Question

The current FB stock price is $32 in the market. The FB stock price in a year can be either $38 with 55% chance or $30 with 45% chance. What is the implied risk-adjusted discount rate (per year) perceived by the investors in the market? Assume the investors in the market use the common risk-adjusted discount rate and they believe the current stock price is the present value of the next period stock price. That is, no dividend. The interest rate is 3%/year, compounded annually, so is the discount rate for riskless cash-flows.
1) 3.5% /year
2) 4.5% /year
3) 5.5% /year
4) 6.5% /year
5) 7.5% /year

Answer 1

The stock can be at either $ 38 with a probability of 55 % or at $ 30 with a probability of 45 %, one year later

Expected Stock Price After 1 Year = 38 x 0.55 + 30 x 0.45 = $ 34.4

Current Stock Price = $ 32

Further, the current price is expected to be the present value of the expected one year price, assuming no dividends, discounted at the implied risk-adjusted discount rate.

Let the same be R

Therefore, 32 = 34.4 / (1+R)

R = [(34.4/32)-1] = 0.075 or 7.5 % per year

Hence, the correct option is (5)