Overview & Learning Objectives Overview: In decision making, planning and analysis, it is important to know the difference between the average and margina

Overview & Learning Objectives Overview:

In decision making, planning and analysis, it is important to know the difference between the average and marginal cost of units produced. An average cost is calculated by adding up the total fixed and variable costs and dividing them by the units produced. The limitation here is that fixed costs- because they are already committed or “sunk” are not relevant in present decision-making because we have no control over them. What is relevant is the marginal cost, which is the cost of producing and selling an additional unit, something firms do have some influence over. Also relevant is marginal revenue, which is the additional revenue made by selling another unit. The goal here, always easier said than done, is the minimize marginal cost and maximize marginal revenue. 

A challenge faced by firms in deciding what opportunities to pursue with their limited resources is that the sacrifice of limited resources is made in the present, but the hoped-for rewards do not arrive until some time or times in the future. In order to evaluate these in the decision-making process, discounting is used, which is the process of translating future cash flows into today’s equivalent amounts. Doing this accurately, as you will see in this week’s learning, is a very desirable and valuable skill to develop and apply. Investment Decisions:
Look Ahead and Reason Back
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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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Avoidable costs can be recovered by shutting down. If the benefits of shutting down (you recover your avoidable costs) are larger than the costs (you forgo revenue), then shut down. The break-even price is average avoidable cost.
If you incur sunk costs, you are vulnerable to post-investment hold-up. Anticipate hold-up and choose contracts or organizational forms that minimize the costs of hold-up.
Once relationship-specific investments are made, parties are locked into a trading relationship with each other, and can be held up by their trading partners. 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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Title?
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.
This story illustrates both the effect of the bursting credit bubble on real estate valuations and, more importantly, the relevant costs and benefits of investment decisions.
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Background: Investment Profitability
All investments represent a trade-off between possible future gain and current sacrifice.
Willingness to invest in projects with a low rate of return, indicates a willingness to trade current dollars for future dollars at a relatively low rate.
This is also known as having a low discount rate (r).
Individuals with low discount rates would willingly lend to those with higher discount rates.
Discounting helps you figure out if future gains are larger than current sacrifice.
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Compounding
To understand discounting, let’s first look at compounding:
(future value, k periods in the future) = (present value) x (1 + r)K
Example: If you invest $1 (present value) today at a 10% (r), then you would expect to have $1.10 in one year.
In two years, $1 becomes $1.21 = $1.10 x (1+.1)
A good compounding rule of thumb:
“Rule of 72”: If you invest at a rate of return r, divide 72 by r to get the number of years it takes to double your money
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Discounting
Discounting (the inverse of compounding):
Present value = (future value, k periods in the future)
(1 + r)k
Example: At a 10% r, $1 is worth:
Next year: ($1)/1.1 = $0.91
Two years: ($0.91)/1.1 =$0.83
Discussion: If my discount rate is 10%, would I lend to or borrow from someone with a discount rate of 15%?
What does this say about behavior?
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Example: Nashville Pension Obligations
The city of Nashville uses discounting to decide how much to save for future pension obligations.
For a pension that pays out $100,000 in 20 years, with a discount rate of 8.25% Nashville must save:
$100,000/(1.0825)20 =$20,485
If the city invests the $20,485 and earns 8.25%, then the savings will compound in 20 years – unrealistic!
Somewhat of high savings rate that may not be returned; however, a high savings rate means less current spending, which is politically popular
A more realistic (but less popular) discount rate would be 6.5%, which would lead to saving $28,380 now.
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Determining the Profitability of Investments
Remember the simple rule: discount the future benefits of an investment, and compare them to the current cost.
Companies use 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, then the project earns more than the cost of capital.
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The NPV Rule In Action
Consider two projects that each require an initial investment of $100
Project 1 returns $115 at the end of the first year
Project 2 returns $60 at the end of the first, and $60 at the end of the second
The company’s cost of capital is 14%
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Project 1 earns more than the cost of capital. Project 2 does not.

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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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Another Method: Break-Even Quantities
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)
FC: fixed costs P: price MC:marginal cost
(P-MC) is the “contribution margin” – what’s left after marginal cost to “contribute” to covering fixed costs
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Break-Even Example: Nissan Truck
Nissan’s popular truck model, the Titan, had only two years remaining on its production cycle. Redesigning the “Titan” would cost $400M.
Cost of capital was 12%, implying annual fixed cost of $48M
Contribution margin on each truck is $1,500
Break-even quantity is 32,000 trucks
The decision to redesign or not came down to a break-even analysis
Nissan had a 3% share of the market, implying only 12,000 Titan sales per year – not enough to break even.
Instead they decided to license the Dodge Ram Truck, which would reduce the fixed cost of redesign, and a lower break-even point.
After the Government took over Chrysler, Nissan reconsidered.
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Deciding Between Two Technologies
In 1983, John Deere was in the midst of building a Henry-Ford-style production line factory for large 4WD tractors
Unexpectedly, wheat prices fell dramatically reducing demand for large tractors
Deere decided to abandon the new factory and instead purchased Versatile, a company that assembled tractors in a garage using off-the-shelf components
Deere chose one manufacturing technology over another
A discrete investment decision – the factory had big FC and small MC, Versatile had small FC but bigger MC
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John Deere: Right Decision?
Was purchasing Versatile the right choice?
It depends… on how much John Deere expected to sell.
Suppose the capital-intensive technology would
involve $100 FC and $10 MC
Suppose Versatile’s technology had $50 FC and $20 MC
To determine break-even quantity (point of indifference),
solve for the quantity that equates the costs: $150 for 5 units
If you expect to sell less than 5 units, choose the
low-MC technology
If you expect to sell more than 5 units, choose the
low-FC technology
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John Deere Lesson
John Deere made the right decision by acquiring Versatile; however, the Antitrust Division of he U.S. Department of Justice challenged the acquisition as anticompetitive.
John Deere and Versatile were only two of 4 firms selling 4WD tractors in North America.
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Break-Even Advice
Remember this advice: Do not invoke break-even analysis to justify higher prices or greater output.
Managers sometimes believe they must raise prices to cover fixed costs or they must sell as much as possible to make average costs lower
These are extent decisions though!
They require marginal analysis, not break-even
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The Decision to 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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Cost Taxonomy
Example: FC=$100, MC=$5, and you produce 100 units/year
How low of a price before you shut down? IT DEPENDS
It depends on which costs are avoidable
Long-run: fixed costs become avoidable so they are included
in the shutdown price
Short run: they are unavoidable and should not be included
in the shutdown price
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Fixed Costs
(avoidable in long run)

Variable Costs
(avoidable in short run)

Avoidable
Costs

Unavoidable
or “Sunk” Costs

Costs

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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?
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Sunk Costs and Post-Investment Hold Up Example
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 renegotiating 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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Vertical Integration
One possible solution to post-investment hold-up is vertical integration.
Example: Bauxite mine and alumina refinery
Refineries are tailored to specific qualities of ore
The transaction options are:
Spot-market transactions
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
Discussion: How is vertical integration a solution to hold up?
Contractual view of marriage
Long-term contracts induce higher levels of relationship-specific investment
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