Question

A(n) 99​% convertible bond carries a par value of​ $1,000 and a conversion ratio of 21. Assume that an investor has​ $5,000 to invest and that the convertible sells at a price of ​$1,000 ​(which includes a 26​% conversion​ premium). How much total income​ (coupon plus capital​ gains) will this investment offer​ if, over the course of the next 12​ months, the price of the stock moves to ​$87.58 per share and the convertible trades at a price that includes a conversion premium of 11%? What is the holding period return on this​ investment? Finally, given the information in the​ problem, determine what the underlying common stock is currently selling for.

Answer 1

The coupon rate is wrongly given at 99. It should be 9.9%. I have solved question by taking 9.9% as the coupon rate.

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Part 1)

The value of total income is arrived as below:

Conversion Value = Price of Stock After 1 Year*Conversion Ratio = 87.58*21 = $1,839.18

Price of Convertible (Within One Year) = Conversion Value + 11%*Conversion Value = 1,839.18 + 11%*1,839.18 = $2,041.4898

Interest Income from Bonds = Number of Bonds*Face Value*Coupon Rate = 5,000/1,000*1,000*9.9% = $495

Now, we can calculate the value of capital gains and total income as below:

Capital Gains = (Price of Convertible - 1,000)*Number of Bonds = (2,041.4898 - 1,000)*5,000/1,000 = $5,207.449 or $5,207.45

Total Income = Capital Gains + Interest Income from Bonds = 5,207.45 + 495 = $5,702.45

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Part 2)

The holding period return on the investment is arrived as follows:

Holding Period Return = Total Income/Value of Investment*100 = 5,702.45/5,000*100 = 114.05%

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Part 3)

The price of underlying common stock is determined as below:

Price of Underlying Common Stock = Conversion Value of Security/Conversion Ratio

Here, Conversion Value of Security = 1,000/(1+26%) = 793.6508 and Conversion Ratio = 21

Substituting these values in the above formula, we get,

Price of Underlying Common Stock = 793.6508/21 = $37.79