Economics Homework

Homework 4 (100 pts)

1. (10 pts) Ross Systems in considering four projects A, B, C and D that have

risks associated with the producing benefits. Based on the information given in

the table below, which project is more desirable for the company?

2. a) (10 pts) Find the expected EUAW from the cost data provided in the table

below for an equipment being considered at John Case Inc. in Dickson,

Tennessee. Because of the uncertainty of technology being used in this

equipment, it has not been possible to get the initial cost accurately. The annual

benefit, however, is estimated to be $20,000 with a possible equipment life of 5

years. The salvage value is expected to be 10% of the initial cost. MARR =8%

First Cost, $ $50,000 $80,000 $100,000 $125,000

Probability 0.25 0.35 0.30 0.10

b) (10 pts) Determine the associated risk measure in this equipment investment

in terms of standard deviation.

3. (10 pts) Three estimators at Tech Engineering have come up with the

estimates of cash flows as shown in the table below for a project with a life of

10 years. Compute the expected NPW at 20%.

Data Estimator I Estimator II Estimator III

First Cost, $ 5,000 8,750 7,500

Benefits /Year, $ 3,750 4,000 3,000

Salvage Value 1,750 1,000 5,000

4. (10 pts) A sample of automobile batteries is tested. The distribution of

battery life is found to be mound-shaped and symmetrical (normal) with a mean

life of 36 months and a standard deviation of six months. The batteries carry

a 24-month guarantee. What percent of batteries will fail in less than 24 months?

5. (15 pts) An investment of $18,000 is expected to generate annual revenue

of $8,000 throughout life of the investment. The risk is based the life of the

investment. The estimate of probabilities for the duration of the investment is

given in the table below. No matter what the life of the investment might be,

Project A Project B Project C Project D

EUAW Prob. EUAW Prob. EUAW Prob. EUAW Prob.

$2,000 0.2 $3,000 0.1 -$5,000 0.2 $4,000 0.4

$1,500 0.5 -$2,500 0.4 $6,500 0.5 $2,500 0.3

$3,000 0.3 $3,500 0.5 $1,000 0.3 -$2,000 0.3

there will be no salvage value. Using a value of 15% MARR, compute the risk

(standard deviation) associated with this investment.

6. (10 pts) A robot has just been installed at a cost of $81,000. It will have no

salvage value at the end of its useful life. Please provide your answer using

EXCEL.

Savings per year Probability Useful life (years) Probability

$18,000 0.2 12 1/6

$20,000 0.7 5 2/3

$22,000 0.1 4 1/6

(a) What is the joint probability distribution for savings per year and useful

life?

(b) Define optimistic, most likely, and pessimistic scenarios by using both

optimistic, both most likely, and bot pessimistic estimates. What is the rate

of return for each scenario?

7. (15 pts) For the data in Problem 6:

(a) What are the expected savings per year, life, and corresponding rate of

return for the expected values?

(b) Compute the rate of return for each combination of savings per year and

life. What is the expected rate of return (Excel can be used in (b))?

(c) Do the answers for (a) and (b) match? Why or why not?

8. (10 pts) The tree below has probabilities (in the brackets) after each chance

node and PW values for each terminal node. What decision should be

made? What is the expected value?

D1

Pick A

C1

H(0.4)

D2

Pick A1

C3

H(0.4)

12,000

L(0.6)

8100

Pick A2

10,000L(0.6)

4000

Pick B

C2

H(0.4)

9000

L(0.6)

5000

Life, Years 3 4 5 6

Probability 0.1 0.4 0.3 0.2