LONDON -- Before I decide whether to buy a company's shares, I always like to look at its return on equity.

This key ratio helps me to understand how successful a company is at generating profits using shareholders' funds, and often has a strong correlation with dividend payments and share price growth.

FTSE 100 insurance firm Aviva (AV -1.13%) (AVVIY -1.50%) has had a tough couple of years, but I think things are now starting to turn around, as I'll explain.

Return on equity
The return a company generates on its shareholders' funds is known as return on equity, or ROE. Return on equity can be calculated by dividing a company's annual earnings by its equity (i.e., the difference between its total assets and its total liabilities) and is expressed as a percentage.

Let's take a look at Aviva's ROE from the last five years:

Aviva20082009201020112012Average
ROE 12.7% 10.9% 14.8% 12% 10.3% 12.1%

Aviva's return on equity has dropped steadily over the last three years, but I think this year may see an improvement as the company's turnaround plan starts to work.

Aviva's first-quarter interim management statement was encouraging, reporting an 18% rise in the value of new business gained in the quarter, a £300 million reduction in internal debt and a 10% fall in operating expenses.

Does Aviva have enough cash?
One of the reasons that Aviva's share price has been so low for the last two years is that investors thought that it lacked the financial strength to deal with the possible fallout from the eurozone crisis.

A recognised measure of an insurance company's financial strength is its Insurance Groups Directive (IGD) capital coverage ratio. This measures the amount of surplus capital held by an insurance company, in excess of its regulatory requirements.

In the table below, I've listed Aviva's IGD capital coverage ratio and its ROE, alongside those of its peers, RSA Insurance and Prudential:

CompanyIGD Capital
Coverage Ratio
5-Year Average ROE
RSA Insurance 190% 11.8%
Aviva 172% 12.1%
Prudential 250% 13.1%

Aviva's IGD coverage ratio is the weakest of the three, but the firm's new management have already managed to increase Aviva's coverage ratio from a low of 125%, at the end of 2011.

Is Aviva a buy?
Aviva's board is focusing on generating robust cash flows from fewer, more profitable businesses. The firm's financial position has already improved, and despite this year's dividend cut, Aviva shares still offer a prospective yield of 4.5%.

I rate Aviva as a buy, and plan to continue to top up my holding, while the price remains below 350 pence.

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