Deck 12: Project Risk and Uncertainty

Question 1

Consider the following investment cash flows over a 2-year life:

Answer 1

Question 2

Assume a project is expected to produce the following cash flows in each year, each cash flow is independent of one another, each cash flow is gamma distributed, the risk-free rate is 5 % , and the MARR =15% .

(a) Calculate the expected net present value
(b) Calculate the standard deviation of the net present value
(c) Determine the probability that the NPV will be less than 600 .
(d) Determine the probability that the NPV will lie between 800 and 1200 .

Answer 2

(a)
(b)
(c)
(d)

Question 3

You are trying to analyze a risk-reward profile of an investment. There are two random variables of interest:
the price per unit (P) and the demand per unit (D). Then Profit (z) function is related to by the following
expression where the profit margin is known to be 0.6. Given the following information, calculate the mean and
standard deviation of this profit function.

Answer 3

Question 4

As a marketing manager for a large sports apparel manufacturer, you are trying to decide whether to open a
new factory outlet store, which would cost about $500,000. Success of the outlet store depends on demand in the
new region. If demand is high, you expect to gain $1 million per year; if average, $500,000; and if low, to lose
$80,000. From your knowledge of the region and your product, you feel the chances are 0.4 that sales will be
average, and equally likely that they will be high or low (0.3, respectively). Assume that the firm's MARR is
known to be 15%, and the marginal tax rate will be 40%. Also, assume that the salvage value of the store at the
end of 15 years will be about $100,000. The store will be depreciated under a 39-year property class.
(a) If the outlet store will be in business for 15 years, should you open the new outlet store? How much would
you be willing to pay to know the true state of nature?
(b) Suppose a market survey is available at $1,000 with the following reliability (values obtained from past
experience where actual demand was compared with predictions made by the market survey). Determine the strategy that maximizes the expected payoff after taking the market survey. In doing so, compute
the EVPI after taking the survey. What is the true worth of the sample information? Assume that you are a
risk-neutral person so that you are interested in maximizing the expected monetary value.

Question 5

A new project will require $X in investment today and is expected to provide a net cash outflow of $1000(Y) for
the next two years where: (a) Determine and simplify the NPV equation assuming the risk-free rate is 6%.
(b) Given the following sequence of uniform random deviates, calculate the first iteration for this NPV
equation. Note that the selling price, once determined at period 1 will be the same value will be assumed in
period 2. In statistical term, selling prices are perfectly positively correlated each other. Also assume that X and
Y are statistically independent.

Question 6

An engineering editor for a large publishing firm is trying to decide whether or not to publish a manuscript he
has received. In making a decision he feels that it is sufficient to imagine that there are just four states of nature
which are
• S1, the book will sell an average of 500 copies per year;
• S2, the average annual sales will be 1500 copies;
• S3, the average annual sales will be 3000 copies; and
• S4, the average annual sales will be 10,000 copies.
3
The prior probabilities which he assigns to these states of nature are, respectively, 0.30, 0.40, 0.25, and 0.05. The
discounted profits if he publishes the book are projected to be, respectively, -$30,000, +$4,000, +$12,000, and
+$100,000. Of course, the discounted profit is $0 if he does not publish it.
To gain additional information, the publisher can send the manuscript to a reviewer who would say he likes the
manuscript. From previous experience with this reviewer, the publisher feels that the conditional probabilities
of the state of nature given this response from the reviewer are respectively 0.1, 0.3, 0.5, and 0.1. Should the
publisher publish the book? To answer this question, do the following:
(a) What is the prior optimal act? Draw your decision tree here.
(b) Calculate the EVPI before sending the manuscript out for review.
(c) What is the posterior optimal act? Draw the decision tree
(d) Calculate the EVSI.

Question 7

Langley Inc. has just invested $600,000 in a manufacturing process that is estimated to generate an after-tax
annual cash flow of $280,000 in each of the next five years. At the end of year five, the firm does not expect any
further market for the product and any appreciable salvage value for the manufacturing process. If a
manufacturing problem delays plant start-up for one year (leaving only four years of process life), what
additional after-tax cash flow will be needed to maintain the same internal rate of return as if no delay had
occurred?

Question 8

Barbara Thompson is considering the purchase of a piece of business rental property containing stores and
offices at a cost of $350,000. Barbara estimates that annual receipts from rentals will be somewhere between
$35,000 and $45,000 but that annual disbursements, other than income taxes, would be fairly close to $18,000.
The property is expected to appreciate at an annual rate of 5%. Barbara expects to retain the property for 10
years once it is acquired. Then it will be depreciated on the basis of the 39-year real-property class (MACRS),
assuming that the property would be placed in service on January 1. Barbara's marginal tax rate is 30%, and her
MARR is 10%. What would be the minimum annual total of rental receipts that would make the investment
break- even?