What is the true value of the convertible security?

Question 4 [25 marks]
Techpikker AG is a manufacturer of high-tech toothpicks, located in Wuppertal, Germany.
Suppose that investors are unsure about the future prospects of Techpikker. They believe that
the firm may have good prospects, in which case the value of the firm (debt and equity)
would be given by: €(220 + X) billion. Alternatively, the firm’s future could be not so good,
in which case the firm value would be €40 billion (less than 220+X). Investors do not know
the value of X, but they believe that the CEO does. Everyone knows that the probability of
the two outcomes (good prospects and bad prospects, respectively) is 50%.
You may assume that everyone is risk neutral, and that interest rates are zero (everyone’s
discount rate is zero). State any additional assumptions, if you believe you need to make any.
a. The firm has senior debt outstanding with face value of €30 billion. Given this
information, what is the value of the firm for outside investors? What is the market
value of equity and the market value of debt? Do the value of equity and debt depend
on X? How? [5 marks]
Now, suppose that X can only take on two values: X = 30 or X = -30 (both in € billion). Keep
in mind that only the manager knows the true value of X.
b. The market believes that each of the scenarios of X = 30 or X = -30 occurs with equal
probability. Given this belief, what is the market value of the senior debt? What is the
value of equity? Given that there are 1 billion shares outstanding, what is the price per
share? [5 marks]
c. The CEO of Techpikker is thinking about issuing convertible debt. Suggest a possible
reason that Techpikker AG favors issuing convertible debt rather than making an
equity issuance. [3 marks]
d. If the CEO of Techpikker decides to issue convertible bonds, convertible into own
(Techpikker) shares, with a face value of €19 billion, what share of the company’s
equity needs to be promised to investors, in case of conversion, to raise the €19
billion? If each warrant that is contained in each convertible bond specifies that the
convertible bondholder obtains one new share upon exercise, how many warrants
have to be issued to raise €19 billion? [7 marks]
e. Suppose the manager knows that X = 30; what is the true value of the convertible
debt? Alternatively, suppose instead the manager knows X = -30; in that scenario,
what is the true value of the convertible security? [5 marks]

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