Question

You just paid $800,000 to become the sole equity investor in an unlevered firm. If things go well, you will sell the firm to Google for $1,600,000 in one year. If things go poorly, you will sell the firm to Facebook for $600,000 in one year. It is equally likely that things will go well versus poorly. What is your expected return on this investment?

(only answer question below)

Assume it’s an alternate reality, and you just paid $400,000 to become the sole equity investor in the same firm described in the prior question, except the firm has a debt-to-value ratio of 50%. The interest rate on the firm’s debt is 10%, and the firm plans to retire the debt in one year (i.e. pay it in full). At that point, you will sell your equity to Google/Facebook depending on whether things went well or poorly. Assume it’s an M&M world (no taxes, frictions, etc.). What is your expected return on this investment?

a. 50.2%

b. 65.0%

c. 38.0%

d. 55.7%

Answer 1

To find expected return in second part we need to first solve the first part of the question

In the first company is unlevered or without debt, therefore expected return on investment = cost of unlevered equity = Cost of all equity firm

Initial investment = 800000

If the things go, Selling price to Google after 1 year = $1600000,

Return on investment if things go well = (Selling price to Google after 1 year / Initial investment) - 1 = (1600000 / 800000) - 1 = 2 - 1 = 1 = 100%

If things go bad, Selling Price to Facebook after 1 year = $600000,

Return on investment if things go bad = (Selling price of Facebook after 1 year / Initial investment) - 1 = (600000 / 800000) - 1 = 0.75 - 1 = -0.25 = -25%

Expected return on investment = Probability of things going well x Return on investment if things go well + Probability of things going bad x Return on investment if things go bad = 50% x 100% + 50% x -25% = 50% - 12.5% = 37.5%

Expected return on investment = Cost of unlevered equity = 37.5%

Now we will solve the second part

Now If you become owner of company that has debt , then the company becomes levered.

So Expected return on investment = Cost of equity of levered firm

It is given that Debt / Value = 50%, then Equity value = 1- (Debt/Value) = 1-50% = 50%

Debt / Equity = [Debt / Value] / [ Equity / Value ] = 50% / 50% = 1

Cost of debt = interest rate on debt = 10%

According to Modigliani and Miller Proposition I without taxes

Cost of equity of levered firm = cost of unlevered equity + (cost of unlevered equity - Cost of debt)(Debt / Equity) = 37.5% + (37.5% - 10%)(1) = 37.5% + 27.5% = 65%

So Expected return on investment = 65%

Answer: b. 65%