A week today is likely to be a testing time for Royal Bank of Scotland chief executive Sir Fred Goodwin as he learns whether shareholders have backed his £12 billion rights issue in sufficient numbers. Because the new share issue has been fully underwritten, Goodwin knows that he will get all the money he needs to prop up his balance sheet and pay for the expensive takeover of Dutch bank ABN Amro last year.

But it's not so much the cash as Goodwin's credibility that is on the line. He took a battering when the issue was announced on 22 April, and faced criticism from shareholders at the following day's annual meeting in Edinburgh. The shares have effectively fallen 25% since then.

But if investors shun the issue - and anything less than an 80% take-up would be seen as a failure - Goodwin will be back in the line of fire, and the shells pounding the giant RBS headquarters will be even more explosive.

Private shareholders - and RBS has at least 175,000 of them - will have to make up their minds this weekend whether to part with their hard-earned cash by buying more shares. Many of them will also face similar decisions in the next month over HBOS's £4 billion rights issue and Bradford & Bingley's £300 million share offer.

The sums are fairly straightforward. RBS is offering shareholders the right to buy 11 new shares at 200p each for every 18 shares they already own. In other words, someone with 180 shares is being asked to stump up another £220 to lift their shareholding to 290 shares. With the existing shares trading at 231¾p at last night's close, that looks like something of a bargain.

However, RBS has already warned that it will only pay this year's first-half dividend in shares, not cash, and will cut future cash dividends from last year's levels. So if punters don't take up their rights, they will certainly see their income go down.

Today is pretty much the last chance for private investors to sell what are called their nil-paid rights. That is their right to subscribe to the new shares. These have a value to other investors who want to buy more than their allocation of the new shares. But last night they were changing hands at just 29¾p a share.

Veteran fund manager Anthony Bolton, formerly the pin-up of private investors at Fidelity, declared last week that he would switch out of commodities and take up the banks' rights issues in the hopes of a recovery in the financial sector.

But what should private punters do?

Nick Raynor of The Share Centre has been advising his clients to tail-swallow - that is to sell enough of the nil-paid rights to fund the take-up of the rest of their allocation. He said: "People could spend last week's RBS dividend cheque and what they need from the nil-paids to take up as much of the rights as they can afford.

"But quite frankly, if you haven't done that by now, don't worry. We still don't really know where the bottom of the bank-share market is. Lots of our clients have been buying bank shares steadily for the last six months but they've carried on getting cheaper."

He added, somewhat worryingly: "If RBS doesn't manage to sell its insurance arm because nobody offers the £7 billion or so it is looking for, it could well have to come back for a second rights issue."

Analyst Nic Clarke at Charles Stanley reckoned the shares look cheap but the outlook for RBS's earnings is deteriorating. He said: "With the credit crunch still ongoing and the outlook for retail, corporate and wholesale earnings depressed, we do not believe it is the right time to put in fresh funds, and therefore we recommend that shareholders sell sufficient nil-paid rights in order to take up the balance of their entitlements."

Individual investors will have to decide on their own personal circumstances, advised Keith Bowman of stockbroker Hargreaves Lansdown. He pointed out that most private investors tend to be overweight in banks anyway.

"Our overall view of the shares is pretty much neutral. That is to say they are certainly not a raging buy," Bowman added. "And the fact that at least two bidders have pulled out of the insurance auction just adds to the short-term nervousness."

Justin Urquhart Stewart of Seven Investment Management is telling his clients to pass on the rights issue. He said: " Short-term, I wouldn't touch it because it's quite likely the shares will get even cheaper. But if you're taking a longer, say five-year, view it would be OK to go for them."

David Buik of BGC Partners has little doubt the issue will get away. He said: "The roadshows surrounding the rights issue have been pretty aggressive by all accounts. The underwriters Goldman Sachs, Merrill Lynch and UBS are solidly behind it, and I expect most of the major institutions to take up their rights.

"Provided that ABN Amro is now the last acquisition RBS makes at those sorts of levels, it makes no sense for the institutions to shun the issue. Certainly if the underwriters were left with more than 15% of the issue, that would be very bad news for Sir Fred and the bank. But in the end the Scottish mafia will make this one gets away."