Economics work 20 hours

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EPOM/EECS407 Final Exam

Do ALL problems Time allowed: 3 hrs

1. (10 points) A manufacturing plant produces specially crafted engines for high-performance

automobiles. If it takes 3 working days to produce the first engine and the learning curve is such that it

only takes an estimated 70% of the time (required to produce the first engine) to produce the second

engine, determine how long it will take for the plant to be able to produce 2 engines in one working

day.

Name:……………………………………………………

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2. (10 points) An investment amount of $10M has to be raised through equity financing and debt

financing. The required debt ratio is 0.40 and the company tax rate is 35%.

a) The current market price of the company’s common stock is $50 and the current dividend is $5

and the dividend is expected to grow at 5% annual rate. The floating cost of issuing a common

stock is 10%. Preferred stocks of $100 par value with 10% fixed annual dividend can also be

issued at 8% floating cost. If the required proportion of funds from retained earnings to common

stocks to preferred stocks are 0.4:0.2:0.4 respectively, what is the cost of equity?

b) Bank loans at 12% annual interest. Also, the company issues 20-year bonds that pay the equivalent

of 9.5% yield to maturity. If the required ratio of funds raised through these two methods of debt

financing is 0.6:0.4 what is the cost of debt?

c) From (a) and (b), what is the cost of capital (WACC)?

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20000 40000 60000 80000 100000

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5

10

15

20

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3. (15 points) EECS Corporation has identified six investment opportunities that will last 1 year. The firm

draws up a list of all potentially acceptable projects, and computes their IRR and PW at 8.5% MARR as

shown below.

Project Initial Investment IRR PW(8.5%) ($)

1 17,000 8% 1300

2 12,000 10% 1120

3 15,000 5% 600

4 20,000 20% 3800

5 10,000 7% 720

6 16,000 15% 1700

a) If the marginal cost of capital for additional funds is 8% for $40,000 and 9% for the next 60,000 and the lending rate (if the company wants to lend their money) is 6% Assume that the company

has an investment budget of (i) $60,000 on hand and (ii) $0 on hand, and that there is no partial

project investment, what is the best investment strategy and MARR in each case? (Note in both

cases, additional borrowing is allowed if it is beneficial to do so.)

Draw an Investment Opportunity Schedule (IOS) and Marginal Cost of Capital (MCC) below.

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3b) Again with the firm budget of $80,000 (no additional borrowing, allowed) formulate (but DO NOT

solve) an integer programming model to help determine an optimal portfolio of the above projects

based on maximizing the present worth at 8.5%. Also, the following conditions must be observed.

Projects1, 4 and 6 are mutually exclusive, and project 5 cannot be taken without either project 2 or 3

taken.

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4. (10 points) A machine has the first cost of $60K. The net annual savings (which depends on the

volume of throughput) and the salvage value at the end of its 8-year economic life (which depends on

the progress in related technology) are given below:

Volume of throughput

High Medium Low

Probability 0.3 0.6 0.1

Annual Savings AS $30K $20K $10K

Rate of technological progress

Incremental Revolutionary

Probability 0.75 0.25

Salvage S $9K $3K

Assume that the progress in technology and the level of throughput volume are independent, and

MARR is 10%.

a) Write the probability distribution of EAW, then compute the expected EAW, the standard deviation

of EAW and the probability the there will be a loss in this investment. You may first write down

the following formula:

EAW(10%) =……………………………………………………………………..

Then fill in the following table: (Note: (A/P, 10%, 8) = 0.1874; (A/F, 10%, 8) = 0.0874)

Combination:

AS ($K) S($K) Prob EAW ($) Prob*EAW Prob*EAW2

30 9 0.225 19,543 4,397 85,304,473

____ ____ ____ _____ _______ ________

____ ____ ____ _____ _______ ________

20 3 0.15 9,018 1353 12,199,190

10 9 0.075 -457 -34 15,691

10 3 0.025 -982 -25 24,098

Sum: _______ ________

E(EAW) =_________________

SD(EAW) =_________________

b) Is this a good investment based on your own return/risk trade-off? Why or why not? If the distribution of PW is approximately normal, what is the probability of loss? (Table of Standard

Normal distribution is given.)

