I am buying a firm with an expected perpetual cash flow of $900 but am unsure of its risk. If I think the beta of the firm is 0, when the beta is really 1, how much more will I offer for the firm than it is truly worth

$10,500

Explanation:

Cost of equity = risk free rate+beta*(expected return on market - risk free rate)

Now beta is taken as 0,

risk free rate = 6% and market return = 20% (assumed).

cost of equity as calculated by you = 6%+0*(20%-6%) = 6%. value of firm = perpetual cash flow/cost of equity = $900/0.06 = $15,000

However, beta is 1, so actual cost of equity will be =  6%+1*(20%-6%) = 6%+14% = 20%

So, value of firm, actually, will be = 900/0.2 = $4,500.

So the amount that you will be paying more = value calculated with 0 beta - value calculated with 1 beta

= 15,000 - 4,500 = $10,500.

answer; i believe the answer is (facework);

the first one $24,630