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Net Present Value of a rolling project

I have a finance homework question that I'm hoping someone can help me with. It goes something like this:

A company jet is not being fully utilised, and could be used to fly corporate officers around at an additional cost of $200,000 a year but would save $1m a year. Using it in this way, though, would decrease the effective life of the aircraft by 25%. The present jet has 4 years (before considering the increased use) remaining before it needs to be replaced.

The cost of a new plane is $2.5 million and is expected to remain constant at this level in real terms. At the original (i.e. under-utilised) usage, the type of jet used has an 8-year effective life. The dicsount rate is 9%, and the company will need to transport its officers for the indefinite future if the plane were to be used in that way.

The question is to determine whether the officers should be allowed to use the plane. I think you can answer it by working out the Equivalent Annual Cost, but am unsure how to apply it to a rolling project (i.e. one where an investment and cash flows follows the same pattern). I'm sure this will be simple for some of you finance gurus!

Thanks

Reply to
Inquisitive
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At least you're being honest. We shouldn't really help, but what the hell. Perhaps we can make you get it wrong. :-)

Straightforward enough. Assuming the jet will be replaced even if not used for the corporate officers, the extra cost of allowing them to use it is the difference between spending $2500k 4 years from now and spending it 3 years from now.

In NPV terms that's $2500k/1.09^3 - $2500k/1.09^4, which is only $160k.

If you invest those $160k now, you will save $800k per year for each of the next 3 years, but to compare like with like, you have to take the 4th year as losing you $1000k for plane tickets you have to buy. This is because you don't want to pre-empt the decision of a policy review which might be taken when the next plane is bought. So you have an added cost of $1000k/1.9^3.5 (the airline tickets are bought throughout the year, so for averaging purposes I'm treating the cost as incurred in the middle, not end, of the year, which is not 4 but

3.5 years from now). That's $740k. Total extra cost: $900k.

It seems like a no-brainer. The NPV of the saving is 3*$800k, appropriately discounted. It's so obvious you hardly need bother with the scaling, but I imagine you'd take $800k*(1.09^-0.5 + 1.09^-1.5 +

1.09^-2.5), to average the per-year saving to the middle of each year.

After that, having bought the next plane, you either replace the plane every 8 years or every 6 years. Ignoring discount, the cost spread out over the replacement cycle will either be $417k per year or $312k per year, so the recurring capital cost will increase by $105k per year if you allow this extra use to achieve an annual saving of $800k.

Again the answer is obvious.

To do the proper NPV calculation for the recurring cycle, it's not the present value you want to reduce all the expenditure to, but rather the time at which you buy the new plane. I guess you'd be expected to apply the perpetuity stuff you mentioned a couple of questions ago.

Reply to
Ronald Raygun

Ronald,

I haven't looked at your advice in detail yet, but I can't thank you enough for your help. Furthermore, please feel morally sound in providing the help as the question is not being explicitly marked but is meant to be an aid to help us understand the concepts. Thanks once again.

Reply to
Inquisitive

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