334 UNCERTAINTYINFUTURE EVENTS -

(a)What is the expected PW for deciding whether to

prQceed?

(b)Find the P(loss) and the standard deviation for

proceeding.

10-23 (a) In Problem 10-22 how much is it worth to the

. firm to terminate the product after 1 year if thenet revenues are negative?

(b) How much does the ability to terminate early

change theP(loss) and the standard deviation?

10-24 Find the probability distribution and the expected PW

JI. to modify an assembly line. The first cost is $80,000,and its salvage value is $0. The firm's interest rate

is 9%. The savings shown in the table depend on

whether the assembly line runs one, two, or three

shifts, and on whether the product is made for 3 or

5 years.

10-25 In Problem 10-24, how much is it worth to the firm

.-to be able to extend the product's life by 3 ye~~,.ata cost of $50,000, at the end of the product's Imtial

useful life?

10-26 Al took a midterm examination in physics and re-
ceived a score of 65. The mean was 60 and the stan-
dard deviation was 20. Bill received a score of 14
in mathematics, where the exam mean was 12 and
the standard deviation was 4. Which student ranked
higher in his class? Explain.

10-27 The Graham Telephone Company may invest in
new switching equipment. There are three possi-
ble outcomes, having net present worth of $6570,
$8590, and $9730. The probability of each outcome
is 0.3, 0.5, and 0.2, respectively. Calculate the ex-
pected return and risk associated with this proposal.
(Answer: Epw= $8212, Uf'W= $1158)

10-28 A new machine will cost $25,000. The machine is

expected to last 4 years and have no salvage value. If

the interest rate is 12%, determine the return and the

risk associated with the purchase.

P

Annual savings

0.3

$7000

0.4

$8500

0.3

$9500

10-29 What is your risk associated with Problem 10-14?

10-30 Measure the risk for Problem 10-19 using theP(loss),

JILrange of PW values, and standard deviation of thePWs. (Answer:Uf'W= $127,900)

10-31 (a) In Problem 10-24, describe the risk using the

P(1oss)and standard deviation of the PWs..

(b)How much do the answers change if the possible

life extension in Problem 10-25 is allowed?

10-32 An engineer decided to make a careful analysis of the

cost of fire insurance for his $200,000 home. From a

fire rating bureau he found the following risk of fire

loss in any year.

Outcome

No fire loss

$ 10,000 fire loss

40,00Q fire loss

200,000 fire loss

Probability

0.986

0.010

0.003

0.001

(a) Compute his expected fire loss in any year.

(b) He finds that the expected fire loss in any year is

less than the $550 annual cost of fire insurance.

In fact, an insurance agent "explains that this is

always true. Nevertheless, the engineer buys fire

insurance. Explain why this is or IS not a logical

decision.

10-33 A firm wants to select one new research and devel-

opment project. The following table summarizes six

possibilities. Considering expected return and risk,

which projects are good candidates? The firm believes

it can earn 5% on a risk-free investment in govern-

ment securities (labeled as ProjectF).

Project

1 2 3 4 5 6 F

IRR

15.8%

12.0

10.4

12.1

14.2

18.5

5.0

Standard Deviation

6.5%

4.1,

6.3

5.1

8.0

10.0

0.0

State

Bad OK Great

Probability 0.3 0.5 0.2

Net revenue -$15,000 $15,000 $20,000

Life, in years^5510

Shifts! Savings! Useful Life

day year Probability (years) Probability

(^1) $15,000 0.3^3 0.6
(^2) 30,000 0.5^5 0.4
(^3) 45,000 0.2