The second lecture for Business Law was interesting. It felt more like a round table discussion and was infused with a lot of back and forth, including both the lecturer and the students. It Depends One interesting comment the teacher made about half way through with respect to law was “It Depends”. In other words, is someone guilty or not? It depends. Is someone liable? It depends. On what does it depend? A host of things, including the context, the timing, the judge or jury. Perhaps most interesting was the discussion of a Reasonable Person. So much of law comes back to what a reasonable person would or would not do. However, there isn’t a definition of a reasonable person. So law is left to the spectrum of human experience and emotion to weigh in on guilt or innocence. Lord Goddard C.J.R. in Regina v. McCarthy, 2 Q.B. 105 (1954) (copied from Cheesman) stated: No court has ever given, nor do we think ever can give, a definition of what constitutes a reasonable or an average man. Certainly there are mechanisms to account for aberrations, such as the option for a judge to recuse himself. Jury selection plays a part. In those few cases where someone feels there has been a miscarriage of justice, the appeals process is available to seek remedy. So, then next time you get caught up in the letter of the law and think you have a sure thing figured out, just remember, it...

According to the morningstar website, both Microsoft and Google have high bond ratings, with Microsoft slightly higher. Microsoft Google Morningstar Credit Rating AAA AA Amt Outstanding $16.9 Bil $3.0 Bil Debt/Assets 10.58% 5.31% Based on the ratings, the bond market appears to favor more experienced borrowers, since from a debt load perspective, Google has better standing. Google’s entire bond issue is encompassed in just three bonds with the longest maturation in 2021. It’s also interesting that all three mature on May 19. Duration Duration is calculated the weighted average of the present values of all future cash flows. It can be represented by the following equation (ref), where PV is the present value.   Calculations like this are easily done in Excel. For this exercise I chose bonds that mature in 2016 and payout semi-annually for both Google and Microsoft. Microsoft bond duration Microsoft Coupn 2.500% Par $1,000.00 Maturity 2/8/2016 Frequency semi-annual Discount rate 2.38% 1 2 3 4 5 6 Total 8/8/2013 2/8/2014 8/8/2014 2/8/2015 8/8/2015 2/8/2016 Payment $25.00 $25.00 $25.00 $25.00 $25.00 $1,025.00 PV(Ct) $24.42 $23.85 $23.30 $22.76 $22.23 $890.09 $1,006.64 PV(Ct)/PV 0.0243 0.0237 0.0231 0.0226 0.0221 0.8842 Duration 0.0121 0.0237 0.0347 0.0452 0.0552 2.6527 2.8236 Google bond duration Google Coupon 2.125% Par $1,000.00 Maturity 5/19/2016 Frequency semi-annual Discount rate 2.04% 1 2 3 4 5 6 Total 11/19/2013 5/19/2014 11/19/2014 5/19/2015 11/19/2015 5/19/2016 Payment $21.25 $21.25 $21.25 $21.25 $21.25 $1,021.25 PV(Ct) $20.83 $20.41 $20.00 $19.60 $19.21 $904.71 $1,004.75 PV(Ct)/PV 0.0207 0.0203 0.0199 0.0195 0.0191 0.9004 0.0104 0.0203 0.0299 0.0390 0.0478 2.7013 2.8486 Based on the data above, the duration for the Google bond is higher than for the Microsoft bond, however the difference is slight. You can download the original spreadsheet...

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...

A review of the stock price and growth rate for Microsoft and Google over the past five years shows that they track very closely in general. However, the last year shows a marked deviation from this tracking as Microsoft stayed mainly flat and Google demonstrated strong growth. Using the data from the source above, we can project the anticipated stock price in 2018 if the growth rate remains constant over that time. Company Stock May 2008 Current Stock Effective Rate Stock May 2018 Google 580.07 909.18 56.74% 1425.05 Microsoft 29.99 34.87 16.27% 40.54 Here are the calculations used to arrive at the effective rates shown above (click to enlarge). Alternate approach In the example above, I calculate the effective rate based on the delta between May, 2008 and May, 2013. Another approach would be to start with the stock price five years ago and use Excel to find the annual rate (assuming annually compounding interest). In this case we get the following details. Company Annual Rate -5Y Today +5Y Google 9.40419% 580.07 909.18 1,425.02 Microsoft 3.0615% 29.99 34.87 40.55 The answers come out the more or less the same, but it helps to know what the annual interest rate is, not just the effective rate over the five year...