Lowell D. Outland
IET310 engineering economic analysis
IET 310: 301 Engineering Economic Analysis: Fall 2011
Homework # 7 (Based on Chapter 10) (50 points)
Due date - November 13’Th (Sunday), 2011, before 11.55 PM EST
Prof. Rajeev Nair
1. A corporation is trying to decide whether to buy the patent for a product designed by another
company. The decision to buy will mean an investment of $8 million, and the demand for the product
is not known. If demand is light, the company expects a return of $1.3 million each year for three
years. If demand is moderate, the return will be $2.5 million each year for four years, and high
demand means a return of $4 million each year for four years. It is estimated that the probability for a
high demand is 0.4, and the probability for a light demand is 0.2. The firm’s (risk-free) interest rate is
12%. Calculate the expected present worth of the patent. On this basis, should the company make the
investment? (All figures represent after-tax values) (10 points).
-$8.000.000 + $1,300,000(3.037) = -$4,051,900
-$8.000.000 + $2,500,000(3.037) = -$407,500
-$8.000.000 + $4,000,000(3.037) = $4,148,000
Two of the options result in negative cash flow, these two options equal up to 60% or a probability of
.6. With only a probability of .4 or 40% chance of making a profit I would not make this investment.
2. A new product’s sales and profits are uncertain. The marketing department has predicted that sales
might be as high as 15,000 units per year with a probability of 10%. The most likely value is 9,000
units annually. The pessimistic value is estimated to be 6,000 units annually with a probability of
20%. Manufacturing and marketing together have estimated the most likely unit profit to be $32. The
pessimistic value of $24 has a probability of 0.3, and the optimistic value of $38 has a probability of
0.2. Construct the probability distributions for sales and unit profits (10 points).
Annual
expected unit
sales
15,000
9,000
6,000
15,000
9,000
6,000
15,000
9,000
6,000
Probability
Expected
Unit Profit
Probability
Joint
Probability
PW
10%
70%
20%
10%
70%
20%
10%
70%
20%
$38
$38
$38
$32
$32
$32
$24
$24
$24
20%
20%
20%
50%
50%
50%
30%
30%
30%
2%
14%
4%
5%
35%
10%
3%
21%
6%
$518,130
$201,096
$189,924
$436,320
$169,344
$159,936
$327,240
$127,008
$119,952
3. Two mutually exclusive investment projects are under consideration. It is assumed that the cash
flows are statistically independent random variables with means and variance estimated as given in
the table below (10 points)?
Lowell D. Outland
IET310 engineering economic analysis
End of
year
0
1
2
Project A
Mean
-$5,000
$4,000
$4,000
Project B
Variance
1,0002
1,0002
1,5002
Mean
-$10,000
$6,000
$8,000
Variance
2,0002
1,5002
2,0002
(a) For each project, determine the mean and standard deviation of the NPW, using an interest rate of
15%.
(b) On the basis of results of part (a), which project would you recommend?
4. The tree in the figure below has probabilities after each chance node and PW values for each
terminal node. What decision should be made? What is the expected value (10 points)?
Lowell D. Outland
IET310 engineering economic analysis
5. A new machine will cost $25,000. The machine is expected to last 4 years and it has no salvage
value. If the interest rate is 12%, determine the return and the risk associated with the purchase. (10
points).
P
Annual
savings
0.3
$7,000
0.4
$8,500
0.3
$9,500
-$25000 +$ 7000(3.037) = -$3741 risk= .7 or 70 %
-$25000 + $8500(3.037) = $814.50 risk= .6 or 60 %
-$25000 + $9500(3.037) = $9503.04 risk= .7 or 70 %
Note – Units are important. If units are not present, 10% per problem will be deducted.
Lowell D. Outland
IET310 engineering economic analysis