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• Form above we can obtain breakeven quantity: Revenue = P*Q Variable cost = C *Q [C is a unit cost] Total Cost = FC + VC Breakeven output is: Q* = FC/ (PC)
• In analysis of cost we must take into account all explicit and implicit
costs Breakeven Analysis, Continued Oil Exploration • Sunk Cost
– After investment takes place the only way to recoup the
investment is through depreciation. Initial capital investment is
a sunk Cost. This also impact negotiation between contractor
and sponsor • Why lumpiness of capital important?
– Once activities increase beyond certain point additional capital
investment would be required. If capital is lumpy, then part of it
may stay ideal. In this case the total cost would be allocated to
the project, which could bring profitability low or negative. • How to deal with lumpiness?
– lease – outsourcing – alliances Impact of Inflation • Inflation impacts a number of variables in in the NPV
equation. Therefore, calculation of NPV, using real
value for variables provides different results than if
nominal values were used.
NPV = I + ∑(Rc  Cc)(1 ta)(1+i) /(1+r)^t (1+i)^t
Where Rc, Cc, and Rc are constant rates and i is the inflation rate – Impact of inflation on different costs parameters maybe
different. Therefore, if nominal values were being used
each cost components would have to be discounted by its
own price index. Impact of Inflation on Tax Shield • Impact of inflation on tax shield is another
important aspect. Inflation reduces tax shield
of depreciation. This is because, based on USA
accounting rules, depreciation is a fix value of
the cost of capital good. The difference is
particularly important in when there is hyper
inflation
NPV = I + ∑(Rc  Cc)(1 ta)(1+i) /(1+i)(1+r)t + ∑ta D/(1+i)(1+r)^t + SV/(1+i) (1+r)t Example of Inflation Company XYZ is considering three different projects, A, B, C.
Project A does not need any initial investment, while project B
and C require $1,000 and $10,000 investment respectively. All
projects have 10 year life span and use straight line
depreciation. Annual cash flow of A, B, and C are $361.4,
$671.4 and 3460.6. Assuming a discount rate of 20% and tax
rate of 34% calculate :
After tax NPV of each project
Determine the impact of 4.17 % inflation rate on the NPV of
each project. Example
A B C 0 1000 10000 10 10 10 0 100 1000 Annua l Ca sh Fl ow 361. 4 671. 4 3460.6 R(1ta ) 238. 5 443 2283 0 34 340 238. 5 477 2623 Sum [(1ta )+ T*D]/(1+ R)t 1000 2000 11000 NPV 1000 1000 1000 Initia l Inve stm e nt
Proj e ct life
De pre ci a ton (D/ n) t*D
Afte r Ta x Ca sh Flow
(1ta )R+ T*D (1) Note : ta x Shie l d is 34*4.19 = 140 (1) $1 a nnuity a t 20% inte re st for t= 10 is e qua l to $4.192
238.5*4. 192 = 1000
477.1*4. 192 = 2000
2623.9*4. 192 = 11000 Example Continues Nominal Discount Rate
Annual Inflation Rate
4.17%
8.33%
12.50%
16.67% (1+interest rate)(1+ inflation rate)
(1.0417)(1.2) = 1.25
(1.0833)(1.2) = 1.3
(1.125)(1.2) = 1.35
(1.1667)(1.2) =1.4 Ten Years annuity at discount
rate of 25% is 3.57 and not 4.19
Shown in previous case Example Continues With 4.17% Inlfation
A B C Initial Investment 0 1000 10000 Depreciation 0 100 1000 Cash Flow (CF) 361.4 671.4 3460.6 After tax return 238.5 443.1 2283.6 0 34 340 1000 1857.5 1214.2 0 121.4 1214.1 Annual Depreciation tax shield
PV of cash flow
PV. Of depreciation tax shield
PV of total cash flow 1000 1978.8 10788.1 Net Present Value 1000 978.8 788.1 238.5*4.19=1000
443.1*4.19=1857.5
34*3.57= 121.4
340*3.54= 1214.1 MIT OpenCourseWare
http://ocw.mit.edu 1.040 Project Management
Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Cost Benefit Analysis Massood V.Samii Outline • What is cost benefit analysis?
• Why should we use CBA as oppose to
NPV?
• What are the complexity of CBA?
• Issue of consumer surplus and its role in
determination of social benefit
• Example of cost benefit analysis Public Projects • Public projects are those that are undertaken by
government. Their objective is not necessarily to maximize
profit or NPV as discussed earlier
• The main objective of public projects is to maximize social
benefits and return to the society
• Problem arises regarding quantification of benefits and
costs. Often there is no tradable market for public goods
(parks, environmental clean up, nontoll road) or even if
there is, it does not reflect the true value to the society
(public education, public transportation).
• Method used for the evaluation of project from public
point of view ( as oppose to private firm which looks
purely from private value creation for owner/stockholders)
is called CostBenefit Analysis ( value creation for
society). Cost Benefit Analysis • “CostBenefit Analysis is a procedure for evaluating the desirability of
a project by weighting benefits against costs. Results may be expressed
in different ways, including internal rate of return, net present value
and benefitcost ra...
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 Spring '12
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