IFT Notes for Level I CFA^{®} Program

Net present value is the present value of the future after tax cash flows minus the investment outlay.

**Decision rule:**

For independent projects:

If NPV > 0, accept.

If NPV < 0, reject.

For mutually exclusive projects:

Accept the project with higher and positive NPV.

**Example**

Compute NPV for projects A and B given the following data:

Cost of capital = 10% |
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Expected Net after Tax cash flows |
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Year |
Project A (in $) |
Project B (in $) |

0 | -1,000 | -1,000 |

1 | 500 | 100 |

2 | 400 | 300 |

3 | 300 | 400 |

4 | 100 | 600 |

**Solution:**

**Project A:**

NPV =

On the exam, you can save time by using the calculator to solve for NPV instead of using the above formula. The key strokes are given below:

Key strokes |
Display |

[CF][2^{nd}][CLR WORK] |
CF0 = 0 |

1000 [+|-] [ENTER] | CF0 = -1000 |

[↓] 500 [ENTER] | C01 = 500 |

[↓] | F01 = 1 |

[↓] 400 [ENTER] | C02 = 400 |

[↓] | F02 = 1 |

[↓] 300 [ENTER] | C03 = 300 |

[↓] | F03 = 1 |

[↓] 100 [ENTER] | C04 = 100 |

[↓] | F04 = 1 |

[NPV] 10 [ENTER] | I = 10 |

[↓] CPT | NPV = 78.82 |

**Project B:**

NPV = =49.18

IRR is the discount rate that makes the present value of future cash flows equal to the investment outlay. We can also say that IRR is the discount rate which makes NPV equal to 0.

**Decision rule:**

For independent projects:

If IRR > required rate of return (usually firms cost of capital adjusted for projects riskiness), accept the project.

If IRR < required rate of return, reject the project.

The required rate of return is also called hurdle rate.

For mutually exclusive projects:

Accept the project with higher IRR (as long as IRR > cost of capital).

**Example**

Compute IRR for projects A and B given the following data.

Cost of Capital = 10%; Expected Net After Tax Cash Flows |
||

Year |
Project A (in $) |
Project B (in $) |

0 | -1,000 | -1,000 |

1 | 500 | 100 |

2 | 400 | 300 |

3 | 300 | 400 |

4 | 100 | 600 |

**Solution:**

**Project A:**

A very tedious method is to set up the equation below and solve for r using trial and error.

r = 14.49%

A much faster method is to use the calculator:

Key strokes |
Display |

[CF][2^{nd}][CLR WORK] |
CF0 = 0 |

1000[+|-] [ENTER] | CF0 = -1000 |

[↓] 500 [ENTER] | C01 = 500 |

[↓] | F01 = 1 |

[↓] 400 [ENTER] | C02 = 400 |

[↓] | F02 = 1 |

[↓] 300 [ENTER] | C03 = 300 |

[↓] | F03 = 1 |

[↓] 100 [ENTER] | C04 = 100 |

[↓] | F04 = 1 |

[IRR][CPT] | 14.49 |

**Project B:**

r = 11.79%