CH12-EX01. VAT-Inclusive Displayed Price + Both Fee Types Present

• Related Chapter: CH12. MODE C — Allowable Cost Reverse Calculation
• Related Tool: MODE C (core/engine/modes/mode_c.py, run_mode_c)
• Source: docs/features/mode_c_allowable_cost/CASE.md, TC5 (hypothetical data, client_id: sample_co_epsilon — not a real company)

Input Values

Item	Value
price_includes_vat	true
target_market_price	110,000 (VAT-inclusive, i.e., G)
vat_rate (v)	0.10
target_contribution_margin_rate (t)	0.3
b (sum of rate_of_net_sales)	0.1
a (sum of rate_of_gross_payment)	0.03
F (sum of fixed-amount variable_selling_delivery)	1,000

Exercise

When the market price is already fixed, work out how much allowable cost you can spend while keeping the target CM rate.

1. What is the allowable direct cost (ADC)? (The displayed price includes VAT, so work out N and G first.)
2. Use the ADC you found to self-check that the CM rate matches the target of 0.3.
3. If the same underlying economics (N=100,000, G=110,000) were entered as a VAT-exclusive display (price_includes_vat=false), would the ADC change?

Show answer and walkthrough

What This Example Illustrates

This example shows how MODE C’s allowable-cost formula is calculated when (1) a VAT-inclusive displayed price, (2) a fee based on net sales (b), (3) a fee based on gross payment (a), and (4) a fixed-amount cost (F) are all present at the same time. It also confirms, via the self-check (expected_contribution_margin_rate), that the calculated result matches the target CM rate exactly.

Calculation Process

Since price_includes_vat = true:
  G = target_market_price = 110,000
  N = G / (1+v) = 110,000 / 1.1 = 100,000

D = 1 − t − b − a×(1+v)
  = 1 − 0.3 − 0.1 − 0.03×1.1
  = 0.567

ADC = N × D − F
    = 100,000 × 0.567 − 1,000
    = 56,700 − 1,000
    = 55,700

Self-Check

aG = 0.03 × 110,000 = 3,300
CM = N − ADC − F − bN − aG
   = 100,000 − 55,700 − 1,000 − 10,000 − 3,300
   = 30,000
CMR = 30,000 / 100,000 = 0.30 = t  ✓

Result

Metric	Value	Status
market_net_sales_ex_vat (N)	100,000	OK
market_gross_payment_incl_vat (G)	110,000	OK
allowable_direct_cost (ADC)	55,700	OK
expected_contribution_margin	30,000	OK
expected_contribution_margin_rate	0.30	OK

Note (the display method does not change the result)

CASE.md’s TC6 enters the same underlying economics (N=100,000, G=110,000) with price_includes_vat=false (VAT-exclusive display), and produces the same ADC of 55,700. This shows that the VAT display method (inclusive/exclusive) does not change the actual allowable cost itself — a principle already established in MODE A/B that holds equally in MODE C.