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BUSI 620
Answers for QCT 7
Salvatore’s chapter 14:
a.Discussion Questions:
12. The rationale behind the minimax regret decision rule is to minimize the maximum
regret or opportunity cost of making the wrong decision under each state of nature, after a
particular state of nature has actually occurred. The regret associated with each
decision is measured by subtracting the payoff from that decision from the maximum
payoff under the same state of nature. The decision maker then chooses the strategy with
the minimum of these maximum regrets under any possible state of nature.
Some of the more informal and less precise methods of dealing with uncertainty are (1)
the acquisition of additional information (until the marginal benefit equals its marginal
cost); (2) referral to such authorities as the Internal Revenue Service, the Securities and
Exchange Commission, the Labor Relations Board, etc., to remove the uncertainty about
specific points within their competence; (3) attempting to control the business
environment in which the firm operates by patents, copyrights, and exclusive franchises;
(4) hedging (i.e., entering into a contract to buy or sell a specific quantity of a
commodity, security, foreign currency, etc., for delivery at a future date, at a price agreed
upon today); and (5) diversification into various product lines by a firm, different
securities in a portfolio, and various lines of business by a conglomerate corporation.
The minimax regret rule is useful when the decision maker wants to minimize the
maximum regret or the opportunity cost of a decision under whatever state of nature
occurs. The other more informal and less precise methods of dealing with uncertainty are
useful under particular circumstances, and are often employed by experienced business
executives. Which of the more formal decision rules or more informal methods of dealing
with uncertainty are best depends on the circumstances, the firm's attitude toward
uncertainty, the type of investment decision that the firm faces, and so on.
15. Since credit-card companies must charge the same interest rate to all borrowers, they
attract more low- than high-quality borrowers (i.e., more borrowers who either do not
repay their debts or repay their debts late). This leads to an adverse selection problem and
forces up the interest rate charged, which increases even more the proportion of low-
quality borrowers, until interest rates would have to be so high that it would not pay even
for low-quality borrowers to borrow.
Credit-card companies reduce the adverse selection problem that they face by sharing the
credit histories of borrowers with other credit-card companies. The sharing of borrowers'
credit histories by credit-card companies in order to reduce the adverse selection problem
that they face gives rise to complaints of invasion of privacy. This is true, but without
sharing credit histories, credit-card companies would have to charge much higher credit
rates, which might be unacceptable to most borrowers.
b.Problems:
Spreadsheet problems
1. The expected value of investment A is ($4,000)(0.2) + ($5,000)(0.3) + ($6,000)(0.3) +
($7,000)(0.2) = $800 + $1,500 + $1,800 + $1,400 = $5,500.
The expected value of investment B is ($4,000)(0.3) + ($6,000)(0.4) + ($8,000)(0.3) =
$1,200 + $2,400 + $2,400 = $6,000.
(a) The standard deviation of investment A is $1,024.70. The standard deviation of
investment B is $1,549.19.
(b) Investment A is less risky than investment B because its standard deviation is smaller,
but it also provides a lower expected income.
(c) It is not clear, therefore, from the information given which investment is best. It
depends on whether the lower expected income from investment A is more than balanced
by its lower risk. This depends on the attitude of the individual toward risk.
2.
(a) From the spreadsheet, the expected value of project A of 2.8 is higher than 2.7 for
project B, so it is preferred.
(b) Project B has a higher expected utility of 2.315, however, so it is preferred under this
criterion.
(c) The individual is risk averse because the utility function of profit increases at a
decreasing rate or faces down so that the marginal utility of profit diminishes
Froeb and McCann’s chapter 17:
a.Individual problems:
17-3
Boat Insurance = $2,150
Payment Probability
$25,0001 – (0.6+0.25+.12) = 0.03
$5,000 0.12
$0 0.25
$0 0.6
Expected payment = 0.03*25,000 + 0.12*5,000 + 0.25*0 + 0.6*0 = $1,350
Expected payment + $200 profit = $1,550
17-4
Hotdog Uncertainty
Compute expected payoffs:
Enter: 0.35(50,000)+.65(0)=$17,500
Do not enter:$15,000
You should enter the market.
