Slide 1 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Applications of Cost Theory Chapter 9 Topics in this Chapter include: Estimation of Cost Functions using regressions »Short run -- various methods including polynomial functions such as cubic or quadratic functions »Long run -- various methods including Engineering cost techniques Survivor techniques Linear Break-Even Analysis and Operating Leverage Business Risk and Risk Assessment

Slide 2 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Computerization and Information Technology Reduce Costs Robots, computers, scanning technology have reduced costs Chevron : lowering costs of finding wells with 3-D modeling of potential oil fields Timken: a ball-bearing manufacturer uses 3-D modeling for precise specification Merck: microchips perform thousands of reactions at once, reducing time to find new drug therapies

Slide 3 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Estimating Cost Functions Firms want to know what their costs are now, what their costs will be, and what they would be at different output levels. Costs issues involve the type of cost (fixed, variable, average, etc.) and issues of time depreciation. »Items often depreciate with use »Items can also depreciate with passage of time Because prices of inputs change with inflation, must consider deflating or detrending cost data.

Slide 4 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Short Run Cost-Output Relationships Typically use TIME SERIES data for a plant or for firm, regression estimation is possible. Typically use a functional form that “fits” the presumed shape. SRTC is often CUBIC SRTC = a+bQ+cQ 2 +dQ 3 STAC is often QUADRATIC SRAC = a+bQ+cQ 2 quadratic is U-shaped or arch shaped. cubic is S-shaped or backward S-shaped

Slide 5 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Empirical Cost-Output Polynomial: In Theory Short run cost functions can be represented by a cubic relationship TC = a + bQ + cQ 2 + dQ 3 From this we can find ATC (average total cost) ATC = TC/Q = a/Q + b + cQ + dQ 2 We can also find MC (marginal cost) MC = dTC/dQ = b + 2cQ + 3dQ 2 Notice that both ATC and MC are U-Shaped as represented by quadratic equations (to the power of 2) Notice also that if “d” is insignificant, the form is even simpler as the last term is zero in each of the above examples

Slide 6 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Estimating Short Run Cost Functions: In Practice Example: TIME SERIES data of total cost Cubic Total Cost (to the power of three) TC = C 0 + C 1 Q + C 2 Q 2 + C 3 Q 3 Time Series Data: TC Q Q 2 Q , , ,859  Predictor Coeff Std Err T-value Constant Q Q-squared Q-cubed R-square =.91 Adj R-square =.90 N = 35 Regression Output:

Slide 7 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. PROBLEMS: 1. Write the cost regression as an equation. 2. Find the AC function. What is MC at Q=10? 3. Find the MC function. What is MC at Q=10? 1. TC = Q - 10 Q Q 3 (1.25) (2.5) (4) (2) 2.AC = 1000/Q Q + 2 Q 2 3.MC = Q + 6 Q 2 t-values in the parentheses NOTE: Total cost is S-shaped Average cost is U-shaped And even MC is U-shaped Find AC at Q=10. AC = 1000/ – 10(10) + 2(10) 2 = 250 Find MC at Q=10. MC = 50 – 20 (10) + 6 (10) 2 = 100 = 450

Slide 8 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. What Went Right What Went Wrong With Boeing? Airbus and Boeing both produce large capacity passenger jets Originally, Boeing built each 747 to order, one at a time, rather than using a common platform »Airbus began to take away Boeing’s market share through its lower costs. As Boeing shifted to mass production techniques, cost fell Now, as sales are rising for this mass produced jets, profits have been positive for Boeing

Slide 9 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Estimating LR Cost Relationships Use a CROSS SECTION of firms »SR costs usually uses a time series Assume that firms are near their lowest average cost for each output A quadratic curve of a cross section of ACs for various firms can be used. Q AC LRAC

Slide 10 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Economies of Scope in Banking Economies of scope occur when producing two or more products jointly by one firm is less than the cost of producing them separately. Banking offers economies of scope through offering people who can help customers with checking, savings, credit cards, mortgages, car loans, trust accounts, and many other services. Banks are expanding into other fields, including brokerage, insurance, bill paying, foreign exchange hedging, and other services expanding economies of scope. Work by Jeffry Clark used a logarithmic cost function such as: Ln TC = a + b Ln Consumer Lending + c Ln Mortgage Lending He found evidence for Economies of Scope in banking up to about $100 million in assets.

