
Net Present Value And Internal Rate Of Return  Payback Rule
When a firm is presented with a capital budgeting decision, one of its first tasks is to determine whether the project will prove to be profitable. The net present value (NPV), internal rate of return (IRR) and payback period (PB) methods are the most common approaches to project selection. Although an ideal capital budgeting solution is such that all three metrics will indicate the same decision, these approaches will often produce contradictory results. Depending on managements' preferences and selection criteria, more emphasis will be put on one approach over another.
The payback rule, also called the payback period, is the length of time required to recover the cost of an investment.
The payback period is calculated as follows:
Cost of Project
Annual Cash Inflows
All other things being equal, the better investment is the one with the shorter payback period.
For example, if a project costs $100,000 and is expected to return $20,000 annually, the payback period will be $100,000 / $20,000, or five years. (Learn more about payback's applications to personal finance in How Long Until Your Hybrid Pays Off? and Cheap Home Renovations That Pay Off.)
Here is another example. If a capital budgeting project requires an initial cash outlay of $1 million, the PB reveals how many years are required to for the cash inflows to equate to the one million dollar outflow. A short PB period is preferred as it indicated that the project will "pay for itself" within a smaller time frame.
In the following example, the PB period would be three and onethird of a year, or three years and four months.
Investment 
Inflows 

Year 0 
Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
1,000,000 
300,000 
300,000 
300,000 
300,000 
300,000 
Payback periods are typically used when liquidity presents a major concern. If a company only has a limited amount of funds, they might be able to only undertake one major project at a time. Therefore, management will heavily focus on recovering their initial investment in order to undertake subsequent projects. Another major advantage of using the PB is that it is easy to calculate once the cash flow forecasts have been established.
While the payback rule appears very straightforward, there are two significant problems with this method.
1. It ignores the time value of money.
2. It ignores any benefits that occur after the payback period and therefore does not measure profitability.
Because of these reasons, other methods of capital budgeting like net present value, internal rate of return or discounted cash flow are generally preferred.
Let's take [E1] a closer look at the two major drawbacks to using the PB metric to determine capital budgeting decisions. Firstly, the payback period does not account for time value of money (TVM). Simply calculating the PB provides a metric which places the same emphasis on payments received in year one and year two. Such an error violates one of the basic fundamental principles of finance. Luckily, this problem can easily be amended by implementing a discounted payback period model. Basically, the discounted PB period factors in TVM and allows one to determine how long it take for the investment to be recovered on a discounted cash flow basis.
The second problem is more serious. Both payback periods and discounted payback periods ignore the cash flows that occur towards the end of a project's life, such as the salvage value. Thus the PB is not a direct measure of profitability. The following example has a PB period of four years, which is worse than that of the previous example, but the large $15,000,000 cash inflow occurring in year five is ignored for the purposes of this metric.
Investment 
Inflows 

Year 0 
Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
1,000,000 
250,000 
250,000 
250,000 
250,000 
15,000,000 
Since the payback period does not reflect the added value of a capital budgeting decision, it is usually considered the least relevant valuation approach. However, if liquidity is a vital consideration, PB periods are of major importance.
The Discounted Payback Period Model
The discounted payback period model is the capital budgeting procedure used to determine the profitability of a project. In contrast to an NPV analysis, which provides the overall value of a project, a discounted payback period gives the number of years it takes to break even from undertaking the initial expenditure. Future cash flows are considered are discounted to time "zero." This procedure is similar to a payback period; however, the payback period only measure how long it take for the initial cash outflow to be paid back, ignoring the time value of money.
Projects that have a negative net present value will not have a discounted payback period, because the initial outlay will never be fully repaid. This is in contrast to a payback period where the gross inflow of future cash flows could be greater than the initial outflow, but when the inflows are discounted, the NPV is negative. (Can a negative ever be a positive? Read more in How Negative Demographics Can Help The Economy.)
Example: Discounted Payback Period
Going back to our earlier example of Newco and the decision about which machine to purchase, let's determine the discounted payback period for Machine A and Machine B, and determine which project Newco should accept. Recall that Newco's cost of capital is 8.4%.
Discounted Cash Flows for Machine A and Machine B
Calculation and Answer:
Payback period for Machine A = 5 + 147 = 5.24
616
Payback period for Machine B = 2 + 262 = 2.22
1178
Machine A violates management's maximum payback period of five years and should thus be rejected. Machine B meets management's maximum payback period of five years and has the shortest payback period.


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