How to Calculate Discounted Payback Period
For calculating discounted payback period (DPP), we will calculate the present value (PV) of each cash flow (CF) starting from the first year as zero point. For said purpose, the management is required to set a suitable discount rate. The discounted cash flow (DCF) for each period is to be calculated using this formula:
DCF = Actual Cash flows / [1 + i]^n
Where,
i is the discount rate;
n is the period to which the cash flow belongs.
The two components i.e. actual cash flows and PV factor i.e. (1 / ( 1 + i )^n ) are used in this formula. Thus DCF is the product of actual cash flows and PV factor. While calculating Discounted Payback Period we use the similar procedure that we use for calculating simple payback period except that we will use the discounted cash flows instead of actual cash flows.
Discounted Payback Period calculation method is illustrated in the Example below.
An initial capital investment of $1,550,000 is expected to generate $300,000 per year for next 5 years. Calculate the DPP of the investment if the discount rate is 12%. We will first calculate the DCF for each period by multiplying the actual cash flows with PV factor. After that we will work out cumulative discounted cash flows.
|
Year(n) |
CF |
PV Factor PV$1=1/(1+i)^n |
DCF=CF x PV$1 |
Cumulative DCF |
| 0 | $(1,550,000) | 1.000000 | $(1,550,000) | $(1,550,000) |
| 1 | 300,000 | 0.89285 | $267,857.14 | $(732,142.86) |
| 2 | 300,000 | 0.79719 | $239,158.16 | $(492,984.69) |
| 3 | 300,000 | 0.71178 | $213,534.07 | $(279,450.62) |
| 4 | 300,000 | 0.63551 | $190,655.42 | $(88,795.20) |
| 5 | 300,000 | 0.56742 | $170,228.06 | $81,432.86 |
Discounted Payback Period = X+Y/Z
X=Last period with –ive DCC
Y=Last value of DCC at the end of period X
Z=DCC during the period after X
Discounted Payback Period = 4 + |-88795.2| / 190655.42≈ 4.47 years
Note: while calculating simple payback period, we can use an alternative formula for instances where all the cash flows are even. That formula wouldn’t be practicable here since it is unlikely to have even values of discounted cash flows.
Decision Rule
We will accept the project if the discounted payback period is less than the specified period, otherwise we will reject it.
Advantage: Since this technique considers Time Value of Money therefore, project analysts rely more on discounted payback period than on simple payback period. If the project has Negative NPV, it would not payback the initial capital value we will invest in this project.
Disadvantage: This technique also do not take into account the cash inflows generated by the project after the payback period.