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. Assuming the opportunity interest rate is 6%, what is the present value of the second
alternative? Which of the two alternatives should be chosen and why? How would your
decision change if the opportunity interest rate was 12%? Please, show all your calculations.
Case I:
Here, NPV= \$ 5.5 M ( 1+0.06)+ \$ 5.5 M (1+0.06)^2 = \$ 10.08 M
This proves that the second alternative is better because of greater NPV (than 10M in the first
case).
Case II:
When when r =0.12
NPV = \$ 5.5 M( 1+0.12)+ \$ 5.5 M (1+0.12)^2 = \$ 9.29 M only.
Because here the NPV is less than \$ 10 M therefore, \$ 10 M lump sump is profitable
2. Volkswagen is considering opening an Assembly Plant in Chattanooga, Tennessee, for
the production of its 2012 Passat, tailored for the US market. The CEO of the company is
considering two potential options for the size of the plant: one is a large size with a projected
annual production of 150,000 cars, and the other one is a smaller size plant, which is cheaper
to build, but can only produce up to 80,000 cars per year. Depending on the expected level of
demand for these cars in the US, Volkswagen has to decide which option is more profitable. The
discount rate is 6% and for simplicity purposes, the CEO is only evaluating a two-year horizon.
The initial factory setup cost, the expected demand scenarios, profit, and probabilities are shows
in the below table. Calculate the Net Present Value in each of the two options. Which option
For Large Factory:
Profit of year 1 will be expectation of year1 profits
E[p1]= 20*0.4 +80*0.4+100*0.2 = \$60 M
expectation of year2 profits
E[p2]=60*0.3 +90*0.5 +150*0.2 =\$93 M
Therefore, we calculate the Net Present Value of all profits as the sum,
= 60 + 93/1.06
=\$147.73 M
For small Factory
Expectation of year1 profits
E[p1]= 30*0.4 +50*0.4+70*0.2 = \$46 M
E[p2]=70*0.3 +80*0.5 +90*0.2 =\$79 M
Thus, the present value of all cash flows = 46+ 79/1.06 =\$120.52 M
So, the CEO should go for Large Factory because it will yield additional profit of \$27mln.
3)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.
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.
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?
Coefficient Of Variation – CV’
The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a
useful statistic for comparing the degree of variation from one data series to another, even if the
means are drastically different from each other.
CV= standard deviation/ expected return
CV1= 40000/100,000 =0.4
CV2= 25000/60,000 =0.417
Risk averse investor will choose lower CV ratio project i.e Business 1 is an innovative protein energy
drink, which has ENPV of \$100,000 with a standard deviation of \$40,000.
b)
the worst outcome in Business 1 is to lose \$5,000
worst outcome in Business 2 is to make only \$5,000 in profit
Maximin criterion:
In decision theory, the pessimistic (conservative) decision making rule under conditions of uncertainty. It
states that the decision maker should select the course of action whose worst (maximum) loss is better
than the least (minimum) loss of all other courses of action possible in given circumstances
Minimum profit in Business 1 = 100,000-5000 =\$95,000
Minimum profit in business 2 =60,000+5000 =65000
So business1 should be chosen by investor
c) certainty equivalents are 2.5 for project1 and 2.4 for project 2so project 1 is preferred ,
here investor in risk averse