Friday 29 March 2013

What is payback period?

What is payback period? 

Payback period (in capital budgeting) is the number of years necessary to recover the original investment.

In other words, as its name suggests, the payback period represents the time it takes the investment to be paid back. The payback period method is commonly used by companies to evaluate investments: the goal is to choose a project that will recover the investment in the shortest time (i.e., with the shortest payback period). Investments taking less time to be recovered are considered as less risky. As the result, sometimes companies might establish a limit on the payback period beyond which no investment is done (i.e., cutoff period).
 
Cutoff period is the per-determined (desired) length of time for an investment to be recovered.
When the payback period is shorter than the cutoff period, the investment can be accepted. When the payback period is longer than the cutoff period, the investment cannot be accepted in accordance with the payback period method.

Though the payback period method is quite useful in assessing a project’s risk and liquidity, other financial capital budgeting methods -- such as present value and rate of return – should be also used to evaluate investment alternatives. An investment should not be based solely on the payback period acceptance.

Advantages and disadvantages of the payback period method

Advantages of the payback period method:

  • Easy to use
  • Can be used with other capital budgeting techniques
  • Considers the risk of investment
Disadvantages of the payback period method:
  • Does not consider the time value of money concept: does not discount cash inflows
  • Does not consider cash inflows after the original investment is recovered
  • Does not measure the profitability of a project
  • Does not effectively evaluate projects with small cash inflows in the beginning and large cash inflows later on
To address some of the above-listed disadvantages, a company should determine an appropriate cutoff period and discount cash flows before calculating the payback period.

Calculation of the payback period 

To determine the payback period, divide the initial investment by annual cash flows:

Payback Period =
Original Investment
Annual Cash Inflows
The calculation of the payback period depends on the uniformity of annual cash flows. When annual cash flows are not equal (i.e., different each year), there are two steps in calculating the payback period. When annual cash flows are equal, or in other words the company is receiving an annuity, the calculation of the payback period is straightforward: divide the original investment by the annual cash flow.  Let us look at the following example to better understand how the payback period is calculated.

Company XYZ is considering an investment of $100,000. The useful life of the project is 10 years. The cutoff period is three (3) years. The board of directors has identified two alternatives A and B. The expected annual cash flows are as follows:

Cost or Cash Flow
Alternative A
Alternative B
Initial cost
($100,000)
($100,000)
Cash flow year 1
35,000
35,000
Cash flow year 2
28,000
35,000
Cash flow year 3
32,000
35,000
Cash flow year 4
40,000
35,000
The payback period for Alternative A is calculated as follows:

  1. $35,000 + $28,000 + $32,000 = $95,000. In 3 years the company expects to recover $95,000 of the initial $100,000 invested. After 3 years the company will need to recover $5,000 more of the original investment.
  2. 2In year 4, the company expects to recover the remaining $5,000, and the annual cash flow that year is $40,000. Assuming the cash flow is uniform throughout the year, we can divide $5,000 by $40,000 to get 0.125 (or 1.5 months).
  3. The payback period for Alternative A is 3.125 years (i.e., 3 years plus 1.5 months). 
The payback period for Alternative B is calculated as follows:

  1. Divide the initial investment by the annuity: $100,000 ÷ $35,000 = 2.86 (or 10.32 months).
  2. The payback period for Alternative B is 2.86 years (i.e., 2 years plus 10.32 months).

As mentioned earlier, Company XYZ’s cutoff period is 3 years. Since Alternative B recovers the investment within the cutoff period (i.e., 2.86 is less than 3), Alternative B can be accepted.
This payback method of evaluating two investment alternatives has its limitation: the time value of money is not considered. To incorporate the time value of money concept, the discounted payback period method can be used.

Calculation of the discounted payback period 

The discounted payback period calculation is almost the same as the payback period method. The only difference is that the annual cash flows are discounted: in other words, the present value of each year’s cash inflow is used. Because the discounted cash flow values are smaller (i.e., money is worth less overtime) in this case, the discounted payback period is longer than the payback period.

