Video Transcript: Internal Rate of Return and Payback Period Analysis

Welcome. We're going to discuss internal rate of return and payback period  analysis. Internal rate of return is the discount rate at which the net present  value of investment becomes zero. In other words, IRR is the discount rate  

which equates the present value of the future cash flows of investment with the  initial investment. It is one of the several measures used for investment  appraisal. The decision rule is a project should only be accepted if its IRR is not  less than the target internal rate of return when comparing two or more mutually  mutually exclusive projects, the project having highest value of IRR should be  accepted. The calculation of IRR is a bit complex than other capital budgeting  techniques. We know that at IRR net present value is zero, thus NPV equals  zero, or present value of future cash flows minus initial investment equals zero.  So we're just taking our cash flow, future cash flow method and finding our  present value on those cash flows. But the problem is, we cannot isolate the  variable which is R or internal rate of return on one side of the above equation.  However, there are alternative procedures which can be followed to find IRR.  The simplest of them is described below number one, guess the value of R and  calculate the NPV of the project at that value, if NPV is close to zero, then IRR is equal to the required internal rate of return. If NPV is greater than zero, then  increase the rate and jump to step five, which would be recalculate NPV using  the new value of R and go back to step two. If NPV is smaller than zero, then  decrease R and jump back to Step five. So you need to keep adjusting R until  you find a net present value of zero. When you find that R that gets you to a net  present value of zero, there is your internal rate of return. Find the R. Find the  IRR of an investment having initial cash outflows of 213,000 the cash inflows  during the first, second, third and fourth years are expected to be 65,200  96,000, 73,001 73,150 5400 respectively. Now we need to assume that the R is  10% okay. NPV at 10% discount rate is 18, 372, since NPV is greater than zero,  we have to increase the discount rate. Thus NPV at 13% discount rate at rate,  13% equals 4521 so we still are trying we see we're guessing the internal rate of return, right? So we're having to adjust it so at 10% NPV equals 18,003 72 at  rate 13% NPV equals 4521, we need NPV to equal zero for us to have our  internal rate of return. But because 4521 is still greater than zero. We need to  continue to increase the discount rate. So a rate at 14% equals $204 we're  getting closer. We're getting closer. NPV at 15% equals a negative 3975 so  obviously it's not 15% it's negative. It's not 14% it's still not zero. Since NPV is  fairly close to zero at 14% value of r, therefore we would say 14% is pretty close. We could say, I don't know, 14.3 would give us zero. So you can just keep  calculating that IRR until you hit a net present value of zero, and then that will be your IRR for that project. Now let's discuss the payback period. Period. Payback period is a time in which the initial cash outflow of an investment is expected to  be recovered from the cash inflows generated by the investment. It is one of the  simplest investment appraisal techniques. So when you understand the decision

rule, except the project only if its payback period is less than the target payback  period. So the formula to calculate payback period of a project depends on  whether the cash flow per period from the project is even or uneven. In case  they are even, the formula to calculate payback period is initial investment over  cash inflow per period. So let's go payback period equals your initial investment  over cash inflow per period. So when cash inflows are uneven, we need to  calculate the cumulative net cash flow for each period and then use the  following formula for the payback period. So here we'll see that A is the last  period with a negative cumulative cash flow. B is the absolute value of the  cumulative cash flow at the end of period A, and C is the total cash flow during  the period after A. Example one, let's work a even cash flows. Example,  Company C is planning undertake a project requiring initial investment of 105  million. The project is expected to generate 25 million per year for seven years.  Calculate the payback period of the project. So we need initial investment  divided by annual cash flow. So what's our initial investment? 105 million. Okay,  we're going to divide that by our expected cash flow. So 25 million per year. How many years is it going to take us to pay to recover our initial investment if we are generating 25 million per year? So simple. Divide 105 105 million by 25 million,  we get 4.2 years. So we will recover our initial investment in 4.2 years. Uneven  cash flows. Company C is planning to undertake another project requiring initial  investment of 50 million, and is expected to generate 10 million in year one, 13  million in year two, 16 million in year three, and 19 million in year 4, 22 million in  five. Calculate the payback value of the project. So now we've got to take right.  Remember our equation, right? A is the last period with a negative cumulative  cash flow. Well, let's look who has what period has a negative cumulative cash  flow looks like year three had a negative 11 cumulative cash flow. So we will put  negative 11 as A equals negative 11. Okay. B is the absolute value of cumulative cash flow at the end of period A. So absolute value means it's always a positive  number. If it's a negative number, and you apply absolute value to a negative  number, it automatically turns a positive. So B would be 19 million. Okay, the last period with the negative cash flow should be C total cash flow during the period  after A. So the total cash flow after A, so remember, A is negative 11, so we have three for that cash flow. Okay, so now we will say three plus absolute value of  negative 11 million. Okay, these brackets indicate present value or absolute  value divided by 19 million. Okay, so absolute value, so we'll do now we'll have  three plus 11 million divided by 19 million. So we'll have three plus 0.58 so now  we can find that 3.58 years is when we will recover our 10 million our $50 million initial investment advantages of payback period are. Payback period is very  simple to calculate. It can be a measure of risk inherent in a project, since cash  flows that occur later in a project's life are considered more uncertain. Payback  period provides an indication of how certain the project cash flows are for  companies facing liquidity problems. It provides a good ranking of projects that 

would return money early the disadvantages of payback period. Are payback  period does not take into account the time value of money, which is a serious  drawback, since it can lead to wrong decisions. A variation of payback method  that attempts to remove this drawback is called discounted payback period  method. It does not take into account the cash flows that occur after the  payback period.