Let’s consider a hypothetical situation: where the Earnings Growth Rate is fixed, and unaffected by ROIC/ROE/etc. This follows on from the train of thought that ROIC/ROE/etc. are not the determinants, but rather it is fueled by sales growth and the free cash flow margin. You can see this from this spreadsheet here: ROIC vs Earnings Growth Rate Spreadsheet

__Case 1: No dividends, earnings growth rate = 10%
__

When ROX = new earnings / (base + earnings) = 10%,

new ROX

= new new earnings / (base + earnings + new earnings)

= new earnings * 1.1 / (base + earnings + new earnings)

= (new earnings + new earnings * 0.1) / (base + earnings + new earnings)

= (0.1 * (base + earnings) + new earnings * 0.1) / (base + earnings + new earnings)

= 0.1

= earnings growth rate

=> ROX stabilises at the earnings growth rate

__Case 2: With dividends, earnings growth rate = 10%__

Let the stabilising ROX = XXX

When new earnings / (base + 0.8*earnings) = XXX,

new ROX

= new new earnings / (base + 0.8*earnings + 0.8*new earnings)

= new earnings * 1.1 / (base + 0.8*earnings + 0.8*new earnings)

= (XXX * (base + 0.8*earnings) * 1.1) / (base + 0.8*earnings + 0.8*new earnings)

To be stabilising, we must have,

new ROX = XXX

=> (XXX * (base + 0.8*earnings) * 1.1) / (base + 0.8*earnings + 0.8*new earnings) = XXX

=> (base + 0.8*earnings) * 1.1 / (base + 0.8*earnings + 0.8*new earnings) = 1

=> (base + 0.8*earnings) * 1.1 = base + 0.8*earnings + 0.8*new earnings

=> (base + 0.8*earnings) * 1.1 = base + 0.8*earnings + 0.8*XXX*(base+0.8*earnings)

=> (base + 0.8*earnings) * 1.1 = (1 + 0.8*XXX) * (base+0.8*earnings)

=> 1.1 = 1+0.8*XXX

=> 0.1 = 0.8*XXX

=> XXX = 0.1/0.8 = 12.5%

=> XXX = Earnings Growth Rate / (1-Payout Ratio)

=> If the Earnings Growth Rate is the fixed determinant, then the ROX will defined by the Earnings Growth Rate (i.e. Earnings Growth Rate / (1-Payout Ratio))

——–

Context-switch: In the hypothetical scenario that ROX is the determinant, which base should be used?

- One property of the “base” (for the equations above and in a previous post to work) is that it increases by the retained earnings.
- The base using equity or book value will be continually increased exactly by the retained earnings, but not the case for tangible assets. because tangible assets can decrease when debt is paid down.
- So then perhaps using equity or book value as base for projection is more logical
- But using tangible assets as base is more logical for determining the real returns-generating capability of the firm – coz that is not impacted by debt levels.
- But when you talk about tangible capital employed, there is no concept of debt — the debt levels (interest-bearing) do not change the tangible capital employed
- If you don’t minus excess cash, then the tangible capital employed indeed increases by the retained earnings
- Hence you can do projections using tangible capital employed (without minusing the excess cash)

——–

Concluding thoughts:

__Earnings Growth Rate & ROX are not the determinants__

- If the Earnings Growth Rate is the determinant, then Returns on “all bases” will be the same (eventually all will become (Earnings Growth Rate / (1-Payout Ratio))) – if the characteristic of the base is additive with retained earnings.
- We don’t see that happening, hence it cannot be the case that Earnings Growth Rate is the determinant.
- The ROX also cannot be the determinant as explained in an earlier post, since the earnings are truly due to sales and margins.
- Why did we want to use ROX to project earnings in the first place?
- Because by doing that, we can model in the effects of different payout ratios (i.e. re-investment), e.g. increasing re-investment thru retained earnings helping to increase future earnings (either by increasing sales or improving margins)
- Can we project without using the ROX and yet be able to model in different payout ratios? <– important question

__Modeling the re-investment process to project earnings__

- Yes, by modeling the re-investment process. We need to estimate the “return on retained earnings” so as to project the impact of retained earnings on future earnings.
- This projection can start at any point in time. If we assume that the earnings for one year can be repeated thereafter (i.e. the old base continues to produce the same earnings year after year after year), then we can project future earnings by using the old base, and adding on the effects of “return on retained earnings” subsequently.
- If we find that the ROX is consistent across many years, then what it means is that the “return on retained earnings” = ROX, then we can project using ROX, Buffettology-style.
- We can estimate the “return on retained earnings” by calculating (Earnings (T + y) – Earnings (T)) / (Retained earnings from T to (T+y)). E.g. (2003 Earnings – 2000 Earnings) / (2000 Retained earnings + 2001 Retained earnings + 2002 Retained earnings). “y” should be varied using 1-year, 3-year, 5-year, 10-year periods. You need to calculate across multiple years as the “fruits” of re-investment may not happen immediately in the next year.

__Modeling re-investment is a “short-cut” to reality__

- The projection using “re-investment return” is a short-cut.
- In reality, the 3 primary drivers are : Sales growth rate, FCF margin, Payout ratio (i.e. re-investment)
- Capital-intensive companies that require lots of re-investment into PP&E will have a bad FCF margin. Re-investing for expansion or advertising can greatly improve the sales growth rate. Share buybacks are also another form of re-investment which doesn’t impact earnings but may impact valuation.
- To really estimate the effects of each different type of re-investment on Sales growth rate and FCF margin seems fraught with guesswork and errors. May be better to use the “re-investment return” short-cut.

Afternote: An article from Tweedy, Browne (Great 10-Year Record = Great Future, right?) highlighted a warning for assuming a consistent ROX

*“The easy-to-calculate Implied Growth Rate (i.e., return on equity times the percentage of earnings that is reinvested in the business and not paid out to stockholders as a dividend) did not predict future earnings growth, on average, for companies that had been highly profitable over the last ten*

years. Return on equity for these companies, as a group, tended to decline over the next seven years. Financial pasts were not related to financial futures for the companies as a group.”

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