CTF Analysis and Terminal Loss

UCC

Time

After-tax PW = P (CTF)P

P

Now suppose we sell the item after N years for a terminal loss..

UCC

Salvage

Terminal Loss

N

How does this modify the present worth?

We gain the salvage payment, but lose its future tax shield

UCC

Salvage

In Year N, this is worth S (CSF)

We get immediate tax relief for the terminal loss, but lose its future tax shield…

UCC

Terminal loss = T

In Year N, this is worth Tt - T(1-CSF)

Tax saving = Tt

Lost shield = T(1-CSF)

UCC

Salvage

Terminal Loss

N

So the net present worth of these cashflows is:

PW = P(CTF) + (S(CSF) + Tt - T(1-CSF))(P/F,i,N)

P

Present Value of a Bank Loan

I borrow P from a bank at interest rate i.

My MARR is j

A = P(A/P,i,N)

PW = P – A(P/A,j,N)

P

A

Uncertainty Analysis

November 10, 2014

Making Confident Decisions in an Uncertain World

If we have probability estimates for different futures,we can undertake risk analysis

Lacking probability estimates, we can try:

break-even analysis

sensitivity analysis

scenario analysis

Break-Even Analysis

The purpose of break-even analysis is to focus our uncertainty:

Rather than ask,

``What is the value of x?’’

we ask

``Is x greater than a threshold x0?’’

That is to say, we set an aspiration level for x

Background to break-even analysis:ProfitProfit

Variable CostsVariable Costs

Fixed CostsFixed Costs

Selling price of 1 unit

Royalties, spoilage, packaging, maintenance,direct labour, raw material, direct supplies,direct supervision, sales commissions

Rent, Interest, Research, Insurance, Depreciation,Property Taxes, Advertising Budget, TechnicalServices, Executive Salaries

ProfitProfit

Variable CostsVariable Costs

Fixed CostsFixed Costs

Units soldBEP

Total Costs

Total Revenue

Contribution = Selling Price – Variable Cost/Unit

So BEP = Fixed Costs/Contribution

Profit Margin

The profit margin is an indicator of the healthof an organization.

Margin = Gross Annual Profit/Fixed Annual Costs

or

Margin =Actual Sales – Break-Even Sales

Break-Even Sales

A pie company has two employees who each earn $30,000 a year, and pays $10,000 rent every year. The ingredients for a pie, including the gas to cook it, cost $10 per pie. If pies are sold at $20 each, the break-even point for the company (calculated pre-tax) is: 

3,500 pies4,000 pies6,000 pies7,000 pies

If the company in the previous question pays taxes at 50%, the (after-tax) breakeven point is: 

7,000 pies8,000 pies12,000 pies14,000 pies

Total CostTotal Cost

ProfitProfitSelling Price

How can this company increase profits?

Volume of Sales

Total CostTotal Cost

ProfitProfit

New Selling Price

Total CostTotal Cost

ProfitProfit

a) Increase price

Total CostTotal Cost

ProfitProfit

Total CostTotal Cost

ProfitProfit

b) Increase sales

Total CostTotal Cost

ProfitProfit

Total CostTotal Cost

ProfitProfit

Total CostTotal Cost

ProfitProfit

c) Decrease costs and price

Total CostTotal Cost

ProfitProfit

Total CostTotal Cost

ProfitProfit

Example: A firm makes units that sell for $35,000 each.Variable costs are $20,000/unit and fixed costs are$600,000. The plant can produce 80 units a year, but is currently only working at 60% capacity. The firm isconsidering reducing selling price by $2,000/unit,adding a feature to each unit that increases variable costsby $1,000, and spending $120,000 on ads to increase sales.

If these measures increase sales to 72 units per year, whathappens to the BEP and the profit margin?

Suppose instead the firm went to 200% capacity and sold theextra units at $25K each, how would this affect gross profits?

Non-Linear Break-Even Analysis

The cost of making one more unit is usually not a fixed amount.

It typically shows a minimum as production goes from under-utilised toover-utilised.