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5. (15 points) A new device is being purchase for a certain project in a local community. The following

financial parameters have been estimated:

Initial cost $100,000

Annual savings (AS) $20,000

Useful life (N) 10 years

Salvage value (end of 10 years) $30,000

MARR (annual) 10%

There is considerable uncertainty surrounding the estimates of annual savings--- between -20% and

+25%, and useful life---7 years to 12 years.

a) Construct the best and worst scenarios

b) Draw a spider plot (PW v.s. %), and conclude whether any of the two is sensitive, and which of the two is more sensitive. First compute the following: (Interest Table for 10% is given)

Nominal PW = -100K+ 30K*(P/F,10%,10) +20K*(P/A,10%,10) =$34,458

PW(AS=80% )= -100K+30K*(P/F,10%,10)+16K*(P/A,10%,10) =$9,879

PW(AS=125% )= -100K+30K*(P/F,10%,10)+25K*(P/A,10%,10) =$65,180

PW(N=70% )= -100K+30K*(P/F,10%,___)+20K*(P/A,10%,___) =______________________

PW(N=120% )= -100K+30K*(P/F,10%,___)+20K*(P/A,10%,___) =______________________

Then draw the spider plot and determine whether (i) PW is sensitive to either parameter and (ii) the

decision is sensitive to either parameter.

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c) Suppose we know that AS is distributed as a triangular distribution with the minimum value = $16K,

the most likely value = $20K and the maximum value = $25K. Suppose we also know that integer N is

uniformly distributed between 7 years to 12 years. Use the following independent uniform random

number series to generate 5 scenarios (i.e. 5 replications of AS using the first series beginning from

left, and 5 replications of N using the second series beginning from left also). Then compute PW at

10% MARR under the five simulated scenarios and the average PW. Compare this with the nominal

PW in part (c) and comment

Uniform random numbers to generate AS and N (begin from left to right):

Series 1: 0.2350 0.9043 0.0418 0.7504 0.1237 0.4578 0.9887 0.7681 0.0348 0.5612...

Series 2: 0.0965 0.9665 0.6484 0.4922 0.4950 0.1014 0.4845 0.2350 0.9043 0.0418...

.Scenario: AS N PW

1 ________ ___ _________

2 ________ ___ _________

3 ________ ___ _________

4 ________ ___ _________

5 ________ ___ _________

Average PW _________

1: If is distributed according to a triangular distribution with min = , most likely = and max = ,

we generate (an instance of ) by first generate (0,1)

Then, if 0 , set

X a b c

x X u U

b a u x a

c a

   

 ( )( )

and if 1, set (1 )( )( )

2 : If a discrete is distributed according to a discrete distribution ( ) , 1, ..,

or with the cummulative distribution of ( )

i i

i

u c a b a

b a u x c u c a c b

c a

X Pr X x p i m

F x c

  

       



  

 1 2

1

, where +...

we generate (an instance of ) by first generate (0,1).

Then, if , set

i i i

i i i

c p p p

x X u U

c u c x x 

 

  

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Large (L)

Small (S)

Large (L|F)

Small (S|F)

No Extraction

Extract

Large (L|U)

Small (S|U)

No Extraction

Extract

Extract without the test well

Dig the test well

Favorable (F)

Unfavorable (U)

Note: (P/A,15%,56) = 6.6640; (P/A,15%,14) =5.7245;

(P/F,15%,56) = 0.0004; (P/F,15%,14) =0.1403

6. (15 points) Crain Energy announced that it has discovered oil in an oil exploration well in Northwestern

India. Initial estimates placed the find between 50 million and 200 million barrels of recoverable oil. To

extract the oil, there is a $400M investment in the field and a $50M remediation cost at the end of the

project. Regardless of the size of the reserve, the net annual revenue of $66M per year can be expected.

