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- 1. Capital Budgeting
- 2. Contents <ul><li>Comparison. </li></ul>10 <ul><li>Standard deviation. </li></ul>5 <ul><li>Coefficient of Variation. </li></ul>9 <ul><li>Sensitivity analysis. </li></ul>4 <ul><li>Certainty Equivalent. </li></ul>8 <ul><li>Rate of discount. </li></ul>3 <ul><li>Inflation. </li></ul>7 <ul><li>IRR. </li></ul>2 <ul><li>Probability. </li></ul>6 <ul><li>NPV. </li></ul>1 Sheet No. Sheet No Particulars Particulars
- 3. NPV <ul><li>NPV equals present value of cash inflows less present value of cash outflows. </li></ul><ul><li>Probable / Expected NPV equals to the Σ(NPV n *probability n ) where n denotes the transaction in an year. </li></ul><ul><li>EANPV equals present value of cash inflows divided by sum of PV factor for n number of years (life of the project). </li></ul><ul><li>Base NPV = Simple NPV. </li></ul><ul><li>Adjusted NPV = Base NPV + Present value of tax saving on </li></ul><ul><li>interest(using interest rate as discount rate) </li></ul><ul><li>– Floatation Cost. </li></ul><ul><li>Overall NPV in case of joint probability = Σ Joint Probability* </li></ul><ul><li>Inflow </li></ul>
- 4. IRR <ul><li>Simple formula = Lower rate + NPV at lower rate </li></ul><ul><li>NPV at _ NPV at </li></ul><ul><li>lower rate higher rate </li></ul><ul><li>Conditional formula = Lower rate + Σ PV factor _ Σ PV factor </li></ul><ul><li>at lower rate at IRR </li></ul><ul><li>Σ PV factor _ Σ PV factor </li></ul><ul><li>at lower rate at higher rate </li></ul><ul><li>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 </li></ul><ul><li>Annual Inflows </li></ul><ul><li>When life is infinite the IRR = (Annual inflow / PV of outflows) </li></ul>
- 5. IRR <ul><li>IRR = 0, when life of project = Σ PV factor at IRR. </li></ul><ul><li>Project IRR is the IRR calculated taking the cash flows as for the project as a whole. </li></ul><ul><li>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). </li></ul><ul><li>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). </li></ul><ul><li>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. </li></ul>
- 6. Rates of Discount <ul><li>These are decided as per the cash flows: </li></ul><ul><li>1. If the cash flows are risky then use riskier rate. </li></ul><ul><li>2. If the cash flows are risk adjusted / certain then use risk adjusted / free rate. </li></ul><ul><li>3. If the cash flows are in real terms then use real rate. </li></ul><ul><li>4. If the cash flows are inflation adjusted then use money / nominal rate. </li></ul><ul><li>(Money rate+1) = (1+Real Rate)(1+Inflation Rate) </li></ul>
- 7. Sensitivity analysis <ul><li>The basic principle of sensitivity analysis is that we, hereby with this </li></ul><ul><li>principle, have to think negative about the project’s NPV. For this we may </li></ul><ul><li>be having two conditions. These are: </li></ul><ul><li>1. Given conditions – The question may provide the elements governing </li></ul><ul><li>NPV, to make it (NPV) zero. </li></ul><ul><li>2. No specific condition – In this particular case we have o make NPV at </li></ul><ul><li>zero by sensitivising Cash Inflows, Cash Outflows, Life & Discount Rate. </li></ul><ul><li>Cash Inflows – Make it equal to Cash Outflows. </li></ul><ul><li>Cash Outflows – Make it equal to Cash Inflows. </li></ul><ul><li>Life – Use the formula of discounted payback period by taking inflows </li></ul><ul><li>as equal to outflows. </li></ul><ul><li>Discount Rate – Use IRRs conditional formula to arrive at NPV at zero. </li></ul><ul><li>Finally we have to see what is the proportion in which the element is </li></ul><ul><li>influencing the NPV to make it at zero. </li></ul>
- 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 <ul><li>In capital budgeting the probability is found out by using normal distribution curve. </li></ul><ul><li>Z = Required NPV – Expected NPV </li></ul><ul><li> </li></ul><ul><li>Prepare normal curve diagram & allocate the required NPV & expected NPV. </li></ul><ul><li>Find probability using the normal distribution table. </li></ul><ul><li>Joint probability is calculated in the condition where the first probability decides the happening of the second conditional event. </li></ul><ul><li>Joint probability = Initial probability*Conditional probability. </li></ul>
- 10. Inflation <ul><li>If the cash flows are inflation adjusted, we use money rate for discounting the flows. </li></ul><ul><li>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. </li></ul><ul><li>Depreciation do not attract inflation. </li></ul>
- 11. Certainty Equivalent <ul><li>Certain cash flows are found out by multiplying certainty equivalent by the given cash flows. </li></ul><ul><li>Then it will be discounted using risk adjusted / free rate to arrive at present value of cash inflows. </li></ul><ul><li>Finally the NPV can be found by deducting present value of cash outflows by above present value. </li></ul>
- 12. Coefficient of Variation <ul><li>Coefficient of Variation = Standard deviation *100 </li></ul><ul><li>NPV </li></ul><ul><li>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. </li></ul>
- 13. Profitability Index <ul><li>PI = PV of inflows </li></ul><ul><li>PV of outflows </li></ul><ul><li>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. </li></ul><ul><li>When there are outflows in multiple period of time the outflows except for the initial outflows are excluded. </li></ul><ul><li>PI = PV of inflows </li></ul><ul><li>Initial outflows </li></ul><ul><li>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. </li></ul><ul><li>Mutually exclusive projects, complimentary projects. </li></ul>
- 14. Replacement Decision <ul><li>Whether to replace the asset or not? </li></ul><ul><li>When to replace the asset? </li></ul><ul><li>When to replace the same kind of machine again? </li></ul>
- 15. Comparison <ul><li>N.P.V – Choose project having higher NPV. </li></ul><ul><li>I.R.R. – Choose project having higher IRR. </li></ul><ul><li>C. V. – Choose project having lower C. V. </li></ul><ul><li> – Choose project having lower standard deviation. </li></ul><ul><li>If IRR & NPV are giving decision in opposite direction then select the project as per C. V. </li></ul>
- 16. General <ul><li>Depreciation have no relevance when no tax is provided as it provides only the tax saving. </li></ul><ul><li>Allocable costs are excluded from the statement. </li></ul><ul><li>Sunk costs are excluded from the statement. </li></ul><ul><li>When we have more than one project to choose from having unequal life then the decision is taken-up by calculating EANPV. </li></ul><ul><li>When there is a missing figure question, the NPV is taken as zero. </li></ul><ul><li>In case of block of assets concept, the only change is that it affects the salvages value & the depreciation. </li></ul><ul><li>Remember TAX & TIME effects. </li></ul>
- 17. Notes
- 18. Thank You

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