- CFA Exams
- CFA Level I Exam
- Topic 3. Corporate Issuers
- Learning Module 5. Capital Investments and Capital Allocation
- Subject 2. Capital Allocation

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**CFA Practice Question**

You have been asked to evaluate two machines. The benefits from ownership are identical. Machine A costs $150 to buy and install, lasts for 5 years, and costs $80 per year to operate. Machine B costs $250, lasts for 7 years, and costs $60 per year to operate. Both machines have zero salvage value. Assuming that this is a one-time acquisition, which machine do you recommend if the cost of capital is 10%?

B. Machine B, because the PV of its costs is $20 less than Machine A.

C. Machine A, even though the PV of its costs is equal to that of Machine B.

A. Machine A, because the PV of its costs is $88.85 less than Machine B.

B. Machine B, because the PV of its costs is $20 less than Machine A.

C. Machine A, even though the PV of its costs is equal to that of Machine B.

Correct Answer: A

PVB = 250 + 60(4.8684) = 250 + 292.10 = 542.10

PVB > PVA

PVA = 150 + 80(3.7908) = 150 + 303.26 = 453.26

PVB = 250 + 60(4.8684) = 250 + 292.10 = 542.10

PVB > PVA

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**User Contributed Comments**
16

User |
Comment |
---|---|

cracklvl2 |
What about the effect of depreciation tax shield? |

wldu |
(3.7908)how? |

robbjm30 |
3.7908 must be their annuity factor. You just treat A as an annuity at $80 per period for 5 periods, 0 FV, and rate 10%. B is annuity at $60 per period for 7 periods, 0 FV and rate 10%. THen you add the upfront cost to each annuity value and you can see the difference. |

george2006 |
I think the answer to this problem is wrong because it ignores that machine B has 2 more years of operating life. The correct approach is to annualize the innital upfront cost into respective annuities to derive the annual cost: machine A: $80+$39.57 = $119.57/year machine B: $60+$51.35 = $111.35/year Assuming both machines makes the same revenue contribution annually, buying machine B is better since its annual cost is lower. |

Done |
The way you would use you calcualtor on this problem is: CFo = +150 CFo = +250 CF1 = +80 CF1 = +60 F1 = 5 F1 = 7 I =10% I = 10% NPV = 453.26 NPV = 542.10 Remember they are all outflows |

patsy |
The different lifespans should be taken into account. |

eddie1609 |
Presumably the benefits of ownership are identical only if B is operated over the full 7 years, thus the costs of years 6 & 7 must be included. |

tagr |
Present value annuity factor = (1 - (1/(1+r)^n)) / r For machine A: (1 - (1/(1+0.1)^5)) / 0.1 = (1 - (1/1.1^5)) / 0.1 = (1 - (1/1.61051)) / 0.1 = (1 - 0.62092) / 0.1 = 0.37908 / 0.1 = 3.7908 |

julescruis |
Thank you eddie for clearing up those people. Ownership benefits are identical so we dont care about anything else here, and please do not start to talk about depreciation tax sheets and all that crap. It is simple discounting nothing more nothing less |

todolist |
this Q. only concerns the PV of costs, one should ignore the return per machine/year when working out this problem |

cfairs |
Depreciaton is factored into Accounting Income and not into Cash Flows; |

gill15 |
they should've put PVA = -453 and PVB = -542 so that PVA > PVB just for consistency. You want the higher PV of the two. |

Kevdharr |
You guys are making this way too complicated. Just enter the values separately into your calculator and write down their respective net present values. They will both be negative because this machine isn't generating any cash. It is COSTING them money on an annual basis. So whichever one costs them less should be the one they choose. |

Inaganti6 |
@kevdharr. best comment in entire page |

Ewan2015 |
Ok this question compares apples to oranges. If the machine B has a 7 yr life then I can either a) use it for 5 years and sell it with some salvage value or b) avoid forking over another 150 in year six when Machine A breaks! |

Haoran |
@Ewan2015: you can always compare these machines using PVs! how much is an apple? How much is an orange? Then you can compare apples with oranges. |