Estimating Earnings from Receivables, Asset Turnover, Debt, and ROE

Summary

The document outlines a backward calculation for estimating a company’s earnings from a limited set of financial ratios and working-capital data. Starting with average accounts receivable and the time needed to collect payment, it estimates annual sales using receivables turnover implied by days outstanding. It then uses the sales-to-assets relationship to infer assets. The stated debt-to-equity ratio is used to relate assets to equity, after which return on equity converts estimated equity into earnings.

The response supplies the relationships and calculation sequence rather than a final numeric estimate, presenting the prompt as a homework-style exercise. The method depends on interpreting the receivable balance and collection period as representative of the year and on using the stated ratios consistently. It uses a 365-day year and assumes the provided asset productivity, debt-to-equity ratio, and ROE are suitable for the estimate. It does not address seasonality, changes in ratios during the year, taxes, or whether average rather than ending balances should be used throughout.

Key ideas

• Days outstanding and average accounts receivable can be used to estimate annual credit sales.
• Sales per unit of assets can convert estimated sales into an implied asset base.
• A debt-to-equity ratio relates assets and equity, subject to the stated balance-sheet definitions.
• Applying return on equity to estimated equity yields the earnings estimate.
• The result relies on representative balances and ratios and omits possible within-year changes.

Tags

# Estimated Earnings from D/E Ratio, Accounts Receivable, and ROE


# Estimated Earnings from D/E Ratio, Accounts Receivable, and ROE












DW Industries has a D/E ratio of 0.5 and an ROE of 0.1. For every dollar it has in its assets, DW produces \$0.2 in sales. In 2019, DW made all of its sales on credit with an average of \$2 million in Accounts Receivables. It took DW 30 days to collect the cash on purchases the clients made. What is your best estimate of the DW's 2020 Earnings ?

## Answer by D Stanley (score 1)

https://quant.stackexchange.com/a/69831

Working backwards from the Days Outstanding (I'll leave the numbers out so as to not give away the complete answer since this seems like a homework problem):

If it took 30 days on average to collect receivables, and their average A/R balance was $AR$, then their sales $S$ were $S = AR * (365/30)$.

Now to get to assets, since they have \$0.2 in sales for every \$1 in Assets, their assets would be $A = S/0.2$.

Since equity is Assets minus debt,

$$ \begin{align} D/E &= \frac{(E-A)}{E} \\ &= 1 - \frac{A}{E}\\ \implies \frac{A}{E} &= (1 - D/E)\\ \implies E &= \frac{A}{(1-D/E)}\\ \end{align} $$

So if their D/E ratio is 0.5, then $E=A/(1-0.5) = A/0.5 = 2*A$

If their ROE is 10% (0.1), then their earnings would be $0.1 * E$.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.