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Throughput Profit Multiplier Based on the books: Building Lean Supply Chains with the Theory of Constraints Managing Business Process Flow

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**Throughput Profit Multiplier (TPM)**

A large fraction of the operating costs are fixed small changes in throughput could be translated into large changes in profits. Throughput profit multiplier (TPM) = TPM = % Changes in Profit/ % Changes in Throughput % Changes in Profit = (Profit2-Profit1)/Profit1 % Changes in Throughput = (Throughput2-Throoughput1)/Throughput1 TPM = (Prof2-Prof1)/Prof1]/[ (Q2-Q1)/Q1] Suppose fixed cost F = $180,000 per month. Sales price per unit P = 22, and variable cost per unit V = 2. In July, the process throughput was 10,000 units. A process improvement increased throughput in August by 2% to 10,200 units without any increase in the fixed cost. Compute throughput profit multiplier.

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**Financial Throughput and Fixed Operating Costs**

We define financial throughput as the rate at which the enterprise generates money. By selling one unit of product we generate P dollars, at the same time we incur V dollars pure variable cost. Pure variable cost is the cost directly related to the production of one additional unit - such as raw material. It does not include sunk costs such as salary, rent, and depreciation. Since we produce and sell Q units per unit of time. The financial throughput is Q(P-V). Fixed Operating Expenses (F) include all costs not directly related to production of one additional unit. That includes costs such as human and capital resources. In our example, F = $180,000 per month, P = 22, and V = 2. In July, financial throughput was 10,000(22-2) = 200,000. In August R increased by 2%.

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**Another Look at Throughput Profit Multiplier**

Financial throughput is (22-2)10000 = Fixed Operating Expense = In this example, Fixed Operating Expense is 90% of Financial Throughput. F= 0.9(P-V)Q Profit = 10% of financial throughput. Profit = 0.1(P-V)Q If Q increases by 1% Financial throughput increases by 1% too, and it is all profit because we have already covered all fixed operating expenses. Therefore increase in profit = 0.01(P-V)Q, and % change in profit = 0.01(P-V)Q/0.1(P-V)Q =0.1 = 10%. 1% change in Throughput, 10% change in profit. 2% increase in throughput 20% increase in profit.

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**Throughput Profit Multiplier**

Let us summarize our notations (these notations benefit from E. Goldratt and M. M. Srinivasan) Throughput: Q Fixed Operating Expenses; cost of human resources and depreciation of capital resources plus all other indirect costs: F Total Revenue: PQ Total Cost: VQ+F Profit Margin; the money generated by producing (and selling) additional unit : P-V Financial throughput. The rate at which the enterprise generates money: (P-V)Q Profit = (P-V)Q-F

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**Relationship Between Financial Throughput and Fixed Operation Expenses**

Suppose F/Financial-Throughput = y = F/(P-V)Q = y; 1>y >0 Therefore, F = y(P-V)Q Profit = (P-V)Q-F = (P-V)Q - y(P-V)Q = (1-y)(P-V)Q If % increase in throughput is x%. Then the increase in profit is x(P-V)Q. % change in profit = [x(P-V)Q]/[(1-y)(P-V)Q] % change in profit = x/(1-y) TPM = % change in profit /% changes in throughput TPM = [x/(1-y)]/x TPM = 1/(1-y)

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Problem 5.6 A company's average costs and revenues for a typical month are $15 million and $18 respectively. It is estimated that 1/3 of the costs are variable and the rest are fixed. What is the throughput profit multiplier? Total Variable Cost =VQ = 5,000,000 Fixed Operating Expenses =F = $10,000,000 Total Revenue = PQ = $18,000,000 Financial Throughput = (P-V)Q = PQ-VQ = $18,000,000-5,000,000 = 13,000,000 F/(P-V)Q = $10,000,000/ 13,000,000 = 10/13 TPM = 1/(1-y) = 1/(1-10/13) = 13/3 If throughput increases by 1% profit will increase by 4.33%.

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A Viable Vision A Viable Vision (Goldratt): What if we decide to have todays total revenue as tomorrows total profit. In our example, Financial Throughput in July was Q1(P-V) = 10,000(22-2). In order to have your profit equal this amount we need to produce Q2 units such that: Q2(P-V) – F = Q1(P-V) Q2(20) -180,000 = 10,000(20) Q2(20) = 380,000 Q2 = 19,000 In order to have your todays total revenue as tomorrows total profit. We should increase our sales by (19,000-10,000)/10,000 = 90%. If we almost double our sales, our current revenue becomes our tomorrows profit.

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**A Viable Vision- Goldratt**

Decide to have your todays total revenue as your tomorrows total profit. What should your sales be equal to? Todays Throughput =R, Today’s Revenue = PR Target Profit = (P-V}R2-F, Target Throughput =R2 = (1+x)R F= y(P-V)R PR2-F = (P-V) (1+x) R-y(P-V)R (P –V)(1+x)R-y(P-V)R= (P –V)R[1+x-y)=PR 1+x-y = P/(P-V) x = P/(P-V)-1 +y x = V/(P-V) +y If V= zP then, x = zP/(P-zP) +y = z/(1-z)+y In our example, P=22, V=2 z =1/11, z/(1-z) = 0.1, F = 180,000, R =10,000, F = 0.9(P-V) y=0.9 x = = 1. If R is doubled, todays revenue becomes tomorrows profit.

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A Viable Vision If Variable cost is less than 60% of the sales prose, the viable vision is achievable by incensing the throughput by less than 2.5x.

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