### The Cash Flows Associated With Three Independent

##### Question

# The cash flows associated with three independent projects (in millions) are as follows Net Cash Flows Proiect Alpha Project Beta Proiect Gamma Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 $1,500,000…

The cash flows associated with three independent projects (in millions) are as follows Net Cash Flows Proiect Alpha Project Beta Proiect Gamma Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 $1,500,000 $300,000 S500,000 S500,000 $400,000 $300,000 $400,000 $100,000 S200,000 $200,000 $100,000 S200,000 $7,500,000 $2,000,000 S3,000,000 S2,000,000 S1,500,000 $5,500,000 a) Calculate the payback period of each investment b) Which investments does the company accept if the cut-off payback period is three years? What if the cut-off is four years? Which one of these projects is a project that almost certainly should be rejected, but might be accepted if the company uses the payback period method? Explain c) d) Which one of these projects almost certainly should be accepted (unless the company's discount rate is very high), but might be rejected if the company uses the payback period method. Explain e) What is the maximum number of internal rates of return that each project can have and why?

## Solutions

##### Expert Solution

Alpha | Beta | Gamma | ||||

Year (n) |
Cash Flow (CF) |
Cumulative Cash Flow (CCF) | Cash Flow (CF) |
Cumulative Cash Flow (CCF) | Cash Flow (CF) |
Cumulative Cash Flow (CCF) |

0 |
(1,500,000) |
(1,500,000) |
(400,000) |
(400,000) | (7,500,000) | (7,500,000) |

1 |
300,000 |
(1,200,000) |
100,000 |
(300,000) | 2,000,000 | (5,500,000) |

2 |
500,000 |
(700,000) |
200,000 |
(100,000) | 3,000,000 | (2,500,000) |

3 |
500,000 |
(200,000) |
200,000 |
100,000 | 2,000,000 | (500,000) |

4 |
400,000 |
200,000 |
100,000 |
200,000 | 1,500,000 | 1,000,000 |

5 |
300,000 |
500,000 |
(200,000) |
– |
5,500,000 | 6,500,000 |

Cumulative cash flow (CCF) = CFn + CCFn-1

a). Alpha: CFs turn positive in year 4 so fraction of year 4 =

-CCF3/CF4 = 200,000/400,000 = 0.50

Payback period = 3 + 0.50 = 3.50 years

Beta: CFs turn positive in year 3 so fraction of year 4 =

-CCF2/CF3 = 100,000/200,000 = 0.50

Payback period = 2 + 0.50 = 2.50 years

Gamma: CFs turn positive in year 4 so fraction of year 4 =

-CCF3/CF4 = 500,000/1,500,000 = 0.33

Payback period = 3 + 0.33 = 3.33 years

b). If cut-off payback period is 3 years then Beta should be

accepted as its payback period is less than 3 years.

If cut-off period is 4 years then any of the 3 projects can be

accepted as all of them have payback periods less than 4 years.

c). Beta would almost certainly be rejected because its CCF

after 5 years in 0. Essentially, it does not earn anything.

However, if payback period is used then it can be accepted.

d). Gamma would be rejected on the payback period of 3 years

criteria but otherwise it should be accepted as it has the highest

CCF of 6,500,000 after 5 years.

e). Alpha and Gamma have normal cash flows (1st outflow,

remaining all inflows) so they will have only one IRR. However,

Beta has abnormal cash flows (2 outflows, 1st and last) so it can

have 2 IRRs.