Payback period meaning and how it is calculated

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Payback period

Payback period is the time period required for an investment to recover the amount of money invested. The project cash flow is expected to equal the original investment of the project after the aforementioned time period. It is complete when an organization or a project has recovered its investment. By focusing on the timing of the cash flow, payback is able to measure the project risk assuming that the risks increase with the time period. Moreover, risks also increases with time due to the period taken to reinvest the invested capital in other ventures. The more time it takes the greater the risk.  Franchises L and S have unequal cash inflows and therefore their payback period is calculated by getting the accumulated cash flows until the initial investment capital is recouped. Payback period is always calculated based on the formula:

Payback period = Cost of Investment/Annual Net Cash Inflows

Franchise S

Year       Annual cash flow      Cumulative Total

0                 $(100)                               $(100)

1                 70                                         30

2                 50                                         20

3                20                                         40

At the end of the first year, all except $30 of the original investment of $100 has been recouped. The $50 inflow of the second year is assumed to evenly apply throughout the year. Consequently, it should take approximately sixty percent ($30 + $50) of the second year to cover the remaining part of the initial investment giving a payback period of 1.6 years (1year and 7.2 months).

On the other hand, the payback period for Franchise L is calculated as follows:

Franchise L

Year       Annual cash flow      Cumulative Total

0                 $(100)                               $(100)

1                 10                                       90

2                 60                                       30

3                 80                                       50

At the end of second year, all but $30 of the original investment have been recouped. The $80 inflow in the third year is assumed to occur evenly throughout the year.  It should take about 38% ($30 + $80) of the third year to cover the remaining sum of the initial investment hence giving a payback period of about 2.38 years (2 years and 4.6months).

Differences between regular payback and discounted payback

Payback encompasses the NPV analysis which provides for the value of a project generally while discounted payback provides the time span, usually the number of years it takes to break even from the original investment. Discounted payback period will not be exhibited by projects with negative NPV since there will be no complete repayment of the initial outlay. On the other hand, gross inflow of the future cash flows could exceed the initial outflow in the payback period. However, the NPV becomes negative when the inflows are discounted. The latter method discounts the cash flows to time zero. The two methods are always similar except that payback period only measures the time taken for the initial cash outflow to be recovered while ignoring the time value of money. This is taken care of by the discounted payback period.

Profitability index (PI) and Net Present Value (NPV)

Profitability Index of a project is usually used to ascertain whether the project should be accepted or not. Fir instance, projects with PI of less than 1.00 should be ignored while those with PI equaling or greater than 1.00 should be accepted. Basically, PI is a ratio of the net cash inflows of the project to the project’s net investment and calculated as:

PI = Present Value of Net Cash Flows + Net Investment

Given the required return (WACC) of 10%, the PI for both the Franchises S and L are calculated as follows:

Franchise S

Year       net cash inflows     10% factor     Present Value     

0                 $(100)

1                 70                        .909              63.63

2                 50                        .826                 41.3

3                20                         .751                15.02

Total Present Value                                     $ 119.95

Therefore NPV = $119.95 – $ 100 = $19.95

Profitability Index is therefore calculated as:

Present Net Value of net cash flows + Net Investment

I.e. $19.95 + $100 = $119.95 Thus PI = 119.95/100 = 1.195

The higher PI of Franchise S above positive number demonstrates that the project has efficiently used the capital invested. This means that the project is more profitable per unit dollar invested.

Due to the fact that Franchise S has an NPV greater than 1.00, the project is worth investing in.

Franchise L on the other hand has NPV calculated as follows:

Year       Net cash inflows     10% factor     Present Value     

0                 $(100)

1                10                        .909                    9.09

2                60                        .826                   49.56

3               80                          .751                  60.08

Total PV                                                         118.73

Therefore NPV of Franchise L = $118.73 – $ 100 = $18.73

Profitability Index is therefore:  $18.73 + $100 = $118.73 Thus PI = 118.73/100 =1.19

The higher PI of Franchise L also shows that the project has efficiently used the capital invested. This means that the project is more profitable per unit dollar invested.

This NPV is greater than 1.00 therefore the project is worth the risk and should therefore be undertaken.

Net Present Value is the total amount of present values of individual cash flows including both the incoming as well as outgoing cash flows. It is an important measure that is used to ascertain the viability of a project by utilizing the projected cash inflows and outflows of the project.

Internal Rate of Return

The internal rate of return (IRR) is the discount rate that makes the present value of a project equals zero. IRR is usually complicated to calculate and therefore the trial and error process is adopted. It equates the cost of the investment and the present value of the cash flows. Generally, the rate exhibits an inverse proportion against the present values. Notably, when the rates are high, fewer Dollars are invested hence yielding lower Present Values. Rate of return gives the managers a clue of the rates they will be receiving on the capital invested.

IRR for Franchise S

Year       net cash inflows     10% factor     Present Value     

0                 -$100                                              -$100

1                 +70                        .909                   +62.51

2                 +50                        .851                   +14.24

3                +20                          .751                  +15.02

Net Present Value                                               +$19.95

IRR is therefore 100 = 70/ (1+IRR) + 50/ (1+IRR)2 + 20/(1+IRR)3 = 23.6%

IRR for Franchise L

Year       net cash inflows     10% factor     Present Value      

0                -$100                                               +$100

1                +10                        .909                   +8.93

2                +60                        .826                  +47.83

3                +80                        .751                    +56.96

Net Present Value                                            +$13.73

IRR= 100 = 10/ (1+IRR) + 60/(1+IRR)2 + 80/(1+IRR)3 = 18.1%

                        Ranking the franchises based on Payback, PI, NPV and IRR

Managers of various organizations are bestowed with the authority to make business decisions concerning the viability of certain projects that they would wish to implement. Such decisions are based on a wide range of measures calculated to ascertain the viability of those projects. To begin with, these measures include Payback, profitability index (PI), internal rate of return (IRR), net present value (NPV) among other ratios. For instance, the investments on the S and L franchises are dependent upon the aforementioned measures. According to the above stipulated calculations, the net present value (NPV) of both S and L franchise are positive and should therefore be accepted under the net present method. Franchise S has a net present value of $19.95 while franchise L has a value of $18.73. Both the projects should therefore be considered. Besides, both the franchises S and L have profitability of more than 1.00 hence are acceptable for investment. The two aforementioned measures can be used to rank the projects based on the evaluation results.

In regard to NPV, franchise S is ranked above franchise L as the former has higher value than franchise L. Moreover, such rankings can be determined by the values of profitability index. Just like the above ranking, franchise should be considered first before franchise L determined by their values of 1.195 and 1.193 respectively. Furthermore, the payback period of the two franchises ranks franchise S before Franchise L due to the shorter period (1year and 7months) the former project takes compared to franchise L’s period of 2years and 4months to recover the invested capital. Projects that take shorter time period to recover the invested capital are more preferred to those taking longer. Finally, internal rate on return can also be used to rank the projects depending on the values of the aforementioned measure. If the hurdle rate is used as the discounted rate then IRR may also be used to make decision on the acceptance or rejection as well as ranking of the proposed projects. Franchise with IRR greater than 10% should be accepted while that below the aforementioned minimum is not worth investing. Both the Franchises S and L have IRR value above 10% i.e. 23.6% and 18.1%. However, such rankings should not be in line with those of the other two aforementioned measures.

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