No. Produced

Unit costs

Marginal cost

Non-Linear Break-Even Analysis

As a result, the average variable cost also increases…

No. Produced

Unit costsAverage variable cost

Marginal cost

Non-Linear Break-Even Analysis

However, the average fixed cost always goes down…

No. Produced

Unit costsAverage variable cost

Average fixed cost

Marginal cost

Non-Linear Break-Even Analysis

So the average total cost of production displays a minimum…

No. Produced

Unit costs

Average total cost

Average variable cost

Average fixed cost

Marginal cost

Non-Linear Break-Even Analysis

Similarly, in order to increase sales beyond a certain level, it may be necessary to drop the selling price

n, No. Produced

Revenue and costs Total Revenue = 21000n0.5

Non-Linear Break-Even Analysis

The fixed costs must be met.

No. Produced

Revenue and costs

Fixed Costs

Non-Linear Break-Even Analysis

Including the variable costs, we see there are two break even points

No. Produced

Revenue and costs

Variable costs

BEP

BEP

Sensitivity Analysis

Having solved a problem, we determine the sensitivity of the solution to changesin the problem parameters. Hence we can decide whether and when to do further research.

Example: a project has an initial cost of $170,000 and is expected to yieldannual receipts of $35,000. There will be a salvage value of $20,000 afterten years, and the annual operating cost will be $3,000. If the MARR is13%, should the investment be made?

10,000

20,000

30,000

-10,000

-20,000

-30,000

+10% +20% +30%-10%-20%-30%

Salvage costs have littleeffect

10,000

20,000

30,000

-10,000

-20,000

-30,000

+10% +20% +30%-10%-20%-30%

Nor do the running costs…

10,000

20,000

30,000

-10,000

-20,000

-30,000

+10% +20% +30%-10%-20%-30%

But the solution is sensitive to the worth of the annual receipts…

10,000

20,000

30,000

-10,000

-20,000

-30,000

+10% +20% +30%-10%-20%-30%

And to the assumed life of theequipment….

10,000

20,000

30,000

-10,000

-20,000

-30,000

+10% +20% +30%-10%-20%-30%

Lastly, the MARR has an effect on the present value.

Another way of presenting these results is by plotting acceptance-rejection zones.

Consider the same proposal, and compare theeffect of annual receipts, x, and costs, y, on theEAW:

EAW = -130,000(A/P,13,10)+35,000(1+x) -3,000(1+y)+20,000(A/F,13,10)

= 1757 +35,000x – 3,000y

+10% +20% +30%-10%-20%-30%

x-axis: Receipts

+10%

+20%

+30%

-10%

-20%

-30%

y-axis: Disbursements

Rejection Zone(EAW < 0)

Rejection Zone(EAW < 0)

Isoquants

An isoquant is a curve showing what combinationsof two parameters would yield the same present worth

Lif

e of

Ass

et

Annual Receipts30,000 35,000 40,000

5

10

15

Accept

Reject

Comparison of Alternatives

Factor Alternative 1 Alternative 2

Annual Receipts $35,000 $35,000

First Cost $170,000 $116,400

Salvage Value $20,000 0

Annual Costs $3,000 $3,000 increasing annually by $2,500

Based on a ten-year study period, both alternatives look about the same. How sensitive is this conclusionto the length of the study period?

10,000

20,000

30,000

-10,000

-20,000

-30,000

15 20105

Study Period

Present Worth

Alt. 1

Alt. 2

Scenario Analysis

…also sometimes known asthe `Goldilocks’ method…

Scenario Analysis

We compare the base case with plausible `best case’ and `worst case’scenarios:

Item Worst Base Best

Additional units 60,000 75,000 100,000

Price/unit $2 $3 $3.50

Annual income $120,000 $225,000 $350,000

Duration of income 5 years 6 years 7 years

Training cost/year $45,000 $35,000 $30,000

Intensive training 2 years 2 years 1 year

Operating costs $90,000 $160,000 $275,000

Consumables $30,000 $30,000 $30,000

PW

Scenario Analysis

We compare the base case with plausible `best case’ and `worst case’scenarios:

Item Worst Base Best

Additional units 60,000 75,000 100,000

Price/unit $2 $3 $3.50

Annual income $120,000 $225,000 $350,000

Duration of income 5 years 6 years 7 years

Training cost/year $45,000 $35,000 $30,000

Intensive training 2 years 2 years 1 year

Operating costs $90,000 $160,000 $275,000

Consumables $30,000 $30,000 $30,000

PW -$2,594 $156,086 $255,493