I’m a firm believer in the thought that if you take care of the dividends, the share prices will take care of themselves. And today, there are so many strong dividends to be had it’s hard to choose. Here are two big yields that deserve some consideration.

Building cash

The EU referendum result hit the UK’s housebuilding and construction sector pretty hard, irrationally so in my opinion, and one result of the subsequently depressed share prices is a nice hike in dividend yields.

Galliford Try (LSE: GFRD) looks, on the face of it, to be offering an irresistible dividend now. The shares slumped in the days following the Brexit vote, and though they’ve recovered a good bit of the loss, they’re still down 11% at 1,175p. That’s boosted the prospective dividend yield to 6.8%, based on this year’s forecasts, rising as high as 8.6% for 2017.

The first question is whether there will be sufficient cash to cover the payments, and the answer appears to be yes. The City’s analysts are expecting earnings per share to rise by 11% this year and a further 17% next, and that would provide dividend cover of 1.6 times and 1.5 times for the two years respectively.

That seems ample to me, for a company with low net debt (down to £2m at 30 June, from £17m a year previously) and expecting to report “record full-year results” this year, according to July’s trading update.

Analysts’ forecasts for the firm have remained steady, with the tiniest of cuts in earnings forecasts since the referendum — and they’ve actually lifted their consensus for the 2017 dividend. I reckon this is one of the best times to buy Galliford Try that we’ve seen for a while.

Profit from payments

Shares in PayPoint (LSE: PAY) hit a bit of a slump after peaking in March 2014. But since a low in March this year we’ve seen a 45% rise to 1,046p, as the firm has sold off its mobile and online payments business to concentrate on its retail network.

Paypoint looks set to continue its impressive earnings growth of the past five years, with forecasts suggesting EPS rises of 8% and 6% this year and next, putting the shares on P/E multiples of around 16. An interim update in July told us that net revenue (excluding the online business) had risen by 8% to £29m in the first quarter of the year, so those forecasts are looking good.

A strong balance sheet with net cash of £74m on the books at 30 June lends support to the company’s predicted dividend yields of 5.8% and 6% for the next two years. And that’s despite this year’s share price gains — had you bought at the bottom, you’d have tied in effective yields of 8.4% and 8.7%!

Paypoint’s dividend cover isn’t so high, at a little under 1.1 times, but it’s the kind of highly cash-generative business that doesn’t really need much in the way of cover — and May’s full-year results reiterated PayPoint’s intention to “continue with a progressive dividend policy.” We might possibly see future dividend rises pegged back a little to maintain cover, but in the medium term, with that balance sheet awash with cash, the payments look safe to me.

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Alan Oscroft has no position in any shares mentioned. The Motley Fool UK owns shares of PayPoint. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.