Q. No.Ex-1

23

Prob-1234568

10

Topic CoveredEV & SD of the project & probability of various NPVs of dependent projectsEV and SD of the probability distribution of the possible consisting existing & new productsCash flows with probability of success and failure, investment inbetween & NPV analysisExpected vaklue & Standard deviation of the project & probability of various NPVsEV & SD of the project & probability of various NPVs of independent dependent projectsJoint probability and calculation of NPVMean NPV & calculation of SDDominance of one project over the other, probability of NPV greater than zeroComparision of projects interms of NPV and SDNPV analysis and investment in between the life of the project, probability analysis & NPVJoint probability and calculation of mean NPV

Q1-Gomez Drug Product Company could invest in a new drug investment project with an estimated life of three years. If the demand for the new drug in the first period is favorable, it is almost certain that it will be favorable in periods 2 and 3. By applying the same token, if demand is low in the first period, it will be low in the two subsequent periods as well. Owing to this likely demandrelationship, an assumption of perfect correlation of the cash flows over time is appropriate.The cost of the project is $1 million and possible cash flows of the three periods are:

Period 1 Period 2 Period 3Probability Cash Flows Probability Cash Flows Probability Cash Flows

0.10 - 0.15 100,000 0.15 - 0.20 200,000 0.20 400,000 0.20 150,000 0.40 400,000 0.30 700,000 0.30 300,000 0.20 600,000 0.20 1,000,000 0.20 450,000 0.10 800,000 0.15 1,300,000 0.15 600,000

a- Assuming that risk-free rate is 8 percent and that it is used as discount rate, calculatethe expected value and standard deviation of probability distribution of possible net present values.

b- Assuming a normal distribution, what is the probability of the project providing a net present value of (1) zero or less ? (2) 300,000 or more ? (3) 1,000,000 or more ?

c- is the standard deviation calculated larger or smaller than it would be under assumption of independence of cash flows over time?

Ans1a- Expected ValuePeriod 1 Expected Period 2 Expected Period 3 Expected

Probability Cash Flows Value Probability Cash Flows Value Probability Cash Flows Value0.10 - - 0.15 100,000 15,000 0.15 - - 0.20 200,000 40,000 0.20 400,000 80,000 0.20 150,000 30,000 0.40 400,000 160,000 0.30 700,000 210,000 0.30 300,000 90,000 0.20 600,000 120,000 0.20 1,000,000 200,000 0.20 450,000 90,000 0.10 800,000 80,000 0.15 1,300,000 195,000 0.15 600,000 90,000

400,000 700,000 300,000

Standard DeviationPeriod 1 (CF - Mean)^2 X Period 2 (CF - Mean)^2 X Period 3 (CF - Mean)^2 X

Probability Cash Flows Probability Probability Cash Flows Probability Probability Cash Flows Probability0.10 - 16,000,000,000 0.15 100,000 54,000,000,000 0.15 - 13,500,000,000 0.20 200,000 8,000,000,000 0.20 400,000 18,000,000,000 0.20 150,000 4,500,000,000 0.40 400,000 - 0.30 700,000 - 0.30 300,000 - 0.20 600,000 8,000,000,000 0.20 1,000,000 18,000,000,000 0.20 450,000 4,500,000,000 0.10 800,000 16,000,000,000 0.15 1,300,000 54,000,000,000 0.15 600,000 13,500,000,000

Sum of all prob = a 48,000,000,000 Sum of all prob = a 144,000,000,000 Sum of all prob = a 36,000,000,000

Square Root of a = σ 219,089 Square Root of a = σ 379,473 Square Root of a = σ 189,737 Ans1b-

The standard deviation of the probability distribution of possible net present value under assumption of perfect correlation of cash flowsover time:

σ = 219,089 + 379,473 + 189,737(1.08)^1 (1.08)^2 (1.08)^3

σ = 219,089 + 379,473 + 189,7371.080 1.166 1.260

σ = 202,860 + 325,337 + 150,619

678,816The mean net present value of the project =

NPV = -1,000,000 + 400,000 + 700,000 + 300,000(1.08)^1 (1.08)^2 (1.08)^3

NPV = -1,000,000 + 400,000 + 700,000 + 300,0001.080 1.166 1.260

-1,000,000 370,370 + 600,137 + 238,150

208,657

σ = X - NPV

Probability σ

Zero or less 0 - 208657 = -208,657 -0.307678,816 678,816

300,000 or more = 300000 - 208657 = 91,343 0.135678,816 678,816

1,000,000 or more = 1000000 - 208657 = 791,343 1.166678,816 678,816

Ans1c-From Table C, these standardized differences corresponds to the probabilities of 0.38, 0.45 and 1.2,respectively. The standard deviation calculated under this assumption is much larger than under anassumption of independence of cash flows over time.

