## Case Study-AW132 Online Services

**Question 1**

In the second quarter of 2013, Tesla Motors, Inc. (symbol: TSLA) raised $1 billion in funds by issuing common stock (about 3.4 million shares) and senior convertible bonds. Of this $1 billion, $600M came from the convertible bond issuance. The prospectus supplement that contains details about the convertible bond issuance can be found using the following link from the SEC website (focus on the section below the red-texted Tesla logo and above the table of contents)

http://1.usa.gov/11DpDL0

a) Explain the primary reason why Tesla raised this cash.

b) The prospectus supplement states that conversion is only allowed under certain circumstances. Explain these circumstances and why you think these rules are in place.

c) Explain why a company like Tesla would be interested in issuing convertible bonds as opposed to straight bonds.

d) Each convertible note is priced at $1,000, has a face value of $1,000 and a 5-year maturity, and pays a coupon of 0.75 percent every half-year. Assume that if Tesla were to issue straight debt, it would have an expected return of 5 percent per year (2.5 percent per half-year). What is the value of the option to convert for each convertible bond?

e) Suppose that it is December 1, 2015 and you own one Tesla convertible bond. You are considering two choices: convert the bond now or never convert the bond and receive the interest and principal payments until maturity. Assume that there are no rules in place that prevent you from converting the bond and that the current stock price of Tesla (which can be found online) equals the price on December 1, 2015. Explain why you would or would not convert the bond.

**Question 2 **

In class, we typically infer the value of the conversion option on a convertible bond by subtracting the value of the straight bond component of the convertible bond from the price of the convertible bond itself. In this question, assume you are a CFO that is considering the issuance of a convertible bond and wants to determine the fair price at which this bond should sell.

Specifically, you are considering the issuance of a convertible bond with a face value of $100M, a maturity of 10 years, and an annual coupon rate of 6 percent. The conversion option is European and can only be exercised on the day before maturity. The conversion ratio is 2M shares. Based on your firmβs credit rating and regular bonds that have been issued by your firm in the past, you determine the expected return on straight debt to be 5 percent.

Given that the convertible bond is issued, assume that the stock price can take on only one of three values on the day before maturity: $30 (State B), $60 (State M), or $90 (State G). The respective risk-neutral probabilities are 40 percent, 40 percent, and 20 percent. Because we are given risk-neutral probabilities, the proper discount rate for the expected payoff from the conversion option is the risk-free rate, which we will assume is 4 percent.

a) What is the value of the straight bond component of the convertible bond?

b) What is the payoff of the conversion option in each of the three states of the world on the day before maturity? The option payoff is given by maxβ‘{ππ Γ 2π β πππππβ‘ππππβ‘πππ¦ππππ‘, 0}.

c) What is the value of the conversion option today? This is calculated as the present value of the expected payoff from the conversion option.

d) Based on your numbers in (a) and (c), what is the value of the convertible bond?

**Question 3 **

Your firm wants to issue more equity but finds it costly to do so because of investment banking fees and the adverse selection problem associated with equity issuances. Given this, you decide to issue convertible bonds because you believe that the stock price will significantly appreciate in the future, implying a high likelihood of conversion. That is, you plan to issue equity indirectly by raising money via the convertible bond market.

Specifically, you raise $10M by selling convertible bonds at $1,250 per bond. Each bond has a face value of $1,000, a coupon rate of 4 percent, and a 5 year maturity. The bonds can be exchanged at any time for 50 shares. The expected return on straight debt issued in the past by your firm is 5 percent. Your firm currently has 1.2M shares outstanding priced at $25 per share. There is currently no other debt outstanding.

a) What is the value of each bondβs conversion option? (Hint: first find the value of the straight bond component of the convertible bond.)

b) What is the minimum value of the firm that will induce the bondholders to convert the bonds into stock on the day before maturity?

c) Draw the payoff diagram for the convertible bondholders as a function of the firm value. Specify the slopes of the lines that you draw.

d) Draw the payoff diagram for the current shareholders as a function of firm value. Specify the slopes of the lines that you draw.

**Product code: Case Study-AW132**

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