### Syllabus D4jk)

j) Calculate NPV, IRR and payback (discounted and non-discounted)

k) Interpret the results of NPV, IRR and payback calculations of investment viability

### Payback Period

#### Payback Period (non discounted)

The payback period is the length of time that it takes for a project to recoup its initial cost out of the cash receipts that it generates.

This period is sometimes referred to as "the time that it takes for an investment to pay for itself."

The basic premise of the payback method is that the more quickly the cost of an investment can be recovered, the more desirable is the investment.

Hence, this method focuses on liquidity.

The payback period is expressed in years.

When the net annual cash inflow is the same every year, the following formula can be used to calculate the payback period.

#### Formula / Equation - If annual inflows are the same each year

The formula or equation for the calculation of payback period is as follows:

Payback period = Investment required / Net annual cash inflow

#### Illustration - Constant Cash Flow

Initial cost $3,600,000

Cash in annually $700,000

What is the payback period?

**Solution**

3,600,000 / 700,000 = 5.1429 years

Take the decimal (0.1429) and multiply it by 12 to get the months - in this case 1.7 months

So the answer is 5 years and 1.7 months

#### Illustration - Irregular Cash Flows

When the cash flows associated with an investment project change from year to year, the simple payback formula that we outlined earlier cannot be used. To understand this point, consider the following data:

year 0 - capital out | (800) | -800 |

year 1 - cash in | 100 | -700 |

year 2 - cash in | 240 | -460 |

year 3 - cash in | 200 | -260 |

year 4 - cash in | 250 | -10 |

year 5 - cash in | 120 | +110 |

When the cumulative cashflow becomes positive then this is when the initial payment has been repaid and so is the payback period

So in the final year we need to make $10 more to recoup the initial 800. So, that’s $10 out of $120. 10/120 x 12 (number of months) = 1.

So the answer is 4 years 1 month.

#### Payback Period (discounted)

The payback period incorporates the time value of money into the payback method. All the cash flows are discounted at the company’s cost of capital. The discounted payback period is therefore the time it will take before the project’s cumulative NPV becomes positive.