Froeb and McCann’s chapter 19:
a.Individual problems:
19-3
“Soft Selling” and Adverse Selection
The seller of the product knows whether the product works; the buyer does not (the
asymmetric information). The buyer is worried that the seller has an incentive to lie—to
tell him that the product will reduce costs regardless of whether they will (the adverse
selection). The buyer “signals” the quality of his product by offering to be paid only if it
works. A seller who knew his product didn’t work would not offer this kind of contract.
19-5
Hiring Employees
Expected value = $50,000
Without adverse selection, you would expect to hire an equal number of each type of
employee and your expected value would be $65,000 (E(v) = .25(50,000) + .25(60,000) +
.25(70,000) + .25(80,000) = $65,000)
But with adverse selection, you will not realize this value. If you initially assume an
expected value of $65,000 and therefore offer that as your salary, only the $50,000 and
$60,000 employees will accept. This drives your expected value down to $55,000. If
you lower your offer to $55,000, only the $50,000 employees will accept.
The only reasonable offer you can make is $50,000.
Salvatore’s chapter 15:
a.Discussion Questions:
7.
(a) Only when evaluating mutually exclusive investment projects can the NPV and the
IRR methods provide contradictory signals as to which investment project the firm should
undertake. For a single or independent project the two methods will always give the same
accept/reject investment signal.
(b) The NPV and IRR methods can provide contradictory investment signals because the
NPV method implicitly and conservatively assumes that the net cash flows generated
by the investment project are reinvested at the firm's cost of capital or risk-adjusted
discount rate, while the IRR method implicitly assumes that the net cash flows generated
by the investment project are reinvested at the same higher IRR earned on the given
project.
(c) When contradictory signals are provided by the NPV and the IRR methods, the former
should be used because the firm cannot assume that it can reinvest the net cash flows
from the project at the same higher IRR earned on the project.
b.Problems:
8.
(a) The NPV of each project is obtained by subtracting from the present value of the net
cash flows (PVNCF) for each project the initial cost of the investment (C0).
Thus, NPV = $600,000 for project A, $450,000 for project B, and $300,000 for project C.
With capital rationing, the firm can undertake either project A only or projects B and C.
Ranking projects according to their NPV, the firm would undertake projects B and C with
total NPV of $750,000
(b) Since the firm faces capital rationing, however, it should use the profitability index (PI)
as its investment criterion. The PI of each project is given by the ratio of the PVNCF to the
C0 of each project
For project A, PI = $3,000,000/$2,400,000 = 1.25.
For project B, PI = $1,750,000/$1,300,000 = 1.35.
For project C, PI = $1,400,000/$1,100,000 = 1.27.
Using the PI investment criterion indicates that the firm should undertake projects B
and C. The reason for this is that projects B and C provide a higher rate of return
per dollar invested than project A. Note that the sum of the NPV of projects B and C
exceeds the NPV for project A.
10. The cost of equity capital for this firm (ke) can be calculated with the dividend valuation
model, as follows
ke = (D/P) + g
where D is the amount of the yearly dividend paid per share of the common stock of the
firm, P is the price of a share of the common stock of the firm, and g is the expected annual
growth rate of dividend payments.
Since the company pays half of its expected $200 million in net after-tax earnings in
dividends and there are 100 million shares of common stock of the firm, the dividend per
share is $1. With a share of the common stock of the firm selling for eight times current
earnings, the price of a share of the common stock of the firm is $8.
With the expected annual growth of earnings and dividends of the firm of 7.5 percent, the
cost of equity capital for this firm is
ke = ($1/$8) + 0.075 = 0.125 + 0.075 = 0.20 or 20%
Spreadsheet problem 1: The present value of net revenue is $760. The firm should
purchase the machine since the NPV of the project is positive.
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