## Monday, November 28, 2011

### Reverse Engineering NPV - Part Two

In the last Treasury Café post we discussed approaching the NPV valuation from a different perspective and some of the benefits it holds.
Now we are going to transition from concept-level to demonstration.

The Transformed NPV Equation
By algebra, we can transform the NPV equation in its most familiar form:
To the following:
Notes to this equation are as follows:
a)      EBITDA is equal to cash flow available to investors before tax. This should in theory be equal to pre-tax CF in the first equation. In cases where EBITDA contains a lot of “clutter” with respect to cash, then substitute Cash Flow Available to Investors in the above equation.
b)      Investment is the capital provided by investors
c)      tax_rate is the applicable income tax rate, expressed as a percentage. It is assumed to not change during the investment horizon
d)      dep_rate i is the tax depreciation rate for the investment in year i, expressed as a percentage
e)      discount_factor i is the result of dividing 1 by (1+r)i , where i is the year and r is the required rate of return (calculated using the Capital Asset Pricing Model or other method, see earlier Treasury Café posts)
f)       growth_factor i is the growth (or decline) in EBITDA in year i, expressed as a ratio. For example, if growth is 0%, growth factor would be 1. If growth is 1%, then year 1 would be 1, year 2 would be 1.01, year 3 would be 1.0201, etc.

The Transformed NPV Equation in Action – Case A
Let’s say we have ²10 TCMU’s (² stands for Treasury Café Monetary Units) to invest, and we want to invest in a project that earns 10%. Any returns due to capital structure, interest deductibility for tax purposes, etc. have been factored into this return requirement (i.e. it is the Weighted Average Cost of Capital). We face a 40% tax rate. The assets are expected to last five years, but for tax purposes are allowed to be depreciated over four. We expect the assets to produce a steady income, neither growing nor declining.
This produces an EBITDA requirement of about ²3.003 per year:

What is the less burdensome series of questions for the operating business units:
1)      Tell us what you will invest this coming year? How much will you make on this investment? What is the resulting rate of return?

Or

2)      If you have ²10 to invest, can you make ²3 per year?
Questions in series 1 involve a number of “pencils and paperclips” exercises on the part of the business unit.
The question in series 2, simple and direct, focuses on the part of the financial statements that the business units most control and with which they are most familiar – revenue, cost of goods sold, and direct overhead.

The Transformed NPV Equation in Action – Now For Some Strategic Fun!
If we imagine the example above as a box, and we have two boxes, we can stack them either vertically or horizontally, as follows:

In the first case, vertical combination, we can examine various investment strategies regarding combinations of business units.
For example, if we have two business units, one that declines 5% per year, and one that increases 5% per year. What do we look like in 5 years if we invest ²10 in each one?

In five years, while EBITDA has remained relatively flat, the composition of the company has gravitated from 50-50 to 60-40. With all respects to the efficient market hypothesis, investors are likely to view our business somewhat differently than before.
In the horizontal case, we can evaluate different investment scenarios for the business unit over time, such as a “Cash Cow” strategy vs. a “Star Performer” if we are using Boston Consulting Group’s famous classification. By assessing each of these, we can draw conclusions and insights as to what is possible and under what conditions, providing a roadmap to strategic flexibility as the future unfolds.

Key Takeaways
Analyzing pro forma requirements for EBITDA allows us to assess strategic alternatives in a manner that “speaks the language” of primary decision makers, allowing us to gather their input more effectively. This analysis can be performed without the inefficiencies of full-scale “pencils and paperclips” organizational efforts.

Questions
·         How efficient is your budgeting and forecasting process?