06 November 2015

Better analysis using Gnuplot

My recent posting using images generated from Gnuplot was rather basic. After examining its quite voluminous documentation somewhat cursorily, I have been able to significantly improve the output.

For example, the impact of tax rates and cost of capital on investment in Class 29 assets is illuminated through the use of colour:

Adding a 2D heatmap with the original 3D chart really does clarify the nature of the impact. By specifying different colours to different ranges of after-tax cost, we can more easily gauge the effects.

Here it is for Class 53:

You can easily see that the colours are shifting to the left, thus showing that the net after-tax cost is generally becoming cheaper.

And for Class 43:


You can note the impact quite distinctly between the three graphs.I have only just begun to explore this particular application, but I am already impressed with its power.

05 November 2015

A follow-up on the impact of the federal budget

Last spring, I published a post on the impact of changes in capital cost allowance rates on the after-tax cost of investment. I attempted to quantify the impact, but I have wondered since about what would happen if the variables relating to tax rates and cost of capital changed, and how to express that clearly.

I have recently come across gnuplot, an open-source program that helps to chart questions like this, and inputted the data. I decided to plot all possible combinations from 1% to 99% for both cost of capital and composite corporate tax rates.

For the current Class 29 framework, the chart looks like this:

There are two things that immediately stand out:
  • as the tax rate rises, the net after-tax cost falls; and
  • as the cost of capital rises, the net after-tax cost increases as well.
For comparison, here is the impact on Class 53 assets, which is scheduled to be in effect from 2016 to 2024:

Note that this reduces the net after-tax cost attributable to higher costs of capital. This is especially important when such costs are weighted for risk.

And what about Class 43, which is supposed to return in 2025? While very theoretical, because of the recent change in government in Ottawa, here is what it would look like:

You can see immediately that the cost of capital aberration returns.For that reason alone, I would venture to guess that that option will never return to the Canadian tax structure.

All of these charts do highlight a major flaw in the current system, which all political parties in Canada have failed to see: as lower tax rates make the net after-tax cost of investment much more expensive, that means that current rate reductions given to manufacturing and small business are actually making it more expensive for them to invest in more productive assets. The UK, probably for that very reason, decided recently to abolish its preferential small business rate, and have opted to bring in concepts such as the "patent box" to assign lower tax rates based on the results of specified investments.

That may well be worth implementing here.