## 25 January 2015

### Thoughts on capital investment appraisal

A while back, I posted about the techniques one must use when calculating appraisals in a Canadian context. It was somewhat simplified, as it pertained only to a single alternative. That is unrealistic, as the business world is more complex:
• What if there are alternatives?
• Which one makes more economic sense?
• Assuming that benefits are equal among the alternatives, which project results in the lowest cost?
• What if these alternatives have different economic lives?
• Is leasing or buying the most economical choice?

For the first two questions, the answer is almost always the alternative with the greatest net present value on a discounted cash flow basis. The only plausible exception is where the project represents a major ground-breaking development, and that calls for strategic decision-making at the Board level. That is a discussion for another time.

For the other questions, there is a technique available that has been rarely discussed but is quite powerful, which calls for determining the Equivalent Annual Cost. Put simply, it is the net present value divided by the capital annuity factor, or

$EAC = \frac{NPV}{A_{t,i}}$

where t = number of years, and i = cost of capital. The capital annuity factor is calculated as:

$A_{t,i} = \frac{1-\left(\frac{1}{1+i}\right)^t}{i}$

If there is any salvage value at the end of the project, that can be factored in through using a sinking fund factor, calculated as:

$SFF_{t,i} = \frac{1}{\left(1+i\right)^t-1}$

This is useful for many scenarios:
• What if the asset requires periodic overhauls every few years, and in what circumstances is it cheaper to replace rather than overhaul?
• What commitments must be made for maintaining inventories of parts and maintenance supplies?
• What if a landlord provides rent-free periods at certain points in the lease?
• Are there conditional grants or other incentives that are paid subsequent to acquisition or improvement of an asset?
• Can the asset be sold at the end of its useful economic life, and would that value be different for the various alternatives?
These can be calculated in a rather straightforward manner. Let us take an example of deciding which of two types of storage tanks would represent a more economical investment. A steel tank costing CAD 10,000 with a salvage value of CAD 1,000 and annual operating costs of CAD 1,600 has an estimated useful life of five years. It is being compared to a stainless steel tank costing CAD 25,000 with a salvage value of CAD 2,000 and annual operating costs of CAD 100. Which is the better choice?

In this case, all other things being equal, the stainless steel tank has the lower EAC, and it should be the preferred choice.

For manufacturing and processing operations, assets fall under class 29, which has a different calculation. The result can be modified as follows:

In this case, the end result would still be the same, but note how different the NPVs are for the capital investment.

This is not a new technique: in fact, it was taught to all CMAs and still represents part of the Body of Knowledge that we are expected to use in our work. It was discussed in much greater detail in A Practical Approach to the Appraisal of Capital Expenditures (C. Geoffrey Edge, V. Bruce Irvine (1981), ISBN 0-920212-29-8), which, having been last issued in 1989, does not seem to be widely available these days. I took one of its examples on this subject, and updated it to take into account the "half-year rule" now in effect for claiming first-year CCA, as well as more realistic rates for corporate tax and cost of capital. Otherwise, the logic is still sound.

I am publishing this because I cannot seem to find anything similar on the web, and this is just too useful not to attract a wider audience in the CPA community. Formulas are embedded, so that its working can be better understood.