Convertible bond. Face of 500. If the underlying equity doubles in 5 years, you get 1,000 (cash or equity). So it's up 100pct. If not, you just get your 500 principal.
I'm thinking this is a bond with a binary option? But not sure.
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how i see it:
the conversion seems useless if its 100 cash or equity. convertibles only add value b/c equity from conversion can be worth more than the bond's face.
you just need probability of the equity doubling. Value = P(Double)1000 + P(1-Double)500
Converts don't look like that. You're saying you get 100% of the upside of the stock if it's up, and you get face value if it's down? You can't have both.
This is obviously not an exchange-traded instrument; this is something I'm thinking about putting into a deal structure to lower our cost base. The point is that instead of giving $1,000 of equity, we're guaranteeing $500 and the possibility of $1,000 if the equity doubles.
The tricky part is what vol do you use? Most likely there are no comparable listed options.
You need a strike on the Convertible, as the question is phrased you're saying that the conversion price is 0, if this is the question, the value of the covertible is 500 today, don't wait for next year. If the strike is 500, re the conversion is at the money on Day 1, then the upside is actually 500.
Regardless of what the actual numbers in the question should be, I'd approach as a binary tree with five stages and Std. Dev equal to 14.8%, enough that in the positive of each stage gets you to 1000, all discounted back to today.
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