How do I solve for the fair price of shares?

Question

How do I solve this problem? Please help/advise. Thank you!
You are a mutual fund manager. You are interested in company FAB. Company FAB is an all equity company with 1M shares outstanding. Your research indicates that FAB has a CAPM asset beta of 2. You think that the expected free cash flow of FAB will be $10M in year 1 and will grow at 5% thereafter. FAB stocks are currently trading at $73 per share. FAB pays out all its FCF as dividends. FAB does not have any cash. The risk free rate is 4% and the market risk premium is 7%. Ignore taxes or transaction costs.
a) What is the fair price of FAB shares in year 0?
b) What will be the fair price of FAB shares in year 1?
You expect that FAB shares will be trading at the fair price in year 1. You purchase 10,000 shares of FAB today and hold it for a year.
c) What is your expected return from year 0 to year 1?
d) What is the cost of capital of your portfolio? What is the CAPM alpha of your portfolio?
e) What is the NPV of your portfolio in year 0?

Answer 1

Hey there! I can absolutely help you break this corporate finance and valuation problem down step-by-step. Since this is an all-equity company that pays out all its free cash flow as dividends, we can treat this exactly like a Dividend Discount Model (DDM) with constant growth.

Here is the exact framework and the steps I would use to solve each part of this problem.

First lets find r from CAPM

r = Rf + B(Mkt Risk Premium)

r = 4% + 2(7%)

Fair price of FAB in year 0

Po = Div1 / (r - g)

Div 1 = year 1 FCF / shares outstanding

Div 1 = $10M / 1M

Po = 10 / (18% - 5%)

Po is your answer

Fair price of FAB in year 1

g stays at 5%

P1 = Po * (1 + g)

Expected Return from year 0 to year 1

73 because you are buying the shares today at current mkt rate

Expected Return = (Div1 + P1 - 73) / 73

Cost of Capital & CAPM alpha

Because the entire portfolio consists of FAB stock, the discount rate from CAPM will be the exact same as the Cost of Capital. so r

alpha = Expected Return - r

NPV = (Po - 73) * 10,000