Lecture 5: Review Investment decisions and break even analysis

Lecture 5: Review

Investment 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.

Shutdown decisions

  Shutdown decisions are difficult psychologically, but

economically, the rule of thumb is straightforward

  Avoidable 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.

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

Costs “Taxonomy”

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?

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.

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.”

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?

Lecture 5

 TOPIC #1: Simple

Pricing and demand

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

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.”

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.

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.

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

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

Start from the top… FILL IT IN:

FIXED COST =$5

PRICE Q Demand _{Revnue MR MC Profit}

$7 1 $1.50 $6 2 $1.50 $5 3 $1.50 $4 4 $1.50 $3 5 $1.50 $2 6 $1.50 $1 7 $1.50 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.

Elasticity of demand

•  Price elasticity is a factor in calculating MR.

•  Definition: price elasticity of demand (e)

•  (%Δ in Q

d

_{) ÷ (%Δ 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.

Price change between month 1

and month 2

•  Definition: Elasticity=

[(q

₂

-q

₁

)/(q

₁

+q

₂

_{)] ÷ [(p}

₂

-p

₁

)/(p

₁

+p

₂

)].

•  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?

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.

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;

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).

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?

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!

Example

  Suppose you have the following data:

  Elasticity=–2

  Average Price =$10   Marginal Cost= $8

  Should we raise the price? How do you know?