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Conceptual problem with reinvestment rate formula


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Posted (edited)

A lot of corporate finance tells us that looking at historic reinvestment rate * ROIC gives us a good indication of how much a company's earnings can grow by.

 

In this context, I'm trying to look at different approaches to calculating a company's historic rate of reinvesting capital as a percentage of earnings.  One of the formulas I've come across is;

 

Net CapEx + Change in working capital / NOPAT.

 

I am struggling to conceptualize why we need to add back depreciation in the above formula.  To me, gross CapEx alone plus change in WC seems to be the most appropriate approach since it reflects the actual amount of cash investment that a firm has had to reinvest.

 

In a simple example....

 

NOPAT - $100m

 

Depreciation - $20m

 

CapEx - $20m

 

assume no change in WC

 

According to the conventional formula, the company has not reinvested anything, which is clearly not the case.  If it's reinvested the same amount of CapEx to cover its depreciating assets then while the company won't necessarily grow, that $20m CapEx is still a reinvestment required to sustain the existing level of business operations.  To me, the reinvestment rate is 20%.

 

The only way that I can see this formula working is that the reinvestment rate is implicitly defined solely as any capital that's reinvested into the business over and above the level of reinvestment required simply to maintain the existing business.  But I haven't found any explicit definition to say that's the case, which is a bit confusing.  By 'reinvestment rate' does this actually mean reinvestment 'over and above' investment in existing assets?  In which case 'growth reinvestment rate' would perhaps be a more suitable title?

Edited by Tintin
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Posted (edited)

You might find the answer in Aswath Damodaran's Investment Valuation. I have some notes about the reinvestment rate, so at the very least Damodaran does tackle the concept in that book.

Edited by elliott
replace issue with concept
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On 5/5/2022 at 11:43 AM, Tintin said:

A lot of corporate finance tells us that looking at historic reinvestment rate * ROIC gives us a good indication of how much a company's earnings can grow by.

 

In this context, I'm trying to look at different approaches to calculating a company's historic rate of reinvesting capital as a percentage of earnings.  One of the formulas I've come across is;

 

Net CapEx + Change in working capital / NOPAT.

 

I am struggling to conceptualize why we need to add back depreciation in the above formula.  To me, gross CapEx alone plus change in WC seems to be the most appropriate approach since it reflects the actual amount of cash investment that a firm has had to reinvest.

 

In a simple example....

 

NOPAT - $100m

 

Depreciation - $20m

 

CapEx - $20m

 

assume no change in WC

 

According to the conventional formula, the company has not reinvested anything, which is clearly not the case.  If it's reinvested the same amount of CapEx to cover its depreciating assets then while the company won't necessarily grow, that $20m CapEx is still a reinvestment required to sustain the existing level of business operations.  To me, the reinvestment rate is 20%.

 

The only way that I can see this formula working is that the reinvestment rate is implicitly defined solely as any capital that's reinvested into the business over and above the level of reinvestment required simply to maintain the existing business.  But I haven't found any explicit definition to say that's the case, which is a bit confusing.  By 'reinvestment rate' does this actually mean reinvestment 'over and above' investment in existing assets?  In which case 'growth reinvestment rate' would perhaps be a more suitable title?

 

If I understand the question, I believe it's to make the numerator and denominator apples-to-apples.  Typically, NOPAT includes depreciation.  So a capital expenditure expense (albeit, a backward-looking historical one, rather than a cash one) is already embedded within NOPAT.  Since the expense is embedded in and reduces NOPAT, it's also removed from the numerator via looking at net rather than gross CapEx.

 

Put another way, "Net CapEx + change in working capital" is the amount of capital added to the business beyond the amount that NOPAT assumes (via its use of depreciation) the business consumes in steady state.      

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As KJP mentioned, it's formulaic given the denominator you are using. What if depreciation is overstated and massively reduces EBIT? Then suddenly you're left with a firm that seems to be reinvesting a large portion of its NOPAT; that's why you have to penalize both the denominator and numerator with this accounting figure. Also don't forget you're tying this formula in with ROC(via multiplication) to obtain earnings growth - ROC given it uses net fixed assets, nets out depreciation. Hence your CAPEX assuming all is capitalized as PPE, has to net out depreciation for the multiplication to be accurate. 

 

 

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