Accounting For Value – 3

In the first post we learnt about the pitfalls of P/E ratios and the limitations of using discounted cash flows. Buffett owners earnings fixed most of the shortcomings. In the second post we learnt about valuing a company using residual earnings method. But residual earnings has few limitations. One of them is that return on equity (ROE) can be increased by leverage and this in turn increases residual earnings. In this post we will address this limitation.

1. Leverage increases residual earnings

Given below is the balance sheet and income statement of Company A which I made up. The company does not have any long term debt and it has a positive and constant residual earnings. Also let us assume that A has only one share outstanding. What is the intrinsic value of A?

Book value of A        = $1500
Residual earnings of A = $150
Cost of capital of A   = 10%

Intrinsic value of A = Book value + (Residual earnings / Cost of capital)
Intrinsic value of A = $1500 + ($150 / 0.1)
Intrinsic value of A = $1500 + $1500
Intrinsic value of A = $3000

Now take a look at the balance sheet and income statement of Company B. You can clearly see that A and B have the same net operating assets, sales, and operating margins. The only difference is that B has a long term debt of $750 at 5% interest. Also let us assume that B has only one share outstanding. What is the intrinsic value of B?

Book value of B        = $750
Residual earnings of B = $187.50 (To keep the math simple I ignored 2016 residual earnings)
Cost of capital of B   = 10%

Intrinsic value of B  = Book value + (Residual earnings / Cost of capital)
Intrinsic value of B  = $750 + ($187.50 / 0.1)
Intrinsic value of B  = $750 + $1875
Intrinsic value of B  = $2625

The residual earnings of B is $187.50 which is higher than A’s residual earnings of $150. Is this not weird? How on earth can debt free A have lower residual earnings compared to B with debt? Take a look at 2015 ROE for A and B. You will notice that ROE of A is 20% and B is 35%. ROE is an input for calculating residual earnings. Hence a high ROE for B resulted in high residual earnings. Why is ROE of B higher than A? It’s because of leverage. In the book Accounting for Value Stephen Penman writes

Leverage increases return on equity, earnings per share, earnings growth, and indeed residual earnings, but it is very doubtful that it adds value: Beware of earnings created by leverage. Borrowing does not add value. In the example, this principle simply says that, if the firm borrows at a fair market value and repurchases stock at fair market value, it cannot add value to its stock price. Financing transactions at fair market prices are zero-net-present-value transactions; a firm adds value in its business from trading with customers, not from buying and selling bonds and shares at fair market value.

2. Reformulating the balance sheet

Every company is involved in operating and financing activities. Operating activities involves dealing with customers and suppliers. Financing activities involves trading in the capital markets. The picture given below clearly shows the difference between these two activities. A firm adds value only from trading with customers and suppliers and not by trading in the capital markets at fair market prices. Hence as an investor we should value the operating activities of the firm separately and exclude the effects of financing activities. In order to do this we need to reformulate the balance sheet and income statement by dividing the firms operating and financing activities.

Take a look at B’s reformulated balance sheet. You will notice that I have grouped its operating activities on one side and financing activities on the other side. Also I have assumed that $100 in cash is used in operating activities. From this I have come up with three key formulas. Make sure understand them deeply instead of blindly memorizing them.

1. Net Operating Assets      = Operating Assets – Operating Liabilities
2. Net Financial Obligations = Finance Liabilities – Finance Assets
3. Net Operating Assets      = Shareholders Equity + Net Financial Obligations

To calculate the intrinsic value of B we need to value only its net operating assets. In order to do that we need to reformulate its income statement by removing the effects of interest. To keep the calculation simple I have assumed that B does not owe any taxes.

Net operating assets of B                           = $1500
Residual earnings of B's net operating assets (NOA) = $150.00
Cost of capital of B                                = 10%

Intrinsic value of B's NOA  = NOA of B + (Residual earnings of B's NOA / Cost of capital)
Intrinsic value of B's NOA  = $1500 + ($150.00 / 0.1)
Intrinsic value of B's NOA  = $1500 + $1500
Intrinsic value of B's NOA  = $3000

Value of B’s net operating assets comes to $3000 and it is same as the intrinsic value of A. This should not surprise you as the net operating assets, sales, and operating margins of A and B are the same. Now the final step is to remove the effects of debt to arrive at the intrinsic value of B.

Intrinsic value of B = Intrinsic value of B's NOA - Net financial obligations
Intrinsic value of B = $3000 - $750
Intrinsic value of B = $2250

The intrinsic value of B is $2250. This valuation is 16% lesser than our initial valuation of $2625. By valuing the net operating assets of B separately we have fixed the effects of leverage. Also I did not reformulate the balance sheet and income statement of A. Why is that? A’s net operating assets is fully funded by its equity and its net financial assets is zero. Hence its ROE and RNOA will be the same resulting in the same intrinsic value.

3. Is there a relationship between RNOA and ROE?

There is a deep relationship between RNOA and ROE. Its very important to understand as this shows the key drivers of profitability in the business. Company B’s ROE comes to 35% and I am going to prove that ROE contains RNOA of 20% and the remaining 15% comes from the financial leverage.

ROE = Return on equity
NOA = Net operating assets
NFO = Net financial obligations
CSE = Common shareholders equity
NFE = Net financial expense
NBC = Net borrowing cost
NI  = Net income
OI  = Operating income

ROE = RNOA + (NFO / CSE) * [RNOA - NBC] -- Click on the image given below for the proof.
ROE = 20% + ($750 / $750) * [20% - 5%]
ROE = 20% + 15%
ROE = 35%

Company A’s ROE and RNOA comes to 20% and the formula clearly shows how.

ROE = RNOA + (NFO / CSE) * [RNOA - NBC] -- Click on the image given above for the proof.
ROE = 20% + ($0 / $1500) * [20% - 0%]
ROE = 20% + 0%
ROE = 20%

We have come to the end of this post. But we are not done yet. There are couple of items that I still need to cover (1) Accrual earnings can be fudged (2) Expenses like Advertising and R & D can create durable competitive advantage and they should not be expensed fully but instead kept it in the balance sheet and amortized over time. I do not have enough knowledge on these items and hence I am not qualified to write about them. I am planning to read the following books to improve my knowledge. Maybe sometime in future I will write about them.