Dr. NICHOLAS WATSON

Alternative Investment Criteria and their Limitations

 

 

The Payback Period

 

The length of time required to recover the cost of an investment. The payback period of a given investment or project is an important determinant of whether to undertake the position or project, as longer payback periods are typically not desirable for investment positions.

 

Calculated as:

 

Payback Period = 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.

 

Example 2: Even Cash Flows

Company C is planning to undertake a project requiring initial investment of $105 million. The project is expected to generate $25 million per year for 7 years. Calculate the payback period of the project.

 

Solution

Payback Period = Initial Investment ÷ Annual Cash Flow = $105M ÷ $25M = 4.2 years

 

Example 2: 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 1, $13 million in Year 2, $16 million in year 3, $19 million in Year 4 and $22 million in Year 5. Calculate the payback value of the project.

 

Solution

 

(cash flows in millions)               Cumulative          

    

    Year              Cash Flow            Cash Flow

      0                  (50)                          (50)

      1                   10                           (40)

      2                   13                           (27)

     3                   16                            (11)

     4                   19                              8

     5                   22                             30

 

Payback Period

= 3 + (|-$11M| ÷ $19M)
= 3 + ($11M ÷ $19M)
≈ 3 + 0.58
≈ 3.58 years

 

 

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 inflows are.

 

• For companies facing liquidity problems, it provides a good ranking of projects that would return money early.

 

There are two main problems with the payback period method:

 

1. It ignores any benefits that occur after the payback period and, therefore, does not measure profitability.

 

2. It ignores the time value of money.

 

Because of these reasons, other methods of capital budgeting, like net present value, internal rate of return or discounted cash flow, are generally preferred.

 

Watch this video of detail calculations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Discounted Payback Period

 

A capital budgeting procedure used to determine the profitability of a project. In contrast to an NPV analysis, which provides the overall value of an 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.

 

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.

 

Formulas and Calculation Procedure

 

In discounted payback period we have to calculate the present value of each cash inflow taking the start of the first period as zero point. For this purpose the management has to set a suitable discount rate. The discounted cash inflow for each period is to be calculated using the formula:

 

Discounted Cash Inflow = Actual Cash Inflow

                                               (1 + i)n

Where,

   i is the discount rate;
   n is the period to which the cash inflow relates.

 

Usually the above formula is split into two components which are actual cash inflow and present value factor ( i.e. 1 / ( 1 + i )^n ).

 

Thus discounted cash flow is the product of actual cash flow and present value factor.

 

The rest of the procedure is similar to the calculation of simple payback period except that we have to use the discounted cash flows as calculated above instead of actual cash flows. The cumulative cash flow will be replaced by cumulative discounted cash flow.

 

Discounted Payback Period = A + B

                                                C

Where,
   A = Last period with a negative discounted cumulative cash flow;
   B = Absolute value of discounted cumulative cash flow at the end of the period A;
   C = Discounted cash flow during the period after A.

 

Note: In the calculation of simple payback period, we could use an alternative formula for situations where all the cash inflows were even. That formula won't be applicable here since it is extremely unlikely that discounted cash inflows will be even.

The calculation method is illustrated in the example below.

 

Decision Rule.

 

If the discounted payback period is less that the target period, accept the project. Otherwise reject.

 

Example

 

An initial investment of $2,324,000 is expected to generate $600,000 per year for 6 years. Calculate the discounted payback period of the investment if the discount rate is 11%.

 

Solution

 

Step 1: Prepare a table to calculate discounted cash flow of each period by multiplying the actual cash flows by present value factor. Create a cumulative discounted cash flow column.

 

Year           Cash Flow          Present Value Factor          Discounted Cash Flow          Cumulative Discounted 
n                       CF                  PV$1=1/(1+i)n                            CF×PV$1                                Cash Flow
                                                                 
0                 $ −2,324,000             1.0000                               $ −2,324,000                           $ −2,324,000

1                         600,000                 0.9009                                    540,541                                − 1,783,459

2                         600,000                 0.8116                                    486,973                                 − 1,296,486

3                         600,000                 0.7312                                    438,715                                  − 857,771

4                         600,000                 0.6587                                    395,239                                  − 462,533

5                         600,000                 0.5935                                    356,071                                   − 106,462

6                         600,000                 0.5346                                    320,785                                       214,323

 

Step 2: Discounted Payback Period = 5 + |-106,462| / 320,785 ≈ 5.32 years

 

Advantages and Disadvantages

 

Advantage: Discounted payback period is more reliable than simple payback period since it accounts for time value of money. It is interesting to note that if a project has negative net present value it won't pay back the initial investment.

 

Disadvantage: It ignores the cash inflows from project after the payback period.

 

Watch Calculations Below