# Practical Financial Management 6th Edition (Textbook) Valuation – convertible bond You purchased one of AAA Corp.’s 9%, 15-year convertible bonds at its \$1,000 par value a year ago when the...

Practical Financial Management 6th Edition (Textbook)

Valuation – convertible bond

You purchased one of AAA Corp.’s 9%, 15-year convertible bonds at its \$1,000 par value a year ago when the company’s common stock was selling for \$25. Similar bonds without a conversion feature returned 10% at the time. The bond is convertible into stock at a price of \$35. The stock is now selling for \$40.

Assume no dividends.
a) You exercise the conversion feature today and immediately sold the stock you received. Calculate the total return on your investment.

b) What would your return have been if you had invested \$1,000 in AAA’s stock instead of the bond?

Expert Answers
mathsworkmusic | Certified Educator

If the AAA Corp's (15-year convertible) bonds were \$1,000 one year ago, and the stock was selling for \$25 at that time, then one of those bonds was equivalent to S(0) units of stock, where

S(0) = 1000/25 = 40

So if you as an investor bought one of those bonds a year ago it was, at that time, equivalent to 40 units of stock at the going market price.

a) If an investor opted to buy a bond for £1,000 rather than stock a year ago at the going price of \$25 per unit, a year on they are offered the opportunity to convert their (appreciated) bond back into stock at a guaranteed price of \$35 (an assured value, stated a year ago before market dynamics were known). The appreciation rate on the bond is 9% (assumed per annum, ie per year), so the monetary value of the bond a year on is

B = 1000 x (1 + 9/100) = 1000 x 1.09 = \$1,090

If the conversion feature allows the investor to buy stock at \$35 per unit with their appreciated bond, then the amount of stock S(1) they convert the bond to a year on from buying the bond is given by

S(1) = B/35 = 1090/35 = 31.14286 units of stock  (assuming fractional units can exist)

If the investor immediately sells this stock on at the current market price (assuming fractional units can be sold) of \$40 per unit, the capital C(1) they will make is given by

C(1) = B/35 x 40 = 31.14286 x 40 = 1245.714

So the capital made is \$1,245.71. Given that the initial investment was \$1,000 this implies a return over the elapsed year of

C(1) - 1000 = \$245.71

b) As stated above, if the investor had initially invested in stock rather than a convertible bond they would have been able to purchase S(0) = 40 units of stock. At the current market price (a year on from the investment), this stock is worth a capital amount of

C(0) = S(0) x 40 = 40 x 40 = \$1,600

This implies a return over the elapsed year of

C(0) - 1000 = \$600

This is 2.44 times the return made by investors who bought the convertible bond rather than buying stock outright.

With the benefit hindsight of the appreciation in value per unit of the stock from \$25 to \$40 over the elapsed year (a massive appreciation rate of 60%), buying stock was a better option than buying a convertible bond. However, not knowing what the market will be like a year on, that is a risk for the investor to take. The return of \$245.71 on the convertible bond is contrastingly guaranteed (excepting the company going bankrupt and not fulfilling the promise - which is why the government backs the bonds of major banks, to avoid potential chaos in the economic climate).

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