A five-year convertible with Rs 1,000 face converts into 8 shares. The stock is Rs 110, the straight bond is worth Rs 880 and a five-year call struck at Rs 125 is worth Rs 25. Value the convertible and its conversion premium.

The convertible is worth about Rs 1,080, a conversion premium of 22.7%. Each bond converts into 8 shares, so the conversion price is Rs 125 and the conversion right is 8 five-year calls struck there, worth Rs 200. Add the Rs 880 straight bond: Rs 1,080. Converting today would give 8 shares worth Rs 880, so the holder pays Rs 200 over conversion value, and that premium buys the bond floor if the stock falls.

Think of a flat bought with a clause that lets you swap it for a plot of land at a fixed ratio any time in five years. You own the flat whatever happens, and you own the right to switch if land gets dearer. A convertible is the same: a straight bond the holder keeps, plus the right to exchange it for a fixed number of shares. The conversion ratio is 8, so the share price at which switching breaks even is Rs 1,000 divided by 8, Rs 125. The right to swap a Rs 1,000 claim for 8 shares is economically 8 call options struck at Rs 125, and the question hands you their price: Rs 25 each.

Conversion value is what the bond turns into if exchanged today: 8 shares at Rs 110, Rs 880. The convertible trades Rs 200 above that, a conversion premium of 22.7%, and the premium is the price of not having to convert. If Kalsubai's shares fall to Rs 60, the 8 shares are worth Rs 480 but the holder still owns a bond that pays Rs 1,000 at maturity, worth Rs 880 today if the credit holds. The premium is the gap between owning shares and owning a floor under them, which is exactly what 8 calls plus a bond provide and 8 shares alone do not.

Two coincidences in this question are worth naming so they do not confuse you. The bond floor and the conversion value are both Rs 880, so the premium over the bond and the premium over conversion are both 22.7%; in general they differ. And the conversion price of Rs 125 is 13.6% above the Rs 110 share price, which is the premium an issuer quotes at launch. The 22.7% market premium and the 13.6% issue premium are different numbers answering different questions, and interviewers like candidates who keep them apart.

The decomposition treats the option and the bond as independent, and they are not. If the company's credit weakens, the bond floor drops, and usually the share price falls with it, so the call loses value too; the floor is softest exactly when it is needed. The call price of Rs 25 was given to you, but a real desk would mark it with the stock's volatility and the dilution from the new shares. Issuers often keep a right to redeem early, which caps the option. Say it plainly: the sum of the parts is the right first answer and the wrong last one, because the parts move together through the credit.