Company ABCs common stock is currently trading at S0 = $100. Market consensus is that in 1 year the stock price will either increase to S1up = $140 with 50% probability or decrease to S1Down = $90 with 50% probability. Assuming a risk-free interest rate of 0% in this example:

1. What is the expected price of the stock in 1 year?

2. What is the discount rate (annual required rate of return) implied by the current stock price? How do you interpret this rate as compared to the risk-free interest rate?

Now consider a 1-year European call option on the same ABC stock. The payoff of the call option at expiration T = 1 is payoff = max(S1 K , 0), where K = $100. Assume such option is fairly priced at $10 / option today. We are considering only two investment alternatives: spending $100 to buy either: (i) 1 stock, or (ii) 10 options.

3. Assume the stock price at the end of year 1 is $140.

a. State whether the options should be exercised;

b. Calculate the payoff of the investments (i) and (ii) above;

c. Calculate the profit/loss of investments (i) and (ii) above; and

d. Calculate the % return of investments (i) and (ii) above.

4. Assume the stock price at the end of year 1 is now $90. Answer questions a. through d. above under this scenario.

5. Based on responses to questions 3 and 4, what can you infer about the riskiness of each investment alternative i.e. stock vs. the options? Qualitatively discuss the difference in the discount rate for the stock and the call options.

6. Based on the information above, provide a valuation for the call option. Do you think the option is fairly priced at $10? What is the discount rate (required rate of return) implied by your estimated price for the call option and does it make sense?