Percentage of Days in Which the Highway

¶ … percentage of days in which the highway had traffic was 3/20, or 0.15, or 15%. Thus, the average time that can be expected for the I-20 is (.15)(45) + (.85)(25) = 6.75 + 21.25 = 28 minutes.

The expected time on Shea Boulevard is 35 minutes, and this is consistent. Thus, during normal conditions it is faster on average to take the I-20. The total travel time for the month will be lower.

If in winter the odds of delays are 6/20 = 30%, then the situation might change. The expected average travel time would be: (.3)(45) + (.7)(25) = 13.5 + 17.5 = 31 minutes. The time on Shea Boulevard doesn't change. Thus, even in winter it is still faster to take the I-20.

With the app, two out of three traffic jam days would see them divert to Shea Boulevard. The result is that the expected time would be (.85)(25)+(.1)(35)+(.05)(45) = 21.25 + 3.5 + 2.25 = 27 minutes total time. The average has declined slightly because of the two trips where the accident is avoided.

The present value of the second alternative is 5.5 / (1.06)^2 = 5.5 / 1.1236 = 4.89 million. This combines with the initial 5.5 million for a total of 10.39 million.

Thus, the second alternative delivers more money in terms of net present value than the first option, where it all comes at once. The donation sought should be the second one.

If the interest rate changes to 12%, then present value of the second year payment is 5.5 / 1.2544 = 4.38 million. Thus, the present value of the second option is 5.5 * 4.38 = 9.88 million. Under that circumstance, the first option of the $10 million lump sum is the better of the two options.

2. The coefficient of variation is the ratio of the standard deviation to the mean. For the protein energy drink, this is 0.4 ($40,000/$100,000) and for the chicken wing dipping sauce it is 0.416 ($25,000 / $60,000). Using the coefficient of variation criteria, the first option is the one that would be selected by the angel investor. The angel investor has a preference for risk aversion, so in that case would want to invest in the protein energy drink because its expected returns are just slightly less volatile.

The maximin criterion uses the worst loss scenario to make the decision. Under that criterion, the chicken wing sauce is the best decision, because the worst possible outcome is a $5,000 profit, while the worst possible outcome for the protein energy drink is a $5,000 loss.