Lecture 4: Topic #1Extent (How Much)

DecisionsMarginal Revenue, Costs

(Average and Marginal)Remember, We always

think on the MARGIN

MOST IMPORTANT POINT:

Always take into account the following:

DECISION SHOULD BE MADE SO LONG AS THE MARGINAL BENEFIT OF THE DECISION EXCEEDS MARGINAL COSTThe rule can be used to guide every decision within

an organization.The rule can also be used to understand how to

properly design incentive schemes.

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Lecture 4: Topic 1 – Summary of main points

• Do not confuse average and marginal costs.

• Average cost (AC) is total cost (fixed and variable) divided by total units produced.

• Average cost is irrelevant to an extent decision.

• Marginal cost (MC) is the additional cost incurred by producing and selling one more unit.

Lecture 4: Topic #1 – Summary• Marginal revenue (MR) is the additional revenue

gained from selling one more unit.

• Sell more if MR > MC; sell less if MR < MC. If MR = MC, you are selling the right amount (maximizing profit).

• The relevant costs and benefits of an extent decision are marginal costs and marginal revenue. If the marginal revenue of an activity is larger than the marginal cost, then do more of it.

• An incentive compensation scheme that increases marginal revenue or reduces marginal cost will increase effort. Fixed fees have no effects on effort.

• A good incentive compensation scheme links pay to performance measures that reflect effort.

Background: Average cost

• Definition: Average cost is simply the total cost of production divided by the number of units produced. AC = TC/Q• Average costs often decrease as quantity

increases due to presence of fixed costs• AC = (VC + FC)/Q• FC does not change as Q increases

• Average costs are not relevant to extent decisions

Background: Average cost (cont.)

Background: Marginal cost

• Marginal cost is the cost to make and sell one additional unit of output. MC = TCQ+1 – TCQ.

• Marginal cost is often lower than average cost (due to falling average costs) but not always.

• Marginal costs are what matter in extent decisions

Violation: An example

In 2005, the CEO of Memorial Hospital noticed the following:Cost of delivering 540 babies the previous year was

$3,132,000…. Average cost: $3,132,000/540=$5800.

Revenue from delivery = $2,745,000. Average revenue: $2,745,000/540 = $5,083.33.

The chief of obstetrics proposed the following: Let’s deliver more babies! The CEO’s paraphrased response: “What are you

nuts!”…. “Everytime we deliver a baby we lose $716.67!”

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But average costs include fixed costs!

After taking this class, you won’t make the same mistake.

Fixed costs to the hospital were $1,000,000.

Variable costs at 540 deliveries was about $3,000.

Marginal cost is $3,000. Additional revenue per child was about $5,000. Increasing deliveries would have reduced costs and potentially resulted in a PROFIT.

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Extent (how much?) decisions• Definition: Marginal cost (MC) is

the additional cost required to produce and sell one more unit.

• Definition: Marginal revenue (MR) is the additional revenue gained from producing and selling one more unit.

• If the benefits of selling another unit (MR) are bigger than the costs (MC), then sell another unit.

• So, produce more when MR>MC; less when MR<MC. Profits are maximized when MR=MC.

Extent decisions (cont.)• Examples of extent decisions• Should you change the level of advertising?• Should you increase the quality of service?• Is your staff big enough, or too big?• How many parking spaces should you

lease?

• Marginal analysis answers these questions• This analysis tells you direction of change

but not the distance. • You can only measure MR and MC at the

current level of output – make a change and re-measure

Extent decision example

• Discussion: How much advertising?• A $50,000 increase in the TV ad budget brings in

1,000 new customers

• Estimated MCTV is $50 (the cost to get one more customer)• $50,000 / 1,000 = $50

• If the marginal revenue generated by this customer is greater than $50, do more advertising.

Extent decision example (cont.)

• Even if we do not know the marginal revenue, we can still use marginal analysis to make extent decisions

• Compare TV advertising to telephone solicitation• Say you recently cut telephone budget by $10,000 and lost

100 customers

• Estimated MCPH = $100= ($10,000 / 100)

• So, to get one more customer costs $50 for TV and $100 for phone• MCPH > MCTV so shift ad dollars from phone to TV

• Advice: make changes one-at-a-time to gather valuable information about marginal effectiveness of each medium.

Effort is an extent decision• Discussion: Royalty rates vs. fixed fee

contracts

• You receive two bids to harvest 100 trees on your land

• $150/tree or $15,000 for the right to harvest all the trees.

• On your tract there are pines (worth $200) and fir (worth $100)

• Which offer should you accept?

