Options are a device that allows an investor to hedge potential losses for a cost. A call option gives the purchaser the right, but not the obligation, to buy a stock at a given price. A put option gives the purchaser the right, but not the obligation, to sell a stock at a given price. The counter party to the agreement has the obligation to either sell or buy (call and put) at the agreed price if the option is exercised. The exercise date is always in the future, and the further an option is in the future, the more it will cost. How much more depends on the exercise price, interest rates and the volatility of the stock. To give you an idea, here’s some data from Microsoft and Google showing the call option prices going four months into the future. I obtained this data from Yahoo! Finance for Microsoft and Google. To make monthly analysis more relevant, I’ve included only the call options that have been traded for a given strike price in each of the four months analyzed. I also collapsed recent trade prices for options with the same strike price in some cases. Call Option Pricing Microsoft The stock price at the time these options values were captured was $34.54. July, 2013 August, 2013 September, 2013 October, 2013 Strike Last Last Last Last stdev (annual) $29.00 $5.69 $4.50 $5.35 $5.77 1.743 $30.00 $4.81 $4.75 $4.80 $4.85 0.123 $31.00 $3.66 $3.85 $3.80 $4.09 0.537 $32.00 $2.77 $2.88 $2.97 $3.22 0.575 $33.00 $1.88 $2.20 $2.32 $2.55 0.837 $34.00 $0.77 $1.41 $1.66 $1.85 1.413 $35.00 $0.16 $0.86 $1.13 $1.33 1.533 $36.00 $0.25 $0.50 $0.70 $0.99 0.939 $37.00 $0.09 $0.24 $0.43 $0.63 0.702 $38.00 $0.03 $0.12 $0.28 $0.43 0.530 $39.00 $0.01 $0.03 $0.15 $0.27 0.361 $40.00 $0.02 $0.04 $0.08 $0.16 0.186 $41.00 $0.01 $0.02 $0.05 $0.11 0.135 Google The stock price at the time these options values were captured was $880.37. July, 2013 August, 2013 September, 2013 October, 2013 Strike Last Last Last Last stdev (annual) $700.00 $180.87 $179.00 $216.00 $186.00 51.831 $750.00 $135.10 $144.67 $127.40 $151.80 32.104 $770.00 $103.50 $113.90 $104.20 $126.00 31.591 $780.00 $102.73 $105.50 $122.00 $108.20 25.675 $800.00 $73.12 $87.90 $91.80 $94.40 28.519 $805.00 $81.22 $81.20 $114.04...

When it comes time to inform an investment decision, it’s essential to know whether or not a present opportunity represents enough present value to justify the investment. If so, at what level and over what time period. Certainly risk factors in, and with such a broad range of opportunities today, including stock markets, bonds, start ups, etc., there’s a lot to take in to account. The answer to the value and timing of an investment with respect to other available investments is given by the Present Value formula (ref for all equations). where P is the present value C is the anticipated future cash flow r is the interest rate of an alternative investment of similar risk t is the number of investment periods. This may change depending on compounding Another way to look at this is as a cash flow C and a Discount Factor D. where The rate r above is the opportunity cost of captial, or opportunity cost. Note that for multiple cash flows, the equation can be summed  Amount, Time and Risk From an investment perspective, the focus of the above equation is cash flow. More specifically, Amount of cash flow Timing of the cash flow Risk associate with the cash flow All three items factor in to the present value formula, and the present value formula informs many financial decisions, including being the basis for perpetuity and annuity analysis and...

In the first lecture of my corporate finance course, the professor make a case in favor of having financial markets, including their intermediaries, like banks. He summarized his case into the four following points. Transport consumption over time (save money, invest) Reduction of risk (through diversification) Liquidity (allows trade to happen faster) Information (trends, evaluation of health) Information From a business manager’s perspective, the fourth bullet is critical. The information that comes from financial markets informs nearly every decision he makes, including production schedules, marketing functions, labor decisions, benefits structure and timing, etc. Since business decisions should be informed by data (unfortunately we find that is not always the case, but I’ll comment on that more in another post), the financial markets provide that data. Opportunity Cost of Capital One common question is whether or not some opportunity represents enough value to justify investment. If so, at what level and over what time period. Certainly risk can factor in, but with such a broad range of opportunities today, including stock markets, bonds, start ups, etc., there’s a lot more to take in to account. Ultimately the information that comes from the financial markets drives the valuation of investment opportunities, including their amount, timing and...