So the two techniques we've covered so far have been based upon discounted cash flow analysis. Let's have a look at some alternatives to that approach. Looking back at the survey evidence, what we find is that the pay back period and the accounting rate of return technique are both approaches to project evaluation that also are very popular. Let's consider the payback period first. A project's payback period is the amount of time it takes to recoup the initial cost of the project from the project's after tax net cash flows. So the payback period is focusing on the liquidity created from the project. Because ultimately it doesn't matter how profitable, how much wealth your projects will create in the future, you need to be able to pay your electricity bill today. So, it's giving you a feel for cash flow, and how long it takes to get that cash flow back from a project. So let's consider an earlier example, costing 2 million dollars initially and generating, or expecting to generate, 800,000 dollars in each of the next four years. Assuming that the cash flows occur at year end, the payback period for this project is three years. If the cash flows were evenly spaced throughout the year then the payback period, well after two years we have $1.6 million. We need to generate another $400,000 to recoup the $2 million initially investment. So halfway through that third year, we've recouped the $2 million dollars. So the payback period is two and a half years. So there are three very simple steps to the payback period approach. Once again we forecast the expected cash flows, both the timing and the amount of those cash flows. Secondly, we calculate how long it will take to recoup the initial investment from those net cash flows. Thirdly, we apply the appropriate decision rule. For independent projects, we accept projects with a payback period less than the maximum allowable period. That'll be some external benchmark. For mutually exclusive projects, there's a two-tiered decision rule. Just as with MPV an internal rate of return, we prefer the project with the shortest payback period. Provided that payback period is less than the maximum allowable period. So let's demonstrate how to use the payback period to evaluate mutually exclusive projects. So, we have project seven and eight, and we'll assume the maximum allowable payback period of five years. So just pause for a sec, if both of these projects have a payback period in excess of five years, we would reject them both. So project seven,which reflects the project we had earlier, has a payback period of three years or two and a half years if the cash flows occur continuously over the year. Project eight has a payback period of four years. You'll see that it has much more of it's cashflow concentrated towards the end of it's life, or 3.346 years, if we assume the cashflow occur continuously. So, because those payback periods are less than the maximum allow period, then they're both acceptable if they're independent projects. But, if they're mutually exclusive, we clearly prefer Project 7 of the project day. Now, let's consider some of the problems, potential problems or warnings, that we should be aware of when dealing with the payback period in project evaluation. Once again, let's deal with Project 7 on that. As we saw in the previous slide, Project 7 dominated Project 8 on the basis of payback period. But when we employ the NPV technique, Project 8 generates much more wealth than Project 7. So how do we get that conflict in rankings? Well the reason is very simple, the payback period ignores the fact that cash flows are occurring after we've recouped the initial investment. So this leads to a natural bias against projects with a longer developmental lives. The other point to make is that the payback period fails to explicitly account for the time value of money. So we have Project 9 and Project 10 here, two projects with very different cash flow streams, very different cash flows. Most of the cash flows from project 10 are occurring towards the end of its life. Project 9, the cash flows are much more evenly spread. However, the payback period for these two projects is identical. We wouldn't be able to differentiate between these two projects by solely upon payback period. So the warning here is very simple. Use the payback period, it gives your measure of liquidity, if gives you feedback about the cashflow problems that the firm may face in the future. It gives you a feel for when projects will start delivering cash that you can use to pay the electricity bill. But always back it up with an MPV calculation to make sure you're making the optimal decision. Our next technique is the accounting rate of return. And a project's accounting rate of return is simply the net income or the net rate of earnings generated by the project over it's life divided by the capital invested in the project. With the capital invested could be measured as historical cost or the average book value of the asset over its life. So three simple steps in the Accounting Rate of Return approach. We forecast expected earnings. Earnings this time, not cash flows, and that's an important point. We calculate the average earnings over the life of the project. We express that as a percentage of the cost of the asset, or the average book value of the asset. We then apply the appropriate decision rule, and the decision rule is very straight forward. You'll accept all projects with an accounting rate of return in excess of a minimum benchmark rate. Or for mutually exclusive projects, once again it's a two tier decision rule. Prefer the project with the highest rate of return provided that meets the minimum benchmark. So let's have a look at an example. We have a project here that requires a million dollars initially investment, has a life of four years, and a book value at the end of that four years of only $200,000. Let's assume straight line depreciation, recalling that depreciation in an accounting sense is the allocation of the cost of an asset over it's useful life. So we start with a book value of $1,000,000, ending at $200,000. So the average book value of the asset is $600,000. The average earnings from this asset? 150, 140, 120 and 90 thousand dollars. We add those up, divide by 4, we end with average earnings of $125,000. The accounting rate of return based on the initial investment is 12.5%. The accounting rate of return based upon the average book value, 125,000 divided by 600,000 gives us 20.83%. So we would simply compare those accounting rates of return with our benchmark or hurdle rate to determine the project's acceptability. But once again, there is some potential problems or warnings that go along with the use of the accounting rate of return method. The first point to make, is that the accounting rate of return is based upon earnings, not cash flows. And earnings numbers, as we're aware, can be highly subjective. If we employed one particular inventory valuation or depreciation method over another we'll end up with a different final earnings figure so there's some subjectivity associated with it. The other point to make is that earnings reflect your accrual decisions as well. So you can't buy a can of soda with a million dollars of earnings, you need a dollar of cash. The second point to make is that the accounting rate of return method ignores the time value of money. So let's consider these two projects. These two projects have exactly the same accounting rate of return, assuming the same investment. It fails to account for the fact that the first project generates it's earnings at an earlier point in time than the second project. So in summary, the payback period measures the time it takes to recoup the initial investment in a project. It gives management a lot of very useful information about the future liquidity concerns, or opportunities of the company. It's problematic because it doesn't account explicitly for the time value of money, and ignores the cash flows after investment is payback. One point to make though, is that the Payback Period is very, very popular. But wouldn't be used on a. It tends to be used in tandem with MPV and the Internal Rate of Return technique. The Accounting Rate of Return measures the profitability of a project using Net Income and the Book Value of Asset figures. It's very popular because of the ready availability of accounting data. But it's problematic because it relies upon subjective earnings numbers and doesn't account explicitly for the time value of money.