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You are an analyst at FixInc Corp. whose task is to value a convertible bond of Allana Corp. that matures in 5 years. The bond has face value of $1000, annual coupon rate of 8% and pays coupons semi-annually. Current interest rate for bonds of similar credit risk and maturity is 5% per annum. Current volatility estimate (sigma) for Allana Inc.'s stock return is 25% per annum, dividend yield is 2% per annum and current stock price is $30 per share.
1. Calculate straight bond value for the bond. Assume discrete compounding.
2. Calculate Black-Scholes value of conversion option for this bond assuming that the conversion ratio is 20 shares per 1 bond and the conversion price equals $50. Furthermore, assume that the time to maturity of this option equals bond's time to maturity and the risk free rate is 4% per annum with continuous compounding.
3. What is the total value of this convertible bond?
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