uncertainty analysis
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Uncertainty Analysis. November 13, 2013. 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. - PowerPoint PPT PresentationTRANSCRIPT
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CTF Analysis and Terminal Loss
UCC
Time
After-tax PW = P (CTF)P
P
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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?
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We gain the salvage payment, but lose its future tax shield
UCC
Salvage
In Year N, this is worth S (CSF)
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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)
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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
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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
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Uncertainty Analysis
November 10, 2014
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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
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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
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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
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ProfitProfit
Variable CostsVariable Costs
Fixed CostsFixed Costs
Units soldBEP
Total Costs
Total Revenue
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Contribution = Selling Price – Variable Cost/Unit
So BEP = Fixed Costs/Contribution
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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
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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
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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
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Total CostTotal Cost
ProfitProfitSelling Price
How can this company increase profits?
Volume of Sales
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Total CostTotal Cost
ProfitProfit
New Selling Price
Total CostTotal Cost
ProfitProfit
a) Increase price
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Total CostTotal Cost
ProfitProfit
Total CostTotal Cost
ProfitProfit
b) Increase sales
Total CostTotal Cost
ProfitProfit
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Total CostTotal Cost
ProfitProfit
Total CostTotal Cost
ProfitProfit
c) Decrease costs and price
Total CostTotal Cost
ProfitProfit
Total CostTotal Cost
ProfitProfit
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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?
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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
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Non-Linear Break-Even Analysis
As a result, the average variable cost also increases…
No. Produced
Unit costsAverage variable cost
Marginal cost
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Non-Linear Break-Even Analysis
However, the average fixed cost always goes down…
No. Produced
Unit costsAverage variable cost
Average fixed cost
Marginal cost
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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
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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
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Non-Linear Break-Even Analysis
The fixed costs must be met.
No. Produced
Revenue and costs
Fixed Costs
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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
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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?
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10,000
20,000
30,000
-10,000
-20,000
-30,000
+10% +20% +30%-10%-20%-30%
Salvage costs have littleeffect
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10,000
20,000
30,000
-10,000
-20,000
-30,000
+10% +20% +30%-10%-20%-30%
Nor do the running costs…
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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…
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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….
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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.
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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
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+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)
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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
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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?
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10,000
20,000
30,000
-10,000
-20,000
-30,000
15 20105
Study Period
Present Worth
Alt. 1
Alt. 2
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Scenario Analysis
…also sometimes known asthe `Goldilocks’ method…
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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
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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