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Capital Budgeting
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Capital Budgeting


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  • 1. Capital Budgeting
  • 2. Contents
    • Comparison.
    • Standard deviation.
    • Coefficient of Variation.
    • Sensitivity analysis.
    • Certainty Equivalent.
    • Rate of discount.
    • Inflation.
    • IRR.
    • Probability.
    • NPV.
    1 Sheet No. Sheet No Particulars Particulars
  • 3. NPV
    • NPV equals present value of cash inflows less present value of cash outflows.
    • Probable / Expected NPV equals to the Σ(NPV n *probability n ) where n denotes the transaction in an year.
    • EANPV equals present value of cash inflows divided by sum of PV factor for n number of years (life of the project).
    • Base NPV = Simple NPV.
    • Adjusted NPV = Base NPV + Present value of tax saving on
    • interest(using interest rate as discount rate)
    • – Floatation Cost.
    • Overall NPV in case of joint probability = Σ Joint Probability*
    • Inflow
  • 4. IRR
    • Simple formula = Lower rate + NPV at lower rate
    • NPV at _ NPV at
    • lower rate higher rate
    • Conditional formula = Lower rate + Σ PV factor _ Σ PV factor
    • at lower rate at IRR
    • Σ PV factor _ Σ PV factor
    • at lower rate at higher rate
    • The condition lying above is that the annual cash flows are equal. This is so because the calculation of Σ PV factor at IRR above have a special formula i.e. = Outflows
    • Annual Inflows
    • When life is infinite the IRR = (Annual inflow / PV of outflows)
  • 5. IRR
    • IRR = 0, when life of project = Σ PV factor at IRR.
    • Project IRR is the IRR calculated taking the cash flows as for the project as a whole.
    • Equity IRR is the IRR calculated taking the cash flows as for the equity only (Equity cash flows = Project cash flows - Principal & Interest payment on other finances).
    • IRR for long term funds is the IRR calculated as for the long term funds (Long term fund cash flows = Project cash flows - Principal & Interest payment on short term finances).
    • Modified IRR is the IRR based on the assumption that the internal cash flows are re-invested at cost of capital whereas the simple IRR has an assumption that the internal cash flows are re-invested at IRR.
  • 6. Rates of Discount
    • These are decided as per the cash flows:
    • 1. If the cash flows are risky then use riskier rate.
    • 2. If the cash flows are risk adjusted / certain then use risk adjusted / free rate.
    • 3. If the cash flows are in real terms then use real rate.
    • 4. If the cash flows are inflation adjusted then use money / nominal rate.
    • (Money rate+1) = (1+Real Rate)(1+Inflation Rate)
  • 7. Sensitivity analysis
    • The basic principle of sensitivity analysis is that we, hereby with this
    • principle, have to think negative about the project’s NPV. For this we may
    • be having two conditions. These are:
    • 1. Given conditions – The question may provide the elements governing
    • NPV, to make it (NPV) zero.
    • 2. No specific condition – In this particular case we have o make NPV at
    • zero by sensitivising Cash Inflows, Cash Outflows, Life & Discount Rate.
    • Cash Inflows – Make it equal to Cash Outflows.
    • Cash Outflows – Make it equal to Cash Inflows.
    • Life – Use the formula of discounted payback period by taking inflows
    • as equal to outflows.
    • Discount Rate – Use IRRs conditional formula to arrive at NPV at zero.
    • Finally we have to see what is the proportion in which the element is
    • influencing the NPV to make it at zero.
  • 8. Standard deviation S 1 denotes standard deviation of year 1 Overall  = √ ( S 1 ) 2 + ( S 2 ) 2 (1+K e ) 2 [(1+K e ) 2 ] 2 Independent cash flows Overall  = ( S 1 ) + ( S 2 ) (1+K e ) (1+K e ) 2 Perfectly correlated cash flows Normal conditions  = √ ( S 1 W 1 ) 2 + ( S 2 W 2 ) 2 + 2 ( S 1 W 1 S 2 W 2 R 12 ) S 1 denotes standard deviation of one asset. W 1 denotes weight of that asset. R 12 denotes correlation between those two assets S = √ Σ (Expected NPV- Actual NPV) 2 *probability More than one Asset Single Asset
  • 9. Probability
    • In capital budgeting the probability is found out by using normal distribution curve.
    • Z = Required NPV – Expected NPV
    • Prepare normal curve diagram & allocate the required NPV & expected NPV.
    • Find probability using the normal distribution table.
    • Joint probability is calculated in the condition where the first probability decides the happening of the second conditional event.
    • Joint probability = Initial probability*Conditional probability.
  • 10. Inflation
    • If the cash flows are inflation adjusted, we use money rate for discounting the flows.
    • Inflation adjusted cash flows = (Normal cash flows)(1+Inflation rate) for next year. The normal cash flows denotes the cash flows in real term i.e. at period zero.
    • Depreciation do not attract inflation.
  • 11. Certainty Equivalent
    • Certain cash flows are found out by multiplying certainty equivalent by the given cash flows.
    • Then it will be discounted using risk adjusted / free rate to arrive at present value of cash inflows.
    • Finally the NPV can be found by deducting present value of cash outflows by above present value.
  • 12. Coefficient of Variation
    • Coefficient of Variation = Standard deviation *100
    • NPV
    • When the standard deviation & the NPV are not sufficient to make a perfect decision about the project the decision is taken up using C. V.
  • 13. Profitability Index
    • PI = PV of inflows
    • PV of outflows
    • When the organisation, don't have sufficient funds to select different projects, it use the process of PI i.e. project having high PI is selected.
    • When there are outflows in multiple period of time the outflows except for the initial outflows are excluded.
    • PI = PV of inflows
    • Initial outflows
    • Firstly find NPV of all the projects leaded by the step to find minimum number of projects with maximum amount arrange projects in the deceasing order of NPV & draw a table to finally conclude the result.
    • Mutually exclusive projects, complimentary projects.
  • 14. Replacement Decision
    • Whether to replace the asset or not?
    • When to replace the asset?
    • When to replace the same kind of machine again?
  • 15. Comparison
    • N.P.V – Choose project having higher NPV.
    • I.R.R. – Choose project having higher IRR.
    • C. V. – Choose project having lower C. V.
    •  – Choose project having lower standard deviation.
    • If IRR & NPV are giving decision in opposite direction then select the project as per C. V.
  • 16. General
    • Depreciation have no relevance when no tax is provided as it provides only the tax saving.
    • Allocable costs are excluded from the statement.
    • Sunk costs are excluded from the statement.
    • When we have more than one project to choose from having unequal life then the decision is taken-up by calculating EANPV.
    • When there is a missing figure question, the NPV is taken as zero.
    • In case of block of assets concept, the only change is that it affects the salvages value & the depreciation.
    • Remember TAX & TIME effects.
  • 17. Notes
  • 18. Thank You