• Discussion: Sales Commissions

• Expected sales level: 100 units @ $10,000/unit=$1M

• Option 1: 10% commission

• Option 2: 5% commission + $50,000 salary

Tie pay to performance• A consulting firm COO received a flat salary of

$75,000

• After learning about the benefits of incentive pay in class, the CEO changed COO compensation to $50K + (1/3)* (Profits-$150K)

• Profits increased 74% to $1.2 M

• Compensation increased $75K $177K

• Discussion: what are the disadvantages to incentive pay?

Alternate intro anecdote• American Express offers a Platinum Card to affluent customers

• In 2001, there were approximately 2,000 Platinum cardholders in the Japanese market. Numbers had been limited to ensure high quality customer service

• With customer service technology advances, company considered expanding number of card holders

• How many more should be added?• As more members are acquired, average spending per card member

decreases because the financial threshold for membership is lowered

• Costs of customer service rise for each additional member added, and growing beyond a certain point would require building and operating an additional call center

• After analyzing the costs and benefits, American Express realized that it should expand its offering to only 15,000 more Platinum Card members

• We call this an “extent” decision, because the company needed to decide “how many” platinum cards to provide. In this lecture, we show you how to make profitable extent decisions.

Review question

You run a game day shuttle service for parking services for the Frisco Rough Riders. Your costs for different customer loads are: 1: $30, 2: $32, 3: $35, 4: $38, 5: $42, 6: $48, 7: $57, 8: $68…. What are the marginal costs for each customer load level?

If you are compensated $10 per ride, what customer load should you want? What are your total profits?

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Additional questions

1. A retailer has to pay $9 per hour to hire 13 workers. If the retailer only hires 12 workers, a wage rate of $7 per hour is sufficient. What is the marginal cost of the 13th worker?

2. A firm produces 500 boxes of screwdrivers per week. It hires 20 full-time workers (40 hours/week) at an hourly wage of $15. Raw materials are ordered weekly and they cost $10 for every unit produced. The weekly cost of the mortgage for the factory is $2,250. How do the overall costs breakdown in terms of total variable cost, total fixed cost, and total cost?

3. Kenny’s Burger Joint produces 500 burgers per week. Each burger is priced at $3. A business ordered 750 burgers for an upcoming event. Jim decided to offer a discount by reducing the price of the burgers to $2.50 for the party. What is the marginal revenue of selling the 50th burger for the party?

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Lecture 4: Topic #2Investment decisions

and break even analysis

Summary• Investments imply willingness to trade dollars in the present for dollars in the

future. Wealth-creating transactions occur when individuals with low discount rates (rate at which they value future vs current dollars) lend to those with high discount rates.

• Companies, like individuals, have different discount rates, determined by their cost of capital. They invest only in projects that earn a return higher than the cost of capital.

• The NPV rule states that if the present value of the net cash flow of a project is larger than zero, the project earns economic profit (i.e., the investment earns more than the cost of capital).

• Although NPV is the correct way to analyze investments, not all companies use it. Instead, they use break-even analysis because it is easier and more intuitive.

• Break-even quantity is equal to fixed cost divided by the contribution margin. If you expect to sell more than the break-even quantity, then your investment is profitable.

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Shutdown decisions

Shutdown decisions are difficult psychologically, but economically, the rule of thumb is straightforwardAvoidable costs are costs that can be recovered from

shutting down.Shutdown if the marginal benefits associated with

recouping avoidable costs exceeds marginal costs, in this case, the foregone revenue from shutting down.

If you incur sunk costs specific to a trade relationship, you are subject to the hold-up problem.

Anticipate hold-up and choose organizational or contractual forms to give each party both the incentive to make relationship-specific investments and to trade after these investments are made.

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Introductory anecdote• In summer 2007, Bert Matthews was contemplating

purchasing a 48-unit apartment building.• The building was 95% occupied and generated $550,000 in

annual profit.• Investors expected a 15% return on their capital• The bank offered to loan Mr. Matthews 80% of the purchase

price at a rate of 5.5%

• Mr. Matthews computed the cost of capital as a weighted average of equity and debt.• .2*(15%) + .8*(5.5%) = 7.4% • Mr. Matthews could pay no more than $550,000/7.4% = $7.4

million and still break even.

• Mr. Matthews decided not to buy the building. A good decision – one year later, the cost of capital was 10.125% and Mr. Matthews could offer only $5.4 million for the building.

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Compounding/discounting

The current/future trade-off involves discounting and compounding:Compounding: Consider an interest rate of i per

period. In k-periods, the future value (FV) relative to the present value (PV) is: FV=(1+i)k PV

Discounting: Used to calculate the PV of an investment expected to yield some future payoff: PV=FV/(1+i)k.

