Introduction to Finance: NPV and IRR

1. Introduction to Finance:NPV and IRR

2. Opportunity Cost of Capital機会費用　(資本コスト) “The opportunity cost of taking the project is the return shareholders could have earned had they invested the funds on their own.” CASH Firm Shareholder Investment in Project Investment in Financial Assets N. Takezawa (ICU) 2001

3. Opportunity cost of capital • You have 10 million yen. You can either invest in a project or you can invest in securities (for example - an alternative investment such as stocks). • If you invest in the project, this means you forgo the investment in securities (you can only choose one). It also means you forgo the return from investing in securities. This is an opportunity cost. You have “lost” the opportunity of gaining x% from investing in securities so it is a “cost.” N. Takezawa (ICU) 2001

4. Thus, it follows that the x% return from securities is the opportunity cost (of capital) for investing in the project. You could have earned x% from securities so you “expect” or would like to earn as much from investing in the project. • Let us assume the project is not risky at all (or more realistically - has very little risk). • What would be the opportunity cost of capital? • We could look too the capital market to find an alternative investment which has does not have risk (or very little risk). In other words, an investment with similar characteristics (risk profile, etc.) with the project in question. N. Takezawa (ICU) 2001

5. Cont. • A T-bill or short term government note (bond) could be an alternative. Depositing money in a bank (offshore account) is an alternative. • Hence, the “interest rate” we see in the market becomes a possible candidate for our discount rate. • Assumptions: perfect information and a well functioning capital market. N. Takezawa (ICU) 2001

6. Decision Making: NPV • Using financial tools to help make decisions on investments (projects). • Benefits should be greater (or equal) to the costs. • If the predicted benefits are greater than the predicted costs – invest!! • Benefits=future cash (in) flows • Costs=future costs and initial investment. N. Takezawa (ICU) 2001

7. Obtaining Net Present Value • Obtain the expected value of the future cash flows of the project in question. • Obtain the appropriate discount rate=opportunity cost of capital. • Discount the forecasted cash flows using the appropriate discount rate - present value of project. • Subtract the initial investment cost from the present value to get NPV. N. Takezawa (ICU) 2001

8. Important Feature of NPV • NPV depends only the forecasted cash flows and the discount rate (cost of capital). • NPV takes into account the time value of money; 100 yen today is worth more than 100 yen tomorrow. This is reflected in the discounting process. N. Takezawa (ICU) 2001

9. The NPV rule. Invest if NPV is greater than or equal to zero. Do not invest if NPV is less than zero. In other words, if the estimated benefits (positive discounted cash flows) is greater than the cost (initial investment), then the project is “rewarding.” N. Takezawa (ICU) 2001

10. Notation • C0=initial cost (negative, cash outflow) • Ct=cash flow at time t in future • r=discount rate (opportunity cost of capital) • T=last period for the project N. Takezawa (ICU) 2001

11. Simple Examples • One year project. The forecasted cash flow is 110 million yen. The initial cost is 98 million yen. The opportunity cost of capital is 10%. Invest? • Two year project. The forecasted cash flow in year one is 9 million yen and 15 million yen year two. The initial cost 20 million yen. The cost of capital is 20%. N. Takezawa (ICU) 2001

12. Sensitivity Analysis • What happens if r increases? • The denominator increases in magnitude. The sum of the discounted cash flows decrease. NPV declines given all else constant. • What happens if the estimated cash flows increases? • NPV increase given all else constant since the numerator in DCF increases. N. Takezawa (ICU) 2001

13. Decision Making: IRR • The opportunity cost of capital is the return the investor expects to receive. • Thus, if the project provides a return greater than this cost of capital, the investor should be “happy.” • The return on the project is called the internal rate of return (IRR, 内部収益率) • A return internal to the project. N. Takezawa (ICU) 2001

14. Obtaining IRR • The “discount rate” for which NPV is equal to zero • Set the NPV equation equal to zero. • Plug in cash flow number. • Solve for the “discount rate.” • This is IRR. N. Takezawa (ICU) 2001

15. If IRR>opportunity cost of capital, then invest. If IRR<opportunity cost of capital, then do not invest. • Often in practice a benchmark rate is used place of the opportunity cost of capital. For example, 10% could be used as a basic rule by the company. • This is a “hurdle rate.” A rate the project IRR must “leap over.” N. Takezawa (ICU) 2001

16. IRR is obtained by solving the above equation. Since we are given the cash flows and initial investment, we find an IRR that sets the above equation equal to zero. When there are many periods, the exercise can be time consuming. With the power of spread sheets (solver function or financial function), it is very easy to calculate. N. Takezawa (ICU) 2001

17. Simple IRR example Initial cost is 100. Cash flow next year is expected to be 110. What is IRR?　If the cost of capital is 5%, do you accept or reject the project? If the hurdle rate is 12%? -100+110/(1+IRR) = 0 110 = (1+IRR)100 110/100=1+IRR 1.1-1=IRR IRR=0.1 or 10% N. Takezawa (ICU) 2001

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19. IRR and NPV NPV one possible opportunity cost of capital, negative NPV IRR discount rate 0 one possible opportunity cost of capital, positive NPV N. Takezawa (ICU) 2001

20. NPV and IRR • Notice, in our simple case, the IRR and NPV rules will give you the same answer. • This is not always the case. N. Takezawa (ICU) 2001

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22. Opportunity cost of capital • Discount rate • Cost of capital • Hurdle rate • Required return • Expected return N. Takezawa (ICU) 2001