Corporate Finance Lecture 3 PDF

SKEMA BUSINESS SCHOOL Lecture 3 The internal rate of return and other investment rules Reading requirements Chapter 6 Net present value and other investment rules Corporate Finance, European edition, by Hillier, Ross, Westerfield, Jaffe...

SKEMA BUSINESS SCHOOL Lecture 3 The internal rate of return and other investment rules Reading requirements Chapter 6 Net present value and other investment rules Corporate Finance, European edition, by Hillier, Ross, Westerfield, Jaffe and Jordan, McGraw-Hill ed., 4th. Get access to the book @ https://k2.skema.edu in the course Corporate Finance Outlines How is internal rate of return determined ? The limits of the internal rate of return Nominal, effective and proportional rates How is internal rate of return determined ? The internal rate of return (IRR) is the rate of discount which makes NPV = 0 We want IRR such that: C1 C2 Cn 0  C0    1  IRR 1  IRR 2 1  IRR n Also called discounted-cash-flow (DCF) rate of return How is internal rate of return determined ? The internal rate of return (IRR) is the rate of discount which makes NPV = 0 How is internal rate of return determined ? $-4000 + $2000 + $4000 How is internal rate of return determined ? If net present value (NPV) is inversely proportional to the discounting rate, then there must exist a discounting rate that makes NPV equal to zero. The discounting rate that makes net present value equal to zero is called the “internal rate of return (IRR)” IRR formula : NPV= Net present value N NPV  0, or  Fn n  V0 Fn = Cash flows from the investment n1 (1 r ) r = Internal rate of return N = Duration of the investment How is internal rate of return determined ? The IRR decision making rule is very simple : if an investment’s IRR is higher than the investor’s required return, he will make the investment or buy the security. The major idea is : “If you want to undertake an investment, the IRR’s investment must be sufficient to pay the required return by investors”. The limits of the internal rate of return There are many limits to the IRR : - Sometimes, it is impossible to compare IRR from two investments, because the investments’ maturity are different. In this case, we should use the Modified IRR. (not in the program for this course). - We can face a problem of multiple IRR or no IRR - NPV and IRR can be linked positively - The discount rates should change through time - When a firm suffer from capital rationing, mutually exclusive projects can generate a dilemma between NPV and IRR. The limits of the internal rate of return Table 6.3 p157 of Hillier The limits of the internal rate of return Multiple IRR When the sign of the cash is changing through time, an investment can present two IRR. Like in this graph Two IRR ??? Which one is the good ??? The limits of the internal rate of return No IRR Some investment can present a stream of cash flows that gives no IRR. Like in this graph What should I do ?  Invest !!! NPV is always positive !!! The limits of the internal rate of return Investing or Financing When the first cash flow is positive and the next cash flows are negative, we are not in an investment case but rather in a financing case (take the money now and give it back after). In these cases, NPV is positively related to the IRR. The limits of the internal rate of return Changing discount rates Using a constant rate to discount cash flows through all a project’s life may not be appropriate. The investors’ required rate of return can change through time. It can change with interest rate level or with the uncertainty of the cash flows. The IRR seems too constant for long life projects. The limits of the internal rate of return Mutually exclusive projects When a firm is facing a capital rationing (soft rationing or hard rationing). It must decide between investment projects. And sometimes, NPV and IRR can give different solutions  There is a conflict between indicators. Mutually exclusive projects may give rise to two problems : - The scale problem  Use NPV or incremental IRR - The timing problem Use the NPV  The limits of the internal rate of return Mutually exclusive projects - The scale problem  Use incremental IRR - Calculate the incremental cash flows: - Subtract the smaller project’s cash flows from the bigger project’s cash flows - Use the basic IRR rule on this incremental cash flows The limits of the internal rate of return Mutually exclusive projects - The scale problem  Use incremental IRR The IRR = 66,67% 66,67% > 25% Take the larger project Other investment criteria The payback period The payback period is the time necessary to recover the initial outlay on an investment. It is equal to : Initial investment Annual cash flow When the cash flows are not identical, the cumulative cash flows are compared with the initial investment. It is possible to use the discounted payback period to improve the technique with discounted cash flows. 18 Other investment criteria The payback period The payback period (discounted or not) is a risk indicator, since the shorter it is, the lower the risk of investment. But, it is not a well-suited indicator for long term investments and innovative investments. 19 Nominal, effective and proportional rates To complete this chapter on IRR we must make a focus on : - Nominal rates - Effective annual rate - Proportional rates S2.3. Some more financial mathematics Nominal, effective and proportional rates (p. 320-322) We will use an example to highlight the differences between nominal rates, effective annual rate and proportional rates. Example : Suppose that your bank lends you money at 10%, but the deal specifies that you interest are charged on a semiannual basis (i.e. calculated every 6 months). You decide to accept the deal and you borrow $100 on January 1st with a repayment one year later. S2.3. Some more financial mathematics Nominal, effective and proportional rates (p. 320-322) The timeline of your borrowing is : January 1st July 1st January 1st $100 - $5 - $5 - $100 Your nominal rate is 10% : this is the rate included in the contract. But, your effective annual rate is not 10%. S2.3. Some more financial mathematics Nominal, effective and proportional rates (p. 320-322) Paying interest half-yearly makes your borrowing more expensive than 10%. In our example, the lender receives $5 on July 1st which compounded over six months, becomes : 510% 5   $5.25 2 $5 received Interest on $5 received for on July 1st the next 6 months S2.3. Some more financial mathematics Nominal, effective and proportional rates (p. 320-322) So over one year, your lender will have received $10.25 : + $5.25 interest for the compounded interest in July 1st + $5 interest after one year in the next January 1st This is the real cost of the loan. So, the effective annual rate is :  10%  2 re  1  1 10.25%  2  S2.3. Some more financial mathematics Nominal, effective and proportional rates (p. 320-322) The effective rate formula is :  ra  n re = Effective rate re  1  1 ra = Nominal rate  n n = times of compounding The compounding effect increases the effective annual rate (re is increasing with n). So, if the interest payments occurred with a high frequency in a year, your effective annual rate will be higher. S2.3. Some more financial mathematics Nominal, effective and proportional rates (p. 320-322) 10% per year is proportional to 5% per half-year or 2.5% per quarter, but 5% half-yearly is not equivalent to 10% annually. Effective annual rate and proportional rates are two different concepts that should not be confused. Only effective annual rates are comparable. It gives us the true cost of a loan.