## 15 May 2013

### Capital investment appraisal: the importance of assessing it right

I did some work over on Wikipedia on this topic with respect to the Canadian context, and thought it might be a good idea to expand upon it here.

Capital investment projects are always assessed on their cash flows. As we know, cash flows are segregated into streams arising from activities in:
• operations
• investment, and
• financing
The initial assessment of a project will match up the expected streams from operations and investments, in order to assess viability. Streams relating to financing will become relevant when assessing the best option for the acquisition of the assets (ie, lease vs buy, debt vs equity, and so on), but that is by definition the second step of the process, after the initial appraisal has been completed.

Let us assume the following factors for use in our calculations or capital cost allowance fhere:
• I = Investment
• d = CCA rate per year for tax purposes
• t = rate of taxation
• n = number of years
• i = cost of capital, after-tax rate of interest, or minimum rate of return (whichever is most relevant)

### Full-year rule

When CCA is calculated at the maximum rate, the values claimed by year for a specific class under the full-year rule will be broken out as follows:

$Id + Id(1-d) + Id(1-d)^2 + \cdots + Id(1-d)^{n-1}$

Therefore, the tax shield in year n = $Itd(1-d)^{n-1}$, and the present value of the taxation credits will be equal to $Itd \sum\limits_{n=1}^\infty \frac{(1-d)^{n-1}}{(1+i)^n}$.

As this is an example of a converging series for a geometric progression, this can be simplified further to become:

$PV = \frac{Itd}{i+d}$

The net present after-tax value of a capital investment then becomes:

$I \left (1-\frac{td}{i+d}\right )$

### Half-year rule

For capital investments where CCA is calculated under the half-year rule, the CCA tax shield calculation is modified as follows:

\begin{align} PV & = \frac{1}{2}\left (\frac{Itd}{i+d}\right ) + \frac{1}{2}\left (\frac{Itd}{i+d}\right )\left (\frac{1}{1+i}\right ) \\ & =\frac{Itd}{i+d}\left [\frac{1}{2} + \frac{\frac{1}{2}}{1+i}\right ] \\ & =\frac{Itd}{i+d}\left [\frac{\frac{1}{2}\left (1+i\right ) + \frac{1}{2}}{1+i}\right ] \\ & =\left (\frac{Itd}{i+d}\right )\left (\frac{1+\frac{1}{2}i}{1+i}\right ) \\ \end{align}

Therefore, the net present after-tax value of a capital investment is determined to be:

$I \left [ 1-\left (\frac{td}{i+d}\right )\left (\frac{1+\frac{1}{2}i}{1+i}\right ) \right ]$

### Specialized calculations

The methods shown above are the default calculations used for standard pools of undepreciated capital cost using the declining-balance method for accounting for CCA. There are certain classes where different calculations will be employed:

• Class 13 (leasehold improvements) - Over the original lease period plus one renewal period (Minimum 5 years and maximum 40 years, but half-year rule applies)
• Class 14 (franchises, concessions, patents and licenses) - Length of life of property (no half-year rule applies)
• Class 29 (effectively recognized over three years, at 25%/50%/25%)
These are instances where standard spreadsheet calculations will still need to be employed. These are quite well presented in most financial management texts.

There are also special rules for companies that are involved with industrial mineral mines or timber limits and cutting rights. In addition, resource companies will need to assess the impact of the resource and processing allowances that are available to them. These rules are beyond the scope of this article.