However, at the constant extraction rate of 10,000 barrels per day, the smaller reserve will last 14 years,

while the larger reserve 56 years. The chance of hitting a large reserve is 60% and the chance of hitting a

small reserve is 40%. Assume the interest rate is 15%. Before making the initial investment to extract

oil, Crain Energy has the option of digging an appraisal well and performs additional seismic testing to

better understand the amount of reserves. Assume that the testing can be characterized as “Favorable---F”

or “Unfavorable---UF”. More important we know that the test will predict “Favorable” if it is actually

large 90% of the time, and it will predict “Unfavorable” if the well is actually small 80% of the time.

The corresponding decision tree is as follows:

The following computations provide the necessary conditional, marginal and other probabilities. Fill in the

missing entries

Testing Result Prior Joint probability

Favorable F Unfavorable U Probability Favorable F Unfavorable U

Large reserve (L) 0.90 0.10 0.60 0.54 …….

Small reserve (S) 0.20 0.80 0.40 …… 0.32

…….. …… Marginal Pr

Pr(F) Pr(U)

Large reserve (L) Pr(L|F) …… .….. P(L|U)

Small reserve (S) Pr(S|F) …… .….. P(S|U)

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a) Write down all cash flows and probabilities on the tree. Then perform all the necessary roll-back

calculations on the decision tree

b) If the test costs $1M, what would be your optimal strategy?

c) What is the maximum worth of the test (i.e. find EVSI)? And also, what is the value of perfect

information (EVPI)?

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7) (15 points) A new machine costs $25,000 and has the estimated maximum (physical) life of 5 years. It

also has the estimated salvage (market) value (S) and operating and maintenance costs (O&M) in each

of the 5 years of use as shown below:

Year n Sn O&Mn EACn MCn 0 $25,000

1 $16,000 $5,000 $16,000 $16,000

2 $13,000 $8,000 $14,212 $12,280

3 $11,000 $11,000 $14,159 $14,040

4 $10,000 $14,000 $14,541 $15,880

5 $9,500 $17,000 $15,181 $18,300

Suppose the MARR is 8%. The EACn for keeping the machine n years and the marginal cost MCn of

keeping the machine 1 more year during year n can be computed as shown above

a) Verify that the EAC for keeping the machine 2 years is indeed $14,212, and the marginal cost of keeping it 1 more year during year 4 is $15,880 as shown.

b) What is the economic life of this new machine and what is the corresponding EAC?

c) If the machine has been used for 2 years and if there is a new machine which can do a similar job with the EAC at its economic useful life being $16,500, when should the defender be replaced?

Assume that the machine (old or new) will be needed for a long time.

d) Suppose there is no technological change and the candidate for the challenger is exactly the same model as the defender (except it is new of course). Suppose also that the defender has been used

for two years and the machine (old or new) will be needed for a long (infinite) time. Determine if

and when the defender should be replaced using the PW method. First state why we need to

consider only 4 mutually exclusive options.

Answer:………………………………………………………………………….

Then answer the replacement question by first filling the missing entry in the following table:

Option Replace defender PW(8%)

1 Now ……….

2 ……………… ……….

3 2 years from now 177,488

4 3 year from now 181,633

Thus the defender should be replaced………….year(s) from now.

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8. (10 points) Suppose we have to choose from 7 mutually exclusive options based on the expected present

worth (PW), risk level as measured by expected standard deviation of PW--SD, and the probability of

loss---Pr(PW<0). After performing the necessary simulation, we have the following estimated values for

each of the 7 options:

Option # PW ($K) SD ($K) Pr(PW<0)

1 27 8 10%

2 25 11 5%

3 29 8 9%

4 24 6 8%

5 28 10 9%

6 24 7 9%

7 23 12 6%

a) Identify the set of non-dominated options (efficient frontier)

b) Among the efficient options that remain, normalize/scale the score of each of the three attributes using the respective range of the attribute’s values method. Place you results in the following table of

normalized/scaled scores:

Option # Normalized PW Normalized SD Normalized Pr(PW<0)

c) In assessing relative importance of the three attributes considered, if PW is assessed to be three times more important than SD, and four time more important than Pr(PW<0), compute the numerical weights

for the three attributes.

d) Based on your results in parts (b) and (c), which option would you finally select?