Convertible perpetuity valuation valuation, different, following

Siddimaula

How would one value the following security:
1. it is a convertible perpetuity
2. the issuer has (at any time) the option to withhold the payment of interest
3. the issuer and the holder have at any time the option to convert the security into common stock.
All I know is that one need to value three different securities: a perpetuity, a call and a put, but given the indefinite time frame and the issuer option to withhold interest payments I have no idea how to proceed further. Why?For one thing the BS formula tells me that both put and call with extreme time to maturity (I put in 5000 years) have a 0 value when risk free rate is 4% and dividend yield is 2%.
Any thoughs?