,233
−4,129
0
15
+11,040
−690
+126,531
15.72
+11,804
0
+151,919
Per hundred budgeted units, against no discount: commission of 110,400 on either plan, since the gross profit rate is set to pay the same at budget. The company column is uplift × 35,102.04 less 400,000.
At an uplift of 8 per hundred the representative earns 3,648 more and the company is 119,184 worse off over the life of what the discount placed. Every uplift between 4.55 and 11.40 has the same signature: commission up, value down. The third quarter’s 15 per hundred sits just above the zone, which is why it can be defended over the life, and why the defence is thin.
How thin is on the same sheet. The third quarter’s uplift stops paying above a discount rate of 15.03 per cent, and at 10 per cent it survives the loss of at most 21.84 per cent of the downstream stream to other suppliers. Neither input is a measurement: the leakage is an unknown in the model and the 10 per cent is the book’s illustration, not a cost of capital. The representatives had no reason to ask about either, because their answer was yes from 4.55.
Why the rate is the wrong lever
The instinctive fix is to cut the commission rate. It does nothing to the threshold. At 0.60 per cent or at 2.40 per cent the representative on a revenue plan still prefers the discount from 4.55 extra units per hundred, because the rate multiplies both sides of the comparison. It changes how much the representative earns from a bad discount, not whether the discount is attractive. The only thing in the plan that moves the threshold is the base the rate is applied to.
The gap also widens with the size of the discount. The revenue plan’s threshold is 100 × d / (92,000 − d) and barely bends; the company’s rises faster, because a larger discount eats into a smaller unit margin and the downstream stream does not grow with it.
Discount per unit
Revenue plan
Company, conservative, life
Gross profit plan
Revenue plan as a share of the company’s
1,000
1.10
2.62
3.52
0.42
2,000
2.22
5.39
7.29
0.41
4,000
4.55
11.40
15.72
0.40
6,000
6.98
18.13
25.60
0.38
8,000
9.52
25.72
37.31
0.37
Extra units needed per hundred budgeted. The company column is the grid on sheet 1. The rule, E32 to E38; the two plan columns are the formulas of C46 and C47 at each discount.
At every size the revenue plan asks for about two fifths of what the company needs, and a little less as the discount grows. At 8,000 the zone in which the plan rewards a value-destroying discount runs from 9.52 to 25.72 extra units per hundred, sixteen units wide.
The gross profit plan errs the other way. At 15.72 it asks for more than the company’s conservative 11.40, so between the two a representative paid on gross profit will decline discounts the company would have wanted. That is the warning Chapter 16 gives about the tighter dial, and it is not a reason to keep the revenue plan: a plan that is slightly too strict loses the company some upside, while one that is too loose pays people to destroy value, and the third quarter shows which of the two the company is currently running.
What to do on Monday
Change the base before the rate, and do not expect the rate to do the base’s job. Paying on gross profit at a neutral 3.75 per cent costs nothing at budget, would have paid 140,760 less in the third quarter, and moves the representative’s threshold from 4.55 to 15.72.
Until the plan changes, the approval route has to carry the difference, and it can carry it as a rule rather than a judgement. A 4,000 discount is approved where the region can name at least twelve extra placements per hundred that it would not otherwise win; a 2,000 discount needs 5.39. Anything the region proposes between 4.55 and 11.40 per hundred is a discount the representative wants and the company does not, and that range is the one the approver exists to police.
And measure the one figure the thin defence depends on: the share of the installed base that buys its consumables elsewhere. Above 21.84 per cent the third quarter’s own discount did not pay, and the revenue plan paid for it anyway.
Reproducing it
Open Price_Volume_and_Mix.xlsx. The Commission sheet carries the quarter: B4 to B9 for the commission and the 353,280 swing, B13 to B17 for the 83.33, B20 to B26 for the neutral 3.75 per cent, the 140,760 and the 26.67. Its Checks sheet ties each to the book and ends ALL PASS.
The thresholds are in case three of Three_Cases.zip, Case_3_Should_We_Discount_Again.xlsx, sheet 1. The rule. C5 is the discount; D26 to D29 give the company’s four thresholds, C46 and C47 the two plans’, C42 and C43 the 15.03 per cent and the 21.84 per cent. Change C16, the commission rate, and C46 and C47 do not move. Change C5 and the grid in rows 32 to 38 shows where the new discount sits.
The workbooks behind this article
Every figure above is a live formula in the free companion files for
Financial Planning and Analysis. Each workbook ends with a Checks sheet
setting the printed figure beside the computed one. No account and no email address.
At what wealth does a family office pay?A five-person office costs the same $2,442,000 at $100m as at $2bn. Against a tiered multi-family schedule the two curves cross exactly once.
