Lecture 5: ReviewInvestment 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.

2

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.

3

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

4

Costs “Taxonomy”

5

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?

6

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.

7

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. Another, is the so called “exchange of hostages.”

8

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?

9

Lecture 5

TOPIC #1: Simple Pricing and demand

10

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)• 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: Mattel

• Mattel: introduced Hot Wheels in 1968, kept price below $1.00 for 40 years, even as production costs rose

• Finally tested a price increase, experienced profits increase of 20%• Why? Profit=(P-TC)xQ• Businesses tend to focus on TC and Q,

neglect P

Roger Brinner, Parthenon Group

“In many instances, companies can make money by simply raising prices. Pricing is the grossly neglected orphan of profit management. Most companies leave list prices unchanged year after year or simply modestly increase list prices in an unchallenged annual ritual. Other companies perform strategic analyses, producing the facts and generating the confidence to change prices aggressively and to raise profits dramatically.”

14

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

KEY POINT #1

INDIVIDUAL DEMAND CURVES SLOPE DOWN…. THE LAW OF DEMAND!As we raise price, consumers will

respond by purchasing less.

16

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?

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

Pricing trade-off• Pricing is an extent decision

• Profit= Total Revenue – Total Cost

• Demand curves turn pricing decisions into quantity decisions: “what price should I charge?” is equivalent to “how much should I sell?”

• Fundamental tradeoff:• Lower price sell more, but earn less on each unit

sold• Higher price sell less, but earn more on each unit

sold

• Tradeoff created by downward sloping demand

19

Pricing• Marginal analysis finds the profit increasing

solution to the pricing tradeoff.• It tells you only whether to raise or lower price, not

by how much.

• Definition: marginal revenue (MR) is change in total revenue from selling extra unit.

• If MR>0, then total revenue will increase if you sell one more. Highest level of MR doesn’t mean profits are maximized as we saw on our quiz.

• If MR>MC, then total profits will increase if you sell one more.

• We already know: Profits are maximized when MR = MC

20

KEY POINT #2

MARGINAL ANALYSIS TELLS US THAT WHEN MR>MC…. PRODUCE AND SELL MORE!!! HOW???? DECREASE PRICE

WHEN MR<MC…. WE ARE PRODUCING AND SELLING TOO MUCH…. SELL LESS!!! HOW??? INCREASE PRICE

21

Start from the top… FILL IT IN: FIXED COST =$5

22

Let’s tell the truth

Having worked as an economic consultant, I can tell you, you will never see a complete demand curve.

Even still, the analysis we have just seen can give invaluable intuition into understanding pricing decisions.

In particular, what we have just seen is that MR and MC are what we need to know.

We can use this information and market information about elasticities to form the proper decisions.

23

Elasticity of demand

• Price elasticity is a factor in calculating MR.

• Definition: price elasticity of demand (e)• (% in Qd) (% in price)

• If |e| is less than one, demand is said to be inelastic.

• If |e| is greater than one, demand is said to be elastic.

24

Price change between month 1 and month 2

• Definition: Elasticity=

[(q2-q1)/(q1+q2)] [(p2-p1)/(p1+p2)].

• Note, by the law of demand, elasticity of price change should be negative.

• Example: On a promotion week for Vlasic, the price of Vlasic pickles dropped by 25% and quantity increased by 300%.• Is the price elasticity of demand -12?

• HINT: could something other than price be changing?

25

KEY POINT #3

WHEN DEMAND IS ELASTIC, RAISING THE PRICE WILL REDUCE REVENUE.

WHEN DEMAND IS INELASTIC, RAISING THE PRICE WILL RAISE REVENUE!!

Note: Remember revenue is only one side of the coin. We would need to know something about costs to determine if profit are maximized.

26

Example: Grocery Store (MidSouth in 1999).

3-Liter Coke Promotion (Instituted to meet Wal-Mart promotion)• Compute price elasticity of 3 liter coke; cross

price elasticity of 2 liter coke with respect to 3 liter price;

27

Revenue:

Demand for 3-liters was very elastic. Please calculate the revenue that resulted from the price decrease.

Did revenue increase or decrease?

Should increase as we already discussed.

We can show the %change in revenue is equal to the %change in price + % change in quantity.Since prices and quantities move in opposite

directions, total revenue changes will determined by which changes by more (in absolute value).

28

If you want, I’ll show you the math

• Proposition: MR = Avg(P)(1-1/|e|)• If |e|>1, MR>0.

• If |e|<1, MR<0.

• Discussion: If demand for Nike sneakers is inelastic, should Nike raise or lower price?

• Discussion: If demand for Nike sneakers is elastic, should Nike raise or lower price?

29

Example

MR>MC=> avg(P)[1-1/|e|]>MC=>avg(P)-avg(P)/|e|>MC=>avg(P)-MC>avg(P)/|e|=>[avg(P)-MC]/avg(P)>1/|e|

The firm’s actual mark-up exceeds the desired markup! It should lower price!

30

Example

Suppose you have the following data:

Elasticity=–2

Average Price =$10

Marginal Cost= $8

Should we raise the price? How do you know?

31