Let us look at the previous example. We will calculate the discounted payback period for Alternative A. To discount each year’s cash flow, we will multiply the annual cash flows by the present value of $1 for each corresponding year. Let’s assume a cost of capital of 6%.

Illustration 1: Compound interest table for a present value of 1

(n)
Periods
4%
5%
6%
8%
10%
12%
15%
20%
1
0.96154
0.95238
0.94340
0.92593
0.90909
0.89286
0.86957
0.83333
2
0.92456
0.90703
0.89000
0.85734
0.82645
0.79719
0.75614
0.69444
3
0.88900
0.86384
0.83962
0.79383
0.75131
0.71178
0.65752
0.57870
4
0.85480
0.82270
0.79209
0.73503
0.68301
0.63552
0.57175
0.48225
The discounted payback period is calculated as follows:

  1. Discount each year’s cash flows: 
  2. Period
    Annual
    Cash flow
    Discount
    Rate @ 6%
    Discounted
    Cash Flow
    Cumulative
    Total
    A
    B
    C
    D = B x C
    En+1 = D + En
    Year 0
    (100,000)
    (100,000)
    Year 1
    35,000
    0.94340
    33,019
    (66,981)
    Year 2
    28,000
    0.89000
    24,920
    (42,061)
    Year 3
    32,000
    0.83962
    26,868
    (15,193)
    Year 4
    40,000
    0.79209
    31,684
    16,491
    Note that the initial investment does not need to be discounted because the investment takes place at the beginning of the project.

    1. We can see from the table above that after 3 years the company still needs to recover $15,193 of the initial $100,000 investment. The company will recover the investment in year 4. To calculate the fraction of year 4 it takes to recover the remainder of the investment, divide $15,193 by the annual cash inflows that year. Because we are calculating the discounted payback period, use the discounted cash flows: $15,193 ÷ $31,684 = 0.48 (or 5.76 months).
    2. The discounted payback period is 3.48 (i.e., 3 years plus 5.76 months).
    3. The discounted payback period is longer than the payback period (i.e., 3.48 is larger than 3.125).
    4.  
    Both the discounted payback period and payback period methods are useful. The payback period can also be used to approximate the internal rate of return (IRR) on an investment. This technique is called the payback reciprocal method.

    Payback reciprocal method 

    When the useful life of a project is at least twice the payback period and the annual cash flows are uniform each period, the payback period reciprocal gives a quick estimate of the IRR:
     Payback Period Reciprocal =
    1
    Payback Period
    In the example we have previously discussed, Company XYZ is considering an investment of $100,000. The useful life of the project is 10 years. The cutoff period is 3 years. Alternative B provides equal cash flows of $35,000 each year. The payback period is 2.86 (i.e., $100,000 ÷ $35,000).

    The payback period reciprocal for Alternative B is 0.35 or 35% (i.e., 1 ÷ 2.86 = 0.35).
    The precise internal rate of return is as follows:
  3. Useful life 10 years: 33%
  4. Useful life 20 years: 35%
The table for the present value of ordinary annuity of 1 shows that when the useful life of the project (i.e., periods) is 10 years, the payback period value of 2.86 corresponds to 33%; and when the useful life is 20 years, the IRR is approximately 35%.

Illustration 2: Compound interest table for a present value of ordinary annuity of 1
(n)
Periods
5%
6%
10%
20%
33%
35%
1
0.95238
0.94340
0.90909
0.83333
0.75188
0.74074
2
1.85941
1.83339
1.73554
1.52778
1.31720
1.28944
3
2.72325
2.67301
2.48685
2.10648
1.74226
1.69588
10
7.72173
7.36009
6.14457
4.19247
2.85533
2.71504
15
10.37966
9.71225
7.60608
4.67547
2.98826
2.82545
20
12.46221
11.46992
8.51356
4.86958
3.02020
2.85008
We have previously calculated that the payback period reciprocal equals 35%. This example shows that when the useful life of the investment is at least twice the payback period, the payback period reciprocal is a good approximation of the internal rate of return of the project.

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