##### Definition:

Discounted payback period is used to evaluate the time period needed for a project to bring in enough profits to recoup the initial investment.

#### Formula:

Discounted Payback Period (DPP) = 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.
#### Example:

An initial investment of Rs.50000 is expected to generate Rs.10000 per year for 8 years. Calculate the discounted payback period of the investment if the discount rate is 11%.

#### Given,

Initial investment = Rs. 50000
Years(n) = 8
Rate(i) = 11 %
CF = 10000

#### To Find,

Discounted Payback Period (DPP)

#### Solution:

Year(n) |
Cash Flow (CF) |
Present Value FactorPV = 1/(1+i)^{n} |
Discounted Cash Flow (CF x PV) |
Cumulative Discounted Cash Flow (CCF) |

0 | 50000 | 1 | 50000 | 50000 |

1 | 10000 | 0.9 | 9009.01 | 40990.99 |

2 | 10000 | 0.81 | 8116.22 | 32874.77 |

3 | 10000 | 0.73 | 7311.91 | 25562.85 |

4 | 10000 | 0.66 | 6587.31 | 18975.54 |

5 | 10000 | 0.59 | 5934.51 | 13041.03 |

6 | 10000 | 0.53 | 5346.41 | 7694.62 |

7 | 10000 | 0.48 | 4816.58 | 2878.04 |

8 | 10000 | 0.43 | 4339.26 | -1461.23 |

Last period with a negative discounted cumulative cash flow (A) = 7
Absolute value of discounted cumulative cash flow at the end of the period (B) = 2878.04
Discounted cash flow during the period after (C) = 4339.26
**Discounted Payback Period = A + (B / C) = 7 + (2878.04 / 4339.26) = 7.66 years**