Required Rate of Return concept

CFA Level I Equities
#1

I have one question regarding to cost of equity, hopefully you could help me with it. Although I understand it is a required rate of return when taking risks in the equity market, I am still not sure of its meaning. For some technical tweak (such as changing the long-term bond or short-term T-bill, etc), I could have a range of cost of equity, from high to low.

Let’s say there is company X, with no debt. If I use Cost of Equity of 12% for my DCF model, I would have a fair value of, say $40. If I use Cost of Equity of 10% (lower rate) to discount, I would have a higher fair value, say $50. The question is: If I buy stock X, which is trading at $20, and sell at fair value, I would actually gain higher return (ie. selling at $50) using lower required rate of return, and gain lower return (ie. selling at $40) using higher required rate of return. Why this paradox? Do I misunderstand something?

Thank you.

#2

I don’t really understand the question - can you elaborate?

The question is: If I buy stock X, which is trading at $20, and sell at fair value, I would actually gain higher return (ie. selling at $50) using lower required rate of return, and gain lower return (ie. selling at $40) using higher required rate of return.

#3

The fair value derived can be understood as:

Buy at $40 => return of 12%

Buy at $50 => return of 10%

Fair value is an indication of expected return. Actual return depends on your buying/ selling prices and holding period.