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Present value and investment decisions• Companies also have discount rates, which are

determined by cost of capital.• A company’s cost of capital is a blend of debt

and equity, its “weighted average cost of capital” or WACC

• Time is a critical element in investment decisions• cash flows to be received in the future need

to be discounted to present value using the cost of capital

• The NPV Rule: if the present value of the net cash flows is larger than zero, the project if profitable.

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Consider two projects:

Project A: An initial investment of $100 is required. The project will yield $115 after year 1.

Project B: Same initial investment. Project returns $60 in year 1, $60 in year 2.

Which project should be selected if the cost of capital is 14% per year for both?

NPV A: = $115/(1+.14) – 100 = $0.88

NPV B: = $60/(1+.14) + $60/(1+.14)2-$100=-1.20.

GO WITH A.

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NPV and Economic profit

• Projects with a positive NPV create economic profit.

• Only positive NPV projects earn a return higher than the company’s cost of capital.

• Projects with negative NPV may create accounting profits, but not economic profit.

• In making investment decisions, choose only projects with a positive NPV.

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KEY POINT #1

ONLY MAKE INVESTMENTS IF THE ECONOMIC NET PRESENT VALUE IS POSITIVE….

Example: What is the net present value of a project that requires an investment of $10000 and returns $5000 in year 1 and $8000 in year 2? Assume the cost of capital is 10%. Should the investment be made?

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For initial investment, we often use break-even analysis

• The break-even quantity is the amount you need to sell to just cover your costs• At this sales level, profit is zero.

• The break-even quantity is Q=FC/(P-MC), where FC are fixed costs, P is price, and MC is marginal cost• (P-MC) is the “contribution margin” – what’s left

after marginal cost to “contribute” to covering fixed costs

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A recent “real world example”

In 2008, Nissan needed to make a decision about the re-design of the Titan pickup truck line. They had 2 years remaining on their original product design.

Details:The cost of developing a new line was estimated at

$400 million.Nissan’s cost of capital is 15% per year.Relative to variable costs, the contribution margin per

truck was about $1500.How much does Nissan need to produce in order to

break even?

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Analyses

Fixed cost per year: 400 million*0.15 = $60 million

Break even quantity: ($60,000,000)/$1500 = 40,000.

Should they pursue the new line?

Nissan’s forecasting team estimated sales would equal 12,000. Nissan decided NOT to pursue this investment.

Remember this advice: Do not invoke break-even analysis to justify higher prices or greater output. Here, the investment had not yet been made!

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KEY POINT #2

BREAK-EVEN ANALYSIS IS SOMETIMES USEFUL….PRIOR TO INVESTING IN SUNK COSTS, NOT AFTER!!!

EXAMPLE:

A clothing manufacturing firm is deciding whether to invest in a new technology that needs an initial investment of $45,000. This will increase cash flows in the first year by $25,000 and $30,000 in the second year. The firm’s current fixed costs are $9,000 and marginal cost is $15. The firm currently charges $18 per unit.

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Analysis continued

Questions:

If the interest rate in our example is 5% then the firm’s net present value is what? Should the firm undertake the investment?

What is the firm’s “contribution margin?”

What is the break-even quantity?

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Should we shut down?

• Shut-down decisions are made using break-even prices rather than quantities. • The break-even price is the average avoidable

cost per unit• Profit = Rev-Cost= (P-AC)(Q)

• If you shut down, you lose your revenue, but you get back your avoidable cost.• If average avoidable cost is less than price, shut down.

• Determining avoidable costs can be difficult. • To identify avoidable costs firms use Cost

Taxonomy

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Costs “Taxonomy”

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KEY POINT #3

Difficult decisions to shutdown often involve psychological costs. A firm should shut down when average avoidable cost is less than the price.

Example: Consider a firm that produces 500,000 units per year. The firm’s fixed costs are $100,000, marginal costs are $250 and the price per unit is $400. In the short-run, how low can price go before it is profitable to shut down?

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Uh Oh! It’s a hold up!• National Geographic can reduce shipping costs by

printing with regional printers.• To print a high quality magazine, the printer must buy a $12

million printing press.• Each magazine has a MC of $1 and the printer would print 12

million copies over two years. • The break-even cost/average cost is $7 = ($12M / 2M copies)

+ $1/copy• BUT once the press is purchased, the cost is sunk and the

break-even price changes. • Because of this the magazine can hold up the printer by

renogiating the terms of the deal – because the price of the press is unavoidable, and sunk, the break-even price falls to $1, the marginal cost.

