In recent years, economic and political uncertainty in Britain has damaged demand for FTSE 250 shares. So while it’s up in the year to date, the UK’s second-most-prestigious stock index remains jam-packed with cheap stocks.

Investors have several tools at their disposal to find bargain shares. Two commonly used metrics are the price-to-earnings (P/E) ratio and dividend yield, which can be used to assess a stock’s value relative to its growth and income prospects.

Using these indicators, I believe these two FTSE 250 shares are worth serious consideration from value investors this month.

The Renewables Infrastructure Group (TRIG)

The Renewables Infrastructure Group (LSE:TRIG) is a share I already own for my portfolio. And to be honest, it’s proved a disappointing investment for me due to the unfavourable interest rate environment.

When rates rise, earnings at property stocks like this come under pressure. Net asset values (NAVs) fall, and the cost of servicing their high debts tends to increase.

The green energy producer isn’t out of the woods yet. A sudden spike in inflation could alter the the Bank of England’s appetite to periodically cut rates going forward.

However, I still believe now could be a good time to consider buying in. I’m certainly attracted by TRIG’s cheapness relative to the value of its assets. According to Hargreaves Lansdown, the firm trades at a near-18% discount to its NAV per share.

The business also packs an 7.3% dividend yield for 2024, which is more than double the FTSE 250 average of 3.3%.

This is a share I plan to hold for the long haul. I expect earnings (and thus dividends) to rise steadily over time as demand for clean energy heats up. And TRIG’s wide European footprint and exposure to multiple types of renewable energy helps me to effectively spread risk.

Hochschild Mining

Hochschild Mining‘s (LSE:HOC) another FTSE 250 bargain worth a close look in October.

It might not offer a showstopping dividend yield like TRIG. In fact, this sits at a handy-if-unspectacular 0.9% for 2024.

But the gold and silver producer’s P/E ratio of 8.8 times marks it out as a bargain, in my book.

Hochschild shares have soared in 2024 as precious metal prices have lifted off. I don’t think it’s done yet either, given the bright outlook for these expensive commodities.

Gold and silver values should also benefit from interest rate cuts and, by extension, profits at mining companies. Rate cuts help to fuel inflationary pressures.

On top of this, fears over the US and Chinese economies, allied with intensifying conflicts in the Middle East and Eastern Europe, could also push prices higher.

As a major silver producer, Hochschild could also benefit from rising industrial demand if the global economy moves into a growth phase.

Possible production issues at its mines in The Americas are a threat that could weigh on profits. However, I still believe the potential rewards of owning Hochschild shares could outweigh the risks. And especially if the company becomes a takeover target like FTSE 250 peer Centamin.