Does an undrawn revolver count as liquidity?67.4567 per cent of the headroom, and it leaves at a fall in annual revenue of 8.4127 per cent — not the 13.3333 per cent the board deck implies.
Does supply chain finance count as debt?66,049,315 released, and leverage of 2.7622× or 3.1362× depending on which balance the test is asked of — the second is a breach at today's EBITDA.
Does the fulcrum move with enterprise value?A worked capital structure at three enterprise values. The break migrates from the first lien to the subordinated notes without a single document changing.
How many companies does a reserve pool defend?Holding pro rata to the Series D costs $14.76m per company. A $40m reserve defends 2.71 of forty — and 61 per cent of the cost is the last round.
How much room a 1.15x downside actually leaves79 basis points of margin. The leverage covenant fails first, five basis points before the coverage covenant the chapter reports on, and 4.6 per cent of EBITDA is the whole cushion.
How the GP catch-up is actually solvedMost write-ups state the catch-up formula then hardcode the answer. Set it as a solve and it moves on its own when the carry rate does.
How do you set a minimum cash balance?Three components, 124,596,281 in total — and the double count that turns a margin of 27,403,719 into an apparent shortfall of -3,988,281.
Is a 2/10 net 60 discount worth taking?An annualised 14.8980 per cent against a revolver at 4.50 per cent — worth 5,471,890 a year, and 0.3132 turns of reported leverage.
Should corporate debt be fixed or floating?78.1818 per cent of gross debt fixed, and a net floating exposure after cash of -608,000.00 — the proportion, not the instrument.
Six ways to state the same fund's return7.12 per cent, 18.04 per cent, or 1.323 times the public market — one fund, one set of flows. The eleven-point gap is the valuation, and it is not cash.
The IRR at which a closed-ended fund merely tiesA drawdown fund advertising 13.25 per cent ties an evergreen netting 8.64. On committed rather than called capital, 78.7 per cent of the edge vanishes.
The month a remediation trigger has to be armed byMonth 8, on a one-year window and a 14-week hiring lead time. The date is 12W − L/4.33 and holds for any portfolio size — the book only changes the euros.
Two routes to the same NAVFive findings in one quarter-end close, and not one of them was a modelling error. Every one was a control that did not exist.
What a CBAM certificate buffer costs to holdCarry and protection are both linear in the buffer, so the break-even probability is identical at 5 per cent and at 30 — and 2027 costs exactly twice 2026.
What a clawback actually collateralises24 million recovers 13.20 net of tax and 7.20 is escrowed. The rule is e ≥ 1 − t, and every euro won on the tax clause lands uncollateralised.
What a co-investment programme actually saves37 basis points, and a 22.8 per cent total-loss rate erases it. At the usual per-deal cap a single failure is 37 per cent of the annual cohort.
What a diligence exercise actually recoversEighteen basis points is only the part that reaches the yield. Three of the four instruments never do, and the exercise is worth thirty-one.
What a follow-on reserve is actually worth0.019 turns under plain dilution, 0.285 under pay-to-play. The optimum is a property of the shareholders’ agreement, not of the portfolio.
What a lease mark-to-market is actually worth5,788,000 becomes 807,365 once the over-market stream, the expiry dates and the cost of re-letting are priced — and nothing at all below a 43.7 per cent renewal rate.
What a minimum payment actually does£81.53 leaves the account and £20.46 reaches the debt. On minimums alone the set clears in 258 months and repays 1.78 times what was borrowed.
What a month of delay costs in an enforcement463,000 euros of present value a month. No single error about enforcement, and no pair of errors, moves the indifference point from 58.7 cents to the 72 on the table.
What a pro rata cheque actually costsDefending costs 1.25 times the initial cheque across two rounds, not more in each — and below a 521 exit the follow-on dollars come back worth less than they cost.
What a subscription line does to the IRR20 per cent becomes 38.41 on the same asset while the multiple falls. Two dollars of interest buys 18.4 points, and the longer the line runs the cheaper each point gets.
What one point of fees actually costsOne point on the annual charge turns 738,846 into 567,961 over forty years — 23 per cent of the pot, and 2.43 of wealth lost per 1 of fee.
When the promote stops clearingCarried interest is not proportional to performance near the hurdle. It is a step function, and $2m of headroom is what stands between a promote and none.
Why a secondaries bid-ask gap has no zoneThe seller’s floor and the buyer’s ceiling are one formula at two rates. At equal required returns the zone is exactly zero — here it is 11.02 points apart.
Why refining a due diligence rubric makes it weakerThree of twelve managers carry a terminal flaw and the average approves all three. Splitting eight domains into sixteen makes it easier to hide, not harder.