In today’s article I’m going to look at two FTSE 100 heavyweights I believe could turn out to be great value buys in 2016.

Shell must shape up

Shares in Royal Dutch Shell (LSE: RDSB) have fallen by almost 30% over the last year. The falling price of oil obviously hasn’t helped, but FTSE 100 peer BP has only lost 12% of its value over the same period.

Why has Shell done so badly?

One problem is that the market thinks Shell is paying too much for BG Group. The deal was priced at a time when Brent crude oil was trading at about $58 per barrel. Since then, Brent has fallen by nearly 40% to $35. Many big investors believe that Shell could and should negotiate a new deal with BG at a much lower price.

At the moment, Shell’s cash and stock offer is worth about 1,050p per BG share, or around £36bn. BG shares have actually risen by 13% since the offer was made in April 2015, despite the falling price of oil.

In contrast, shares in BG peer Tullow Oil have fallen by 48% over the same period. I imagine that BG stock would also have slumped without the Shell offer. It’s easy to see why the City believes a better deal is possible.

Still a buy?

Despite this concern, I’m still attracted to Shell. The stock currently trades 10% below its book value and on a forecast P/E of 12. Given that Shell’s earnings are at multi-year lows, a P/E of 12 doesn’t seem overly expensive to me.

When the price of oil does start to recover, Shell’s aggressive cost-cutting should mean that profit and free cash flow improve sharply. This should support future dividend payments.

In the meantime, chief executive Ben van Beurden has promised to maintain a payout of at least $1.88 per share until the end of 2016. That gives Shell a prospective yield of 8.3%.

I believe the biggest risk to shareholders is that Shell’s management will focus too much on growth and not enough on shareholder returns. For now however, I’m happy to take this risk.

Aviva’s on its way

Aviva (LSE: AV) is also out of favour with the City, despite making steady progress with its turnaround plan.

During the first nine months of last year, Aviva reported a 13% rise in the value of its new life insurance business, excluding its acquisition of Friends Life. The firm’s investment division also saw strong inflows.

Aviva now trades on a 2015 forecast P/E of 10.7, falling to 9.7 for 2016. The total dividend for 2015 is expected to rise by 15% to 20.9p, giving a potential yield of 4.2%.

In my view, Aviva could be a good income buy at current prices. The dividend payout is expected to rise by another 15% in 2016, giving a forecast yield of 4.8%. Although this rate of growth is unlikely to be maintained, it does put the firm’s dividend yield firmly into income territory.

There are also signs that the City might be gaining confidence in Aviva’s performance. Analysts’ forecasts for the firm’s 2015 and 2016 profits have edged higher over the last month.

If this trend continues, the shares could deliver steady gains as we head into 2016.

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Roland Head owns shares in Royal Dutch Shell and Aviva. The Motley Fool UK has recommended Royal Dutch Shell B. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.