Slide 11 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Engineering Cost Approach Engineering Cost Techniques offer an alternative to fitting lines through historical data points using regression analysis. It uses knowledge about the efficiency of machinery. Some processes have pronounced economies of scale, whereas other processes (including the costs of raw materials) do not have economies of scale. Size and volume are mathematically related, leading to engineering relationships. Large warehouses tend to be cheaper than small ones per cubic foot of space.

Slide 12 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Survivor Technique The Survivor Technique examines what size of firms are tending to succeed over time, and what sizes are declining. This is a sort of Darwinian survival test for firm size. Presently many banks are merging, leading one to conclude that small size offers disadvantages at this time. Dry cleaners are not particularly growing in average size, however.

Slide 13 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Break-even Analysis We can have multiple B/E (break-even) points with non-linear costs & revenues. If linear total cost and total revenue: »TR = PQ »TC = F + VQ where V is Average Variable Cost F is Fixed Cost Q is Output cost-volume-profit analysis Total Cost Total Revenue B/E Q Figure 9.5

Slide 14 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The Break-even Quantity: Q B/E At break-even: TR = TC »So, PQ = F + VQ Q b = F / ( P - V) = F/CM »where contribution margin is: CM = ( P - V) PROBLEM: As a garage contractor, find Q B/E if: P = $9,000 per garage V = $7,000 per garage & F = $40,000 per year

Slide 15 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Amount of sales revenues that breaks even PQ b = P[F/(P-V)] = F / [ 1 - V/P ] Break-even Sales Volume Variable Cost Ratio Ex: At Q = 20, B/E Sales Volume is $9,00020 = $180,000 Sales Volume Answer: Q = 40,000/(2,000)= 40/2 = 20 garages at the break-even point.

Slide 16 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Target Profit Output l Quantity needed to attain a target profit l If  is the target profit, Q target  = [ F +  ] / (P-v) Suppose want to attain $50,000 profit, then, Q target  = ($40,000 + $50,000)/$2,000 = $90,000/$2,000 = 45 garages

Slide 17 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Contribution Analysis Another variation is to find if added sales through a ad campaign or new product is justified. It looks at the incremental contributions and incremental additions to cost. Do the project if: »Added Contribution > Added Cost »(P – v)  Q >  Direct Fixed Cost »When this inequality holds, the project adds more to revenues than it adds to cost. Sometimes the assumptions do not hold 1.Costs may be semi-variable 2.Many times firms sell multiple products or small, medium, and large varieties 3.There is uncertainty as to the P, V, and F in the problem 4.Inconsistency in the planning horizon Limitations of B/E & Contribution Analysis

Slide 18 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Degree of Operating Leverage or Operating Profit Elasticity DOL = E  »sensitivity of operating profit (EBIT) to changes in output Operating  = TR-TC = (P-v)Q - F Hence, DOL =  Q(Q/  ) = (P-v)(Q/  ) = (P-v)Q / [(P-v)Q - F] A measure of the importance of Fixed Cost or Business Risk to fluctuations in output

Slide 19 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Suppose the Contractor Builds 45 Garages, what is the D.O.L? DOL = ( ) 45. {( ) } = 90,000 / 50,000 = 1.8 A 1% INCREASE in Q  1.8% INCREASE in operating profit. At the break-even point, DOL is INFINITE. »A small change in Q increase EBIT by astronomically large percentage rates

Slide 20 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Break-Even Analysis and Risk Assessment One approach to risk, is the probability of losing money. Let Q b be the breakeven quantity, and Q is the expected quantity produced. z is the number of standard deviations away from the mean z = (Q b - Q )/  68% of the time within 1 standard deviation 95% of the time within 2 standard deviations 99% of the time within 3 standard deviations Problem: If the breakeven quantity is 5,000, and the expected number produced is 6,000, what is the chance of losing money if the standard deviation is 500? Answer: z =(5000 – 6000)/500 = -2. There is less than 2.5% chance of losing money. Using table B.1, the exact answer is.0228 or 2.28% chance of losing money. ^