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).
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:
- $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.
- 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).
- 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:
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.
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
The
discounted payback period is calculated as follows:
Illustration 2: Compound interest table for a present value of ordinary annuity of 1
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.
- Divide the initial investment by the annuity: $100,000 ÷ $35,000 = 2.86 (or 10.32 months).
- 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.
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
|
- Discount each year’s cash flows:
- PeriodAnnual
Cash flowDiscount
Rate @ 6%Discounted
Cash FlowCumulative
TotalABCD = B x CEn+1 = D + EnYear 0(100,000)(100,000)Year 135,0000.9434033,019(66,981)Year 228,0000.8900024,920(42,061)Year 332,0000.8396226,868(15,193)Year 440,0000.7920931,68416,491
- 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).
- The discounted payback period is 3.48 (i.e., 3 years plus 5.76 months).
- The discounted payback period is longer than the payback period (i.e., 3.48 is larger than 3.125).
Payback reciprocal method
Payback Period Reciprocal =1Payback Period
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:
- Useful life 10 years: 33%
- Useful life 20 years: 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
|
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