1. CTF Analysis and Terminal LossP
UCC
Time P
After-tax PW = P (CTF)

2. How does this modify the present worth?
Now suppose we sell the item after N years for a terminal loss..
UCC
Terminal Loss
Salvage N
How does this modify the present worth?

3. We gain the salvage payment, but lose its future tax shield
UCC
Salvage
In Year N, this is worth S (CSF)

4. We get immediate tax relief for the terminal loss, but lose
its future tax shield…
UCC
Terminal loss = T
Tax saving = Tt
Lost shield = T(1-CSF)
This assumes that the company is profitable despite the terminal loss
In Year N, this is worth Tt - T(1-CSF)

5. So the net present worth of these cashflows is: PW = P(CTF)
UCC
Terminal Loss
Salvage N
So the net present worth of these cashflows is:
PW = P(CTF)
+ (S(CSF) + Tt - T(1-CSF))(P/F,i,N)

6. 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)
If i > j, is PW positive or negative?

7. Uncertainty Analysis
November 10, 2014

8. 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

9. 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

10. Background to break-even analysis: Profit
Variable Costs
Royalties, spoilage, packaging, maintenance,
direct labour, raw material, direct supplies,
direct supervision, sales commissions
Fixed Costs
Rent, Interest, Research, Insurance, Depreciation,
Property Taxes, Advertising Budget, Technical
Services, Executive Salaries
Selling price of 1 unit

11. Profit Variable Costs Fixed Costs Total Revenue Total Costs BEP
Units sold

12. Contribution = Selling Price – Variable Cost/Unit
So BEP = Fixed Costs/Contribution

13. Profit Margin
The profit margin is an indicator of the health
of an organization.
Margin = Gross Annual Profit/Fixed Annual Costs or
Actual Sales – Break-Even Sales
Margin =
Break-Even Sales

14. 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 pies
4,000 pies
6,000 pies
7,000 pies

15. If the company in the previous question pays taxes at 50%, the (after-tax) breakeven point is:
7,000 pies
8,000 pies
12,000 pies
14,000 pies

16. How can this company increase profits?
Total Cost
Profit
Selling Price
Volume of Sales

17. New Selling Price
Total Cost
Profit
Profit
Total Cost
a) Increase price

18. Total Cost
Profit
Profit
Profit
Total Cost
Total Cost
b) Increase sales

19. Total Cost
Profit
Profit
Profit
Profit
Total Cost
Total Cost
Total Cost
c) Decrease costs and price

20. 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 is
considering reducing selling price by $2,000/unit,
adding a feature to each unit that increases variable costs
by $1,000, and spending $120,000 on ads to increase sales.
If these measures increase sales to 72 units per year, what
happens to the BEP and the profit margin?
Suppose instead the firm went to 200% capacity and sold the
extra units at $25K each, how would this affect gross profits?

21. 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 to
over-utilised.
Marginal cost
Unit costs
No. Produced

22. Non-Linear Break-Even Analysis
As a result, the average variable cost also increases…
Marginal cost
Unit costs
Average variable cost
No. Produced

23. Non-Linear Break-Even Analysis
However, the average fixed cost always goes down…
Marginal cost
Unit costs
Average variable cost
Average fixed cost
No. Produced

24. Non-Linear Break-Even Analysis
So the average total cost of production displays a minimum…
Marginal cost
Average total cost
Unit costs
Average variable cost
Average fixed cost
No. Produced

25. Non-Linear Break-Even Analysis
Similarly, in order to increase sales beyond a certain level, it may be necessary
to drop the selling price
Revenue
and
costs
Total Revenue = 21000n0.5
n, No. Produced

26. Non-Linear Break-Even Analysis
The fixed costs must be met.
Revenue
and
costs
Fixed Costs
No. Produced

27. Non-Linear Break-Even Analysis
Including the variable costs, we see there are two break even points
Variable costs
Revenue
and
costs
BEP
BEP
No. Produced

28. Sensitivity Analysis
Having solved a problem, we determine the sensitivity of the solution to changes
in 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 yield
annual receipts of $35,000. There will be a salvage value of $20,000 after
ten years, and the annual operating cost will be $3,000. If the MARR is
13%, should the investment be made?

29. 30,000
20,000
10,000
-30%
-20%
-10%
+10%
+20%
+30%
-10,000
Salvage costs have little
effect
-20,000
-30,000

30. 30,000
20,000
10,000
-30%
-20%
-10%
+10%
+20%
+30%
-10,000
Nor do the running costs…
-20,000
-30,000

31. 30,000
20,000
10,000
-30%
-20%
-10%
+10%
+20%
+30%
-10,000
But the solution is sensitive to the
worth of the annual receipts…
-20,000
-30,000

32. 30,000
20,000
10,000
-30%
-20%
-10%
+10%
+20%
+30%
-10,000
And to the assumed life of the
equipment….
-20,000
-30,000

33. 30,000
20,000
10,000
-30%
-20%
-10%
+10%
+20%
+30%
-10,000
-20,000
Lastly, the MARR has an
effect on the present value.
-30,000

34. Another way of presenting these results is
by plotting acceptance-rejection zones.
Consider the same proposal, and compare the
effect of annual receipts, x, and costs, y, on the
EAW:
EAW = -130,000(A/P,13,10)+35,000(1+x)
-3,000(1+y)+20,000(A/F,13,10)
= ,000x – 3,000y

35. Rejection Zone (EAW < 0) y-axis: Disbursements +30% +20% +10% -30%
-20%
-10%
+10%
+20%
+30%
x-axis: Receipts
-10%
-20%
-30%

36. An isoquant is a curve showing what combinations
Isoquants
An isoquant is a curve showing what combinations
of two parameters would yield the same present worth 15
Accept 10
Life of Asset
Reject 5
30,000
35,000
40,000
Annual Receipts

37. Comparison of Alternatives
Factor
Alternative 1
Alternative 2
Annual Receipts
$35,000
First Cost
$170,000
$116,400
Salvage Value
$20,000
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 conclusion
to the length of the study period?

38. 10,000
20,000
30,000
-10,000
-20,000
-30,000
Alt. 1
Present Worth
Alt. 2 5 10 15 20
Study Period

39. Scenario Analysis
…also sometimes known as
the `Goldilocks’ method…

40. 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
1 year
Operating costs
$90,000
$160,000
$275,000
Consumables PW

41. 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
1 year
Operating costs
$90,000
$160,000
$275,000
Consumables PW
-$2,594
$156,086
$255,493