CTC 475 Review Taxes

Types of taxes Income tax is graduated

ATCF Calculate Depreciation BTCF-Depreciation=TI Tax=TI*tax rate ATCF=BTCF-Tax

CTC 475

Methods for Evaluating Uncertainty

Objective Know various methods for evaluating

uncertainty Breakeven Sensitivity OMP Probabilistic (Monte-Carlo)

Breakeven Determine quantity needed to break-even

Example Problem-Breakeven Sales Price $12.50 per unit

Revenues =12.5X Equipment cost $200,000 Overhead cost $50,000 per year O&M $25 per operating hour Production time per 1000 units=100 hours (0.1 hr

per unit) Annual O&M cost=0.1*$25*X=2.5X

Planning horizon 5 years MARR 15%

AW

AW=-$200K(A/P15,5)-$50K-2.5X+12.5X AW=-$109,660-2.5X+12.5X AW=-$109,660+10X If set AW=0

Then X=10,966 (Breakeven Value)

Sensitivity Analysis

Used to analyze effects of varying estimated parameters

Non-probabilistic technique

Sensitivity Example Initial Investment: $10K Annual Receipts: $3K Project Duration: 5 years MARR: 12% AW=-10K(A/P12,5)+$3K= +$226

Varying one parameter at a time +/-40%, determine AW

Vary Annual ReceiptsAW(12%)=-10K(A/P12,5)+3K

(1+X)

X Annual Receipts

AW

-40% 1,800 -974

-30% 2,100 -674

-20% 2,400 -374

-10% 2,700 -74

0 3,000 +226

10% 3,300 +526

20% 3,600 +826

30% 3,900 +1,126

40% 4,200 +1,426

Vary Initial InvestmentAW(12%)=-10K(1+X)(A/P12,5)+

3K

X Initial Investment

AW

-40% 6,000 +1,646

-30% 7,000 +1,079

-20% 8,000 +805

-10% 9,000 +530

0 10,000 +226

10% 11,000 -18

20% 12,000 -293

30% 13,000 -567

40% 14,000 -842

Vary MARRAW(12%)=-10K (A/P12(1+X),5)+3K

X MARR AW

-40% 7.2% +1,646

-30% 8.4% +1,079

-20% 9.6% +805

-10% 10.8% +530

0 12% +226

10% 13.2% -18

20% 14.4% -293

30% 15.6% -567

40% 16.8% -842

Vary Project DurationAW(12%)=-10K (A/P12,5(1+X) )

+3K

X Duration AW

-40% 3 -1,163

-30%

-20% 4 -292

-10%

0 5 +226

10%

20% 6 +568

30%

40% 7 +809

Sensitivity Analysis

($1,500)

($1,000)

($500)

$0

$500

$1,000

$1,500

$2,000

-40% -30% -20% -10% 0% 10% 20% 30% 40%

% Change

AW

($)

MARR

Investment

Duration

Revenues

Sensitivity Less sensitive to MARR More sensitive to the other 3 parameters

Can do same type of analysis using PW/IRR, etc.

Varying more than one parameter Varying 2 parameters at a time results in a

3D graph See project 8

OMP Analysis Optimistic

Cash flows occur as well as can be reasonably expected

Most Likely Pessimistic

Cash flows occur as detrimentally as can be reasonably expected

OMP ExampleO M P

Investment -150K -150K -150K

Life 18 10 8

Market Value 0 0 0

Annual Revenues 110K 70K 50K

Annual Expenses -20K -43K -57K

AW +74,000 +4,650 -33,100

OMP AnalysisAnnual Expenses

O M P

Life Life Life

O M P O M P O M P

O 74K 68K 64K 51K 45K 41K 37K 31K 27K

M 34K 28K 24K 11K 5K 9K 3K 9K 13K

P 14K 8K 4K 9K 15K 19K 23K 29K 33K

Probabilistic Analysis (Monte Carlo) Use of probability for analysis of anything

which involves risk and uncertainty Must develop/assume probability

distributions Use random #’s to determine values

based on probabilities Make multiple runs (100x or 1000x) Summarize probabilities

Example using Probabilities

Useful Life Probability Random #

3 20% 00-19

5 40% 20-59

7 25% 60-84

10 15% 85-99

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