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How to calculate Net Present Value and Internal Rate of Return of the Project?

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NPV = 0IRR = Cost of CapitalProvides the minimum return. Probably reject from the cash flow perspective. Others factors could be important.

NPV > 0IRR > Cost of CapitalScreen in for further analysis. Other investments may provide better returns and capital should be rationed, i.e., go to the most profitable projects. Others factors could be important.

IRR > Cost of capital (should be accepted)

IRR = Cost of capital (provides the minimum return)

IRR < Cost of capital (shouldn’t be accepted)

Untill 7,2 the prject which should be chosen is B, whereas below 7,2 A is better. Therefore, there are some exceptions in IRR that in mutual project we always need to consider NPV and cost of capital to see where the balance changes. One way to understand the preference of NPV over IRR, more generally, is to recognize that NPV uses the “correct” rate, i.e., the cost of capital, to discount the cash flows, rather than an “arbitrary” rate, i.e., the IRR, that makes NPV =0.

Another way to understand the superiority of the NPV rule is that the discounting process inherent in both the IRR and NPV techniques implicitly assumes the reinvestment of the cash flows at whatever discount rate is used, either IRR or the cost of capital. When the IRR is very high relative to the cost of capital it is unrealistic to assume reinvestment at that high rate. This is especially damaging when comparing two investments with very different timing of cash flows. We will revisit this reinvestment assumption later, under our discussion of yield to maturity on coupon bonds, where its meaning will become clearer.

- 1. Net Present Value Decision Rules IRR (Internal Rate of Return) in Project Management The two most-used measures for evaluating projects are the net present value and the internal rate of return!
- 2. Agenda 2
- 3. Net Present Value • The difference between the present value of the future cash flows from an investment and the amount of investment. Present value of the expected cash flows is computed by discounting them at the required rate of return. Where, N=total number of periods T= the time of the cash flow i= the discount rate (the rate of return that could be earned on an investment) Rt = the net cash flow i.e. cash inflow – cash outflow at time t (R0: it is subtracted from the whole as any initial investments during first year is not discounted for NPV purpose) 3
- 4. The NPV Decision Rules 4
- 5. Example An Investment of $1,000 in year 1 The discount rate is 10% In Year 2, we receive $110 in year 2 You expect to receive $1,200 in year 3 1 2 3 Investment ($ 1,000) Cash Inflows $0 $ 110 $ 1200 Discounting Factor 1 1.10 1.21 Discounted Cash Inflow 0 $ 100 $ 991.74 Therefore, NPV= ($ 1,000) + $ 100 + $ 991.74= $ 91.74 Hence, we can do this investment. 5
- 6. Internal Rate of Return • The internal rate of return of a project is known as the rate of return where the particular project’s net present value equals to zero. • Formula: – CF: Cash Flow – r: Internal Rate of Return 6
- 7. Internal Rate of Return Rules In IRR decisions, if we have only one project, most of the time we need the basic rule «independent project»: IRR > Cost of capital (should be accepted) IRR = Cost of capital (provides the minimum return) IRR < Cost of capital (shouldn’t be accepted) In addition, we need to take other situations into account too. Especially, eventhough NPV and IRR will generally give us the same decision, there are some exceptions: •Nonconventional cash flows – cash flow signs change more than once •Mutually exclusive projects 7
- 8. Example: Independent Project If we want to decide on to accept the project or not, we should consider the comparison of IRR & cost of capital for an individual project. In this example; •when the cost of capital is 15%, then the NPV is -227,53 (don’t accept) • Alternative: IRR < Cost of capital •when the cost of capital is 10%, then the NPV is 34,27 (accept) • Alternative: IRR > Cost of capital 8
- 9. Example: Mutual Projects 9
- 10. Key differences: NPV versus IRR • NPV Method is preferred over other methods since it calculates additional wealth and the IRR Method does not • The IRR Method is more used in evaluating short-term projects and NPV is more used in evaluating long-term projects. • one significant advantage of IRR -- managers tend to better understand the concept of returns stated in percentages and find it easy to compare to the required cost of capital • Applying NPV using different discount rates will result in different recommendations. The IRR method always gives the same recommendation. Project A Invest compare two mutually exclusive projects Project B -10.000 -25.000 Return +25.000 +50.000 IRR IRR 150% IRR 100% NPV by i=8% 13.148 21.296 10
- 11. Link to Project Management NPV and IRR in the decision taking process Methods to evaluate a project estimate the value of the project choosing which project gets priority By applying NPV as time value of money (money figure) IRR calculate the investments profitability as an interest rate (percentage figure) included in a business case prepared by the controlling department 11
- 12. Contact Ujjwal Kumar Joshi ujjwaljoshi1990@gmail.com 12

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