Question

ABC Corp. is considering investing in a project that offers a 20 percent chance of a $30 million payoff and an 80 percent chance of a $12 million payoff. Currently ABC Corp. has 200 shares of stock outstanding. ABC is proposing to finance this project by selling a convertible bond which entitles the bondholder to a $10 million dollar repayment if the bond is not converted. If the bond is converted the bondholder receives 800 shares of stock. The bondholder makes his/her conversion decision after observing the project’s payoff. Investors discount all cash flows at a 0% rate (i.e., there is no need for discounting).

(a) Calculate the expected payoff to equityholders if the firm invests in the project.

(b) Calculate the expected payoff to convertible bondholders if the firm invests in the project.

Answers: (a) 2.8 million, (b) $12.8 million

Just need to figure out why that is

Spartan Corp. is a private firm with no cash on hand but lots of great ideas. The firm currently has 1,000,000 shares outstanding. All of these shares are held by the firm's founders, executives, and employees. The management of Spartan Corp. believes that if they can raise $1 million in cash to fund promising projects, the firm will be worth $5 million. If they cannot raise this cash, they will sell the firm to an acquirer who is offering $3 million for the firm's assets. If Spartan raises $1 million in equity financing by selling shares to a venture capitalist, what is the lowest stock price that Spartan management would be willing to accept?

Answer:

1. The firm will sell $1 million of equity at a minimum price of $1.50. (Also just need to figure out why)

Answer 1

ABC Corp. is considering investing in a project that offers a 20 percent chance of a $30 million payoff and an 80 percent chance of a $12 million payoff. Currently ABC Corp. has 200 shares of stock outstanding.

Case 1: 20 percent chance of a $30 million payoff

If bondholders convert, the bondholder receives 800 shares of stock. So, total number of shares outstanding = 200 + 800 = 1,000

Per share value = Payoff / Number of shares outstanding = 30 x 10⁶ / 100 = $  30,000

Value to bondholders = 800 x 30,000 = $ 24 mn > $ 10 mn repayment without conversion. Hence the bond holders are better off by converting.

So value left for existing shareholders = 30 - 24 = $ 6 mn

Case 2: 80 percent chance of a $12 million payoff

If bondholders convert, the bondholder receives 800 shares of stock. So, total number of shares outstanding = 200 + 800 = 1,000

Per share value = Payoff / Number of shares outstanding = 12 x 10⁶ / 100 = $ 12,000

Value to bondholders = 800 x 12,000 = $ 9.60 mn < $ 10 mn repayment without conversion. Hence the bond holders are better off by not converting.

So value left for existing shareholders = 12 mn payoff - 10 mn repayment to bond holders = $ 2 mn

Part (a)

Hence, expected payoff to equity holder = 20% x $ 6 mn + 80% x $ 2 mn = $ 2.80 mn

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Part (b)

Expected payoff to the bond holder = 20% x 24 + 80% x 10 = $ 12.80 mn

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Second question:

Let the lowest stock price that Spartan management would be willing to accept = P

Hence, number of shares issued to venture capitalists = Fund raised / Share Price = $ 1 mn / P = 1,000,000 / P

Numbers of shares outstanding prior to fund raise through equity = 1,000,000

Total nos. of shares outstanding = N = 1,000,000 + 1,000,000 / P

Value of the firm = $ 5 mn = 5,000,000

Hence, value per share = 5,000,000 / (1,000,000 + 1,000,000 / P) = 5 / (1 + 1 / P)

Hence, value to Spartan management = nos. of shares held x value per share = 1,000,000 x 5 / (1 + 1 / P)

= 5,000,000 / (1 + 1/ P)

If they are not able to sell equity shares to venture capital, value of the firm = $ 3mn = 3,000,000 all belonging to Spartan management.

For neutral position of Spartan management, 3,000,000 = 5,000,000 / (1 + 1/P)

Hence 1 + 1 / P = 5 / 3

Hence, P = 3 / 2 = $ 1.50 = minimum share price the Spartan management shall consider.

Hence, the firm will sell $1 million of equity at a minimum price of $1.50.