The question about preferred stock in the example on what to recommend to an investor for convertible preferred stock being called, sold at market, held through maturity, or converted to common, makes no sense.
The market price of $103 shouldn’t even be an option, because the prefered stock is callable at 102. Why would it ever trade at a price higher than this?
You are right that, in efficient markets, a callable preferred stock would not typically trade meaningfully above its call price for long. However, it can trade slightly above the call price before the actual call date for a couple of reasons:
The call has not yet been exercised; it has only been announced
There are still dividends payable before the call date
Market forces and short-term supply and demand can temporarily push the price above the call price
In this question, the key is that the call has been announced and will occur in 60 days. Once the call is announced, the upside from holding the preferred is effectively capped at the call price of 102, regardless of the current market price of 103.
Now compare that to the conversion value:
Convertible at 25 means each preferred share converts into 4 shares of common, 100 divided by 25
The common is trading at 26
Conversion value is 4 x 26, or 104
Since 104 is higher than both the call price of 102 and the current preferred market price of 103, the investor should convert to common stock.
So the presence of the 103 market price is intentional. It tests whether the learner understands that once a call is announced, the call price becomes the effective ceiling, and the decision should be based on conversion value versus call value, not just the current trading price.
The pricing may feel slightly unrealistic in a perfectly efficient market, but it is there to force the comparison and reinforce the concept.