Please provide solutions even if they require financial calculator or software.

A convertible bond issued has the following characteristics. Please calculate $(1)$ minimum value and $(2)$

market conversion premium.

Maturity $=12$ years

Coupon rate $=7\%$

Coupon payment twice a year

Conversion ratio $=45$

Par value $=$$$1000$

$,$ Market price of convertible bond $=$$$1575$

$,$ Market price of common stock $=$$$30$

Yield on a comparable straight bond $=6\%$

$(1)$ What is the minimum price of the bond? $(3$pt$)$

$(2)$ What is conversion premium per share? $(3$pt$)$

$(3)$ What is the investment return of the convertible bond when the stock price increases to $$55?(3$pt$)$

$(4)$ What is the investment return of the common stock when the stock price increases to $$55?(3$pt$)$

$(5)$ What is the investment return of the convertible bond when the stock price drops to $$10?(3$pt$)$

$(6)$ What is the investment return of the common stock when the stock price drops to $$10?(3$pt$)$