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Sunk costs and post-investment hold up

• Always remember the business maxim “look ahead and reason back.” This can help you avoid potential hold up.

• Before making a sunk cost investment, ask what you will do if you are held up. • What would you do to address hold up?

• One possible solution to post-investment hold-up is vertical integration.

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Solutions and a final example• Example: Bauxite mine and alumina refinery• Refineries are tailored to specific qualities of ore• Building refineries near mines reduces costs for the

refiner, but, the building of the refinery becomes a sunk cost

• The transaction options are:• Long-term contracts• Vertical integration• Vertical integration refers to the common ownership of two

firms in separate stages of the vertical supply chain that connects raw materials to finished goods

• We can make it expensive to hold up. Incentives should be introduced that cause both parties to adhere to original agreements.

• Contractual view of marriage• What is the hold-up problem?

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Lecture 4 continued

TOPIC #3: Simple Pricing and demand

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Summary of main points• Aggregate demand or market demand is the total number

of units that will be purchased by a group of consumers at a given price.

• Pricing is an extent decision. Reduce price (increase quantity) if MR > MC. Increase price (reduce quantity) if MR < MC. The optimal price is where MR = MC.

• Price elasticity of demand, e = (% change in quantity demanded) ÷ (% change in price)• Estimated price elasticity = [(Q1 - Q2)/(Q1 + Q2)] ÷ [(P1 - P2)/(P1 +

P2)] is used to estimate demand from a price and quantity change.

• If |e| > 1, demand is elastic; if |e| < 1, demand is inelastic.

• %ΔRevenue ≈ %ΔPrice + %ΔQuantity• Elastic Demand (|e| > 1): Quantity changes more than price.

• Inelastic Demand (|e| < 1): Quantity changes less than price.

Summary (cont.)• MR > MC implies that (P - MC)/P > 1/|e|; in words, if the

actual markup is bigger than the desired markup, reduce price• Equivalently, sell more

• Four factors make demand more elastic:• Products with close substitutes (or distant complements)

have more elastic demand.• Demand for brands is more elastic than industry demand.• In the long run, demand becomes more elastic.• As price increases, demand becomes more elastic.

• Income elasticity, cross-price elasticity, and advertising elasticity are measures of how changes in these other factors affect demand.

• It is possible to use elasticity to forecast changes in demand: %ΔQuantity ≈ (factor elasticity)*(%ΔFactor).

• Stay-even analysis can be used to determine the volume required to offset a change in costs or prices.

Introductory anecdote: Gas prices

• US: From early 2007 to mid 2008 gas prices rose in the US.• Gas prices caused people to find alternate methods of work and

travel to avoid using gas. • Some farms began using mules instead of tractors

• India: In Rajasthan, the rising gas prices caused many farmers to switch from tractors to camels on farms.• As oil prices rose, demand for camels increased.• Prices for camels tripled over a two-year period.

• A US company, NNS, that produces potash fertilizer experienced an increase in input costs due to their use of petrochemicals.• NNS doubled the price of the generic fertilizer, and priced it’s

branded fertilizer at a 35% premium above the generic price. • Costs increased rapidly over the first two quarters combined

with NNS’s policy of quarterly price revision led to stockouts and a price that ended up being 25% below the generic – NNS could have earned $13 million but failed to maintain their premium

Background: consumer surplus and demand curves• First Law of Demand - consumers demand (purchase)

more as price falls, assuming other factors are held constant.

• Consumers make consumption decisions using marginal analysis, consume more if marginal value > price

• But, the marginal value of consuming each subsequent unit diminishes the more you consume.

• Consumer surplus = value to consumer - price paid

• Definition: Demand curves are functions that relate the price of a product to the quantity demanded by consumers

Background: consumer surplus and demand curves (cont.)

• Hot dog consumer• Values first dog at $5, next at $4 . . . fifth at $1

• Note that if hot dogs price is $3, consumer will purchase 3 hot dogs

Background: aggregate demand• Aggregate Demand: the buying behavior of a group of

consumers; a total of all the individual demand curves.

• To construct demand, sort by value.

• Discussion: Why do aggregate demand curves slope downward?

• Role of heterogeneity?

• How to estimate?

Price Quantity RevenueMarginal Revenue

$7.00 1 $7.00 $7.00$6.00 2 $12.00 $5.00$5.00 3 $15.00 $3.00$4.00 4 $16.00 $1.00$3.00 5 $15.00 -$1.00$2.00 6 $12.00 -$3.00$1.00 7 $7.00 -$5.00

$0.00

$2.00

$4.00

$6.00

$8.00

$0.00 $2.00 $4.00 $6.00 $8.00