IFT Notes for Level I CFA^{®} Program

The payback period is the number of years it takes to recover the initial cost of the investment.

**Advantages:**

- Easy to calculate.
- Easy to explain.
- Indicator of project liquidity. A project with two-year payback is more liquid than one with a longer payback period as the initial investment is recovered more quickly.

**Drawbacks:**

- Does not consider cash flows after payback period.
- It does not consider the time value of money as the cash flows are not discounted at the project’s required rate of return.
- Does not consider the risk of a project.

Discounted payback method uses the present value of the estimated cash flows; it gives the number of years to recover the initial investment in present value terms.

**Drawbacks of discounted payback method:**

- Does not consider any cash flows beyond the payback period.
- Poor measure of profitability as there may be negative cash flows after the discounted payback period which may result in a negative NPV.

**Example 3**

Compute the payback period and the discounted payback period assuming a rate of 10%.

Year |
0 |
1 |
2 |
3 |
4 |

Cash flows | -800 | 340 | 340 | 340 | 340 |

** **

**Solution:**

Year |
0 |
1 |
2 |
3 |
4 |

Cash flows | -800 | 340 | 340 | 340 | 340 |

Cumulative Cash flows | -800 | -460 | -120 | 220 | 560 |

Discounted Cash flows | -800 | 309.1 | 280.99 | 255.45 | 232.22 |

Cumulative Discounted Cash flows | -800 | -490.9 | -209.91 | 45.54 | 277.76 |

Payback period = Last year with negative cumulative cash flow + unrecovered cost at the beginning of the next year/ cash flow in the next year

Payback period = = 2.35 years

Discounted payback period = = 2.82 years

The discounted payback period is always going to be greater than the payback period, as long as the interest rate is positive. If the interest rate is 0%, both payback periods will be the same.

The average accounting rate of return (AAR) can be defined as:

Average accounting rate of return =

Profitability Index is the present value of a project’s future cash flows divided by the initial investment.

Profitability Index PI =

Profitability Index PI =

**Investment decision rule for PI:**

Invest if PI > 1.

Do not invest if PI < 1.

**Difference between PI and NPV**

Consider two projects A and B. Project A has an initial investment of $1 million and an NPV of 0.1 million. Project B has an initial investment of $1 billion and an NPV of 0.2 million. If projects A and B are mutually exclusive, then project B would be chosen because of higher NPV. But, if you consider the profitability index, it gives a different picture.

PI of project A = 1 + 0.1/1 = 1.1

PI of project B = 1 + 0.2 /1000 = 1.0002

Based on PI, project A is more profitable than project B.

NPV profile is a graph that plots a project’s NPV for different discount rates. The NPV is shown on the y-axis with the discount rates on the x-axis. Given the data below, create the NPV profile for project X.

Year |
0 |
1 |
2 |
3 |
4 |

Project |
-400 | 160 | 160 | 160 | 160 |

Discount rate |
NPV (in $ million) |

0 | 240 |

5 | 167 |

10 | 107 |

22 | 0 |

Two important points on the graph:

- The point where the profile goes through the Y-axis (240) is the NPV of the project when the discount rate is 0. This is equal to the sum of the undiscounted cash flows.
- The point where the profile goes through the X-axis (22) is where the discount rate is equal to the IRR of the project.

**Example 4**

Draw the NPV profiles for projects X and Y. Discuss the significance of crossover point.

Year |
0 |
1 |
2 |
3 |
4 |

Project X | -400 | 160 | 160 | 160 | 160 |

Project Y | -400 | 0 | 0 | 0 | 800 |

The NPV profile for projects X and Y at different discount rates is tabulated below. Based on these values, the NPV profiles are depicted graphically.

*Note: The values are computed for each discount rate using the calculator.*

Discount Rate (in %) |
NPV for Project X |
NPV for Project Y |

0 | 240 | 400 |

5 | 167.35 | 258.16 |

10 | 107.17 | 146.41 |

15 | 56.79 | 57.40 |

18.92 | 22.82 | 0 |

20 | 14.19 | -14.19 |

21.86 | 0 | -37.22 |

Let us plot the NPV profile for both the projects now.

The point at which the NPV for both projects intersect is called the crossover point.

If X and Y are mutually exclusive, the discount rate is used to decide which project is better. At lower discount rates, i.e., to the left of the crossover point, Project Y is better. At higher discount rates, i.e., to the right of the crossover point, Project X is better. For example, at a discount rate of 10%, Project Y is better, whereas at a discount rate of 20%, Project X is better.