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So i have this question:

RainMan Inc. is in the business of producing rain upon request. They must decide between two investment projects; a new airplane for seeding rain clouds or a new weather control machine built by Dr. Nutzbaum. The discount rate for the new airplane is 9%, while the discount rate for the weather machine is 39% (it happens to be higher risk). Which investment should the company select and why?

Cash flow of airplane= -900,500,600 (life span of 2 years) Cash flow of weather machine=-900,550,600,685 (life span of 3 years)

I proceed calculating the NPV of the airplane=63.72 and the NPV of the weather machine=61.29.

I calculate the annuity factor of the airplane which is 1.759 and the annuity factor of the weather machine which is 1.60935.

Then the annuity payment of the airplane is 36.38 and the annuity payment of the weather machine is 38.08.

It would appear to me that since the annuity payment (or the equivalent annual annuity) of the payment is lower, then it should be chosen

HOWEVER! Thesere are the possible answers to the question :

A) Airplane, because it has a higher equivalent annual cash flow

B) Airplane, because it has a higher NPV

C) Weather machine, because it has a higher NPV

D) Weather machine, because it has a higher equivalent annual cash flow

The answer on the sheet states to choose D. It says that since they have different life spans the weather machine has a higher EAA and should be accepted.

My current knowledge has taught me to choose the project with the lowest equivalent annual annuity . Other questions on my text book had answers that preffered projects with lower equivalent annual annuities.

Then what am i doing wrong ? Am i confusing the equivalent annual cost principle with the equivalent annual annuity approach which states to choose the project with the highest equivalent annuity ?

I am quite confused since the methods used to calculate the EAA and the EAC appear to be the same on my answer sheet ( different questions obviously ) but yet this question tells me to choose the highest annuity payment and some the lowest?

The other question in which the answer was to choose the project with the lowest EAC is this:

Two machines, A and B, which perform the same functions, have the following costs and lives. Machine A has a PV of costs of 6000 and its life is equal to 5 years. Machine B has a PV of costs of 8000 and its life is 7 years. Which machine would you choose? The two machines are mutually exclusive and the cost of capital is 15 percent.

Yet again i would still do the same process (other than calculating the NPV which is already states) and i would come to the conclusion that the EAC(A) is 1789.89 and the EAC(B) is 1922.88.

The possible answers to this question are:

A) Machine B, because it has longer life

B) Machine A, because it has lower PV costs

C) Machine B, because the EAC is $1,922.88

D) Machine A, because the EAC is $1,789.89

Then obviously I would choose D (which is correct since the EAC of machine A is 1789.89 which is indeed lower than B)

Please explain in the simplest way possible what i am not understanding. Thank you !

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You're missing the distinction between costs and benefits. In your first probem you have positive NPVs and therefore the equivalent annual value is the equivalent annual cashflows that comes in.

In your second problem you have costs only. Converting that that to an EAV means converting it to an annual cash flow that goes out. Obviously you want the former to be as large as possible and the latter to be as small as possible.

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