There are still plenty of cheap shares on the FTSE 100 despite the recent rally, and I’m buying as many as I can afford.

I like going bargain hunting for cut-price UK stocks. This way, I avoid the risk of paying for frothy, overpriced shares. Typically, I’ll get a higher yield too.

It’s not a guaranteed winning strategy though. Cheap shares are often cheap for a reason. Turning around a struggling company takes time. Value investors like me need bags of patience.

FTSE 100 bargains

Lately, I’ve been busy loading up my self-invested personal pension (SIPP). Now I’m turning my attention to this year’s Stocks and Shares ISA.

Looking at the FTSE 100 today, one stock leaps out at me. Oil and gas giant BP (LSE: BP) trades at just 6.6 times earnings. That’s well below the 15 times normally seen as fair value. The share price has been falling in recent weeks, a period when Brent crude dipped below $80 a barrel. Over 12 months, the BP share price is down marginally, falling 0.25%.

I think this is a buying opportunity but there’s one underlying risk. The world is supposed to be weaning itself off fossil fuels. BP is building its renewables capacity, but not half as fast as campaigners would like. It knows the carbon transition will be costly and risky.

Last week, the International Energy Agency predicted that oil demand will peak by 2029, leading to a major supply glut. If correct, that would be a blow for big oil. It would be good for the planet but I’m not totally convinced it will happen. The world seems to be using more energy than ever, and needs every source it can get including fossils. Oil will be with us for a long time yet. So will BP, in my view.

Top value stocks 

Like many commodity stocks, the BP share price can be cyclical. That’s why I’d rather buy when the oil price is down and the stock is out of favour, as appears to be the case today. The dividend outlook is positive with a forecast yield of 5.23% in 2024 and 5.56% in 2025. The board has been generous with the share buybacks too.

BT isn’t the only cheap blue-chip offering a mighty yield today. China-focused bank HSBC Holdings trades at just seven times earnings and yields 6.91%. Tobacco maker Imperial Brands Group trades at 7.5 times earnings and yields 7.1%. Mining giant Rio Tinto trades at 9.1 times earnings and yields 6.57%. I could go on.

Let’s say I scraped together every spare penny and was able to invest my full £20,000 ISA allowance, not this year but in future years as well.

The long-term average total return on the FTSE 100 is 6.9%. It’s not guaranteed, but if I matched that, it would take me 21 years to make a million. I’d have £1,029,374.

If my hand-picked portfolio of cheap shares outperformed the index and grew at 9% a year, I’d get there in just over 18 years. No time to lose then.