1. A generous university benefactor has agreed to donate a large amount of money for student scholarships. The money can be provided in one lump-sum of $10mln, or in parts, where $5.5mln can be provided in year 1, and another $5.5mln can be provided in year 2.
a) Assuming the opportunity interest rate is 6%, what is the present value of the second alternative? According to Douglas, “a dollar received in the present period is worth more than a dollar received in a future period” (2010, ch. 1.4). The reasoning behind this is that an amount received today can be deposited into a bank and earn interest. Therefore an amount received in a year, for example, is valued less today, and conversely, an amount received today is valued to be more in a year from now. For this scenario, using the formula, PV=FVn/(1+r)n for the present value where n represents number of years in the sequence and r represents the rate, which in this case is the opportunity rate of 6%, the present value of the second alternative is $10,070,000. The calculation for this equation is PV($10m) = $5.5m/(1.06) + $5.5m/(1.06)(1.06) = $5.18m + $4.89m = $10,070,000.
b) Which of the two alternatives should be chosen and why? Using the present value method, I would chose the second alternative as it would net an extra $70,000 that could be put to very good use at the University.
c) How would your decision change if the opportunity interest rate was 12%? My decision would definitely change if the opportunity rate was 12% instead of 6% because the present value of the second alternative would change to $9,290,000. The calculation would be PV($10m) = $5.5m/(1.12) + $5.5m/(1.12)(1.12) = $4.91m + $4.38m = $9,290,000.
2. An angel investor is considering investing in one of two start-up businesses and is evaluating the expected returns along with the risk of each option in order to choose the better alternative. * Business 1 is an innovative protein energy drink, which has ENPV of $100,000 with a standard deviation of $40,000. * Business 2 is a unique chicken wings dipping sauce with an ENPV of $60,000 and a standard deviation of $25,000.
a) Apply the coefficient-of-variation decision criterion to these alternatives to find out which is preferred by the angel investor, assuming that he/she is risk-averse. The text defines the coefficient-of-variation decision criterion as “a statistic of a probability distribution and is calculated as the ratio of the standard deviation to the mean” (2012, ch. 2.2). In this case, the CV of Business 1 is 40,000/100,000 = 0.4 and for Business 2 the CV is 25,000/60,000 = 0.4. The CV criterion is does not take into consideration the different levels of risk that individual investors may have making it an unsuitable decision making platform when the measure of individual risk preferences is necessary. The coefficient-of-variation decision criterion would be an inferior decision-making model in this case because it does not definitively distinguish which of the two businesses is best to invest in and does not address an individual investors risk preference.
b) Apply the maximin criterion, assuming that the worst outcome in Business 1 is to lose $5,000, whereas the worst outcome in Business 2 is to make only $5,000 in profit. The maximin decision rule, is a basic comparison of two minimum outcomes (Douglas, 2012). Under this rule the highest or best out of the worst outcomes would be the right choice. In light of this fact, Business 2 would be chosen under this rule. Making $5,000 in profit is a better worst-case scenario than losing $5,000 in Business 1.
c) If you were the angel investor, what is your certainty equivalent for these two projects? Are you risk-averse, risk-neutral, or risk-lover? As an angel investor, I would be risk-averse. In angel investing, you have to be since you will be constantly evaluating the risk involved in investing your hard-earned capital into projects that may succeed or fail. In this case, certainty-equivalent-based model I would rely on for deciding among these two projects would be the Maximin Rule. It would be prudent to consider the worst possible scenario and it would be wise to choose the highest and best of the worst. Here, my choice would be to invest in the chicken wing dipping sauce, Business 2.