- CFA Exams
- CFA Level I Exam
- Study Session 7. Corporate Finance (1)
- Reading 19. Capital Budgeting
- Subject 2. Comparing projects with unequal lives

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**CFA Practice Question**

Ecodevelopment Company has two mutually exclusive construction projects to evaluate. Each type of project can be duplicated repeatedly in different geographic locations around the country, but each requires a very different set of assets to construct. Thus, Ecodevelopment uses the equivalent annual annuity method to evaluate such projects. Project type A costs $6 million initially and generates expected end-of-year cash flows of $3 million, $5 million, and then $10 million when it is sold after 3 years. Project type B costs $9 million initially and has projected end-of-year cash flows of $3, $3, $6, and $6 million in Year 1 through Year 4, and then $10 million in Year 5. The project types are equally risky and the firm's cost of capital is 12 percent. What is the EAA of the higher valued project type, in terms of EAA?

A. $2.726 million

B. $4.389 million

C. $3.240 million

**Explanation:**Calculate each project's original life NPV:

NPV(A) = $3.0(PVIF(12%,1)) + $5.0(PVIF(12%,2)) + $10.0(PVIF(12%,3)) - $6.0

= $3.0(0.8929) + $5.0(0.7972) + $10.0(0.7118) - $6.0 = $7,782,700.

NPV(B) = $3.0(PVIFA(12%,2)) + $6.0(PVIFA(12%,2))(PVIF(12%,2)) + $10.0(PVIF(12%,5)) - $9.0

= $3.0(1.6901) + $6.0(1.6901)(0.7972) + $10.0(0.5674) - $9.0 = $9,828,400.

Calculate the equivalent annual annuity:

NPV(A) = $7,782,700 = EAA(A)(PVIFA(12%,3))

EAA(A) = $7,782,700/2.4018 = $3,240,361.40.

NPV(B) = $9,828,400 = EAA(B)(PVIFA(12%,5))

EAA(B) = $9,828,400/3.6048 = $2,726,475.81.

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**User Contributed Comments**
16

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

ahan |
How do you get PVIFA(12%,3) = 2.4018? |

timspear |
By PVIFA(12%,3) they mean the present value of $1 at the end of years 1,2 & 3 ie. 1/1.12 +1/1.12^2 + 1/1.12^3 |

max111 |
how do you gret PVIFA(12%,3) = 2.4018? |

julamo |
and of course don't forget that you have 1.5 minutes to read the whole thing and make the calculations, good luck! |

thekapila |
guys skip big questiosn like this...else you wont be able to make it.. |

Birdy101 |
is this possible to do it quicker with the TI BA II Plus Prof ? |

Birdy101 |
PVIFA(12%,3) = 2.4018 = Sum of the discount factors over the 3 years = 1/1.12 + 1/1.12^2 + 1/1.12^3 |

wineo |
Use the CF function will work. For the 2 projects, input all the necessary cash flows and compute NPVs. For the EAA portion, I just input, say for proj A: CF0=0, C01=1, F01=3, I=12, Cmpt NPV=2.4018 ...much quicker. |

vadklim |
Alternatively, we can use TVM function at BA II Plus Pro: N=3,PMT=1,I/Y=12, Cmpt PV = 2.4018 Or even easier way taking NPV from the step 1: N=3, PV = $7'782'700, I/Y=12, Cmpt PMT= 3'240'319 |

StanleyMo |
2. Equivalent-Annual-Annuity Approach While easy to understand, the replacement-chain method can be time consuming. A simpler approach is the equivalent-annual-annuity approach. This is the procedure for determining EAA: 1) Determine the projects' NPVs. 2) Find each project's EAA, the expected payment over the project's life, where the future value of the project would equal zero. 3) Compare the EAA of each project and select the project with the highestEAA. From our example, the NPV of each project is as follows: -NPV of Machine A is equal to $2,926. -NPV of Machine B is equal to $1,735. To determine each project's EAA, it is best to use your financial calculator. - For, Machine A (project 1), our assumptions are as follows: i = 8.4% (the company's WACC) n = 6 PV = NPV = -2,926 FV = 0 Find for PMT For Machine A, the EAA (the calculated PMT) is $640.64. -For Machine B (project 2), our assumptions are as follows: i = 8.4% (the company's WACC) n = 3 PV = NPV = -1,735 FV = 0 Find for PMT For Machine B, the EAA (the calculated PMT) is $678.10. i think CFA might come out with this kidn of questions |

aravinda |
Thank you StanleyMo.. your explanation helps a lot |

ljamieson |
wow, be careful with the BAII. I did this in 000,000s instead (ie PV = 7.7827) and get a totaly dif answer then. Tried it both ways and get two different answers. |

cunnye |
Stan, how would solving for PMT answer the question? |

daverco |
The explanation may be right, but from a test-taking perspective uselessly complicated, unhelpful answer. Simply find NPV's for both projects and use this NPV as PV input in TMV calculation (find PMT, FV=0). This can be done in a minute. |

LoCo83 |
Anyone else jump the gun and choose the EAA for the highest NPV project? *palm-to-forehead* ... yet another lesson for me in the importance of reading the question carefully |

darbyland |
just like daverco said, use your calculators. for project A: FV=0, PV=-7.78, N=3,I/Y=12, PMT=? |