Q2-Zell Company would like a new product line- Puddings. The expected value of standard deviationof the probability distribution of of possible net present value for the product line are $12,000 and 9,000respectively. The company existing lines are, ice cream, cottage cheese and yogurt. The expected valueof the net present value and standard deviation for the product lines are:

Net Present Value σIce Cream 16000 8,000 Cottage Cheese 20000 7,000 Yogurt 10000 4,000

The correlation coefficient between the products are:

Ice Cream Cottage Cheese Yogurt PuddingsIce Cream 1.00Cottage Cheese 0.90 1.00Yogurt 0.80 0.84 1.00Puddings 0.40 0.20 0.30 1.00

a- Compute the expected value and standard deviation of the probability distribution of the possiblenet present values for a combination consisting existing products.

b- Compute the expected value and standard deviation for a combination consisting of existing productplus Puddings. Compare your results in part a and b. What can you say about the pudding line.

Ans2a- Existing ProductExpected Net Present Value

Product Net Present ValueIce Cream 16000

Cottage Cheese 20000Yogurt 10000

46000

Standard Deviation

Standard deviation =

((8000^2+(2 X 8000 X 7000 X 0.9)+7000^2+(2 X 8000 X 4000 X 0.8)+4000^2+(2 X 7000*4000 X 0.84)))

328040000

18,112

Ans2a- Existing Product Plus PuddingExpected Net Present Value

Product Net Present ValueIce Cream 16000Cottage Cheese 20000Yogurt 10000Pudding 12000

58000

Standard Deviation

( (σ12 + (2 X (σ1 X σ2) X 0.9) + σ2

2 + (2 X (σ1 X σ3) X 0.8) + σ3

2 + (2 X (σ2 X σ3) X 0.84) )(1/2)

Standard deviation =

((8000^2+(2 X 8000 X 7000 X 0.9)+7000^2+(2 X 8000 X 4000 X 0.8)+4000^2+(2 X 7000*4000 X 0.84)))+((9000^2+(2 X 8000 X 9000 X 0.4)+(2 X 7000 X 9000 X 0.2)+(2 X 4000 X 9000 X 0.3)))

513440000

22,659

( (σ12 + (2 X (σ1 X σ2) X 0.9) + σ2

2 + (2 X (σ1 X σ3) X 0.8) + σ3

2 + (2 X (σ2 X σ3) X 0.84) +

( (σ42 + (2 X (σ1 X σ4) X 0.4) + (2 X (σ2 X σ4) X 0.2) + (2 X (σ3 X σ4) X 0.3) )(1/2))

Q3-Feldstein Drug Company is considering a new drug, which would be sold over the counterwithout a prescription. To develop the drug and to market it on regional basis will cost $12million over the next 2 years. $6 million in each year. Expected cash flows associated with the project for years 3 through 8 are $1 million, $2 million, $4 million, $4 million, $3 million, and $1 million, respectively. If the product is not successful at the end of year 5, the companyhas an option to invest additional $10 million and there will be no expected incrementalcash flows. If successful, however, cash flows are expected to $6 million higher in each of the years 6through 10 than would otherwise be the case with a probability of .5 and $4 million higher with a probability of .5. the company's required rate of return for the project is 14 percent.

a- What is the net present value of the project if it is acceptable?

b- What is the worth of the project if we take account of the option to expand? Is the project acceptable

Success Success FailureAns3- 50% of 60% chance 50% of 60% chance 50% of 40% chance

Year Cash Flow DF 14% PV Add Inv PV Add Inv PV1 - 6,000,000 0.877 - 5,263,158 2 - 6,000,000 0.769 - 4,616,805 3 1,000,000 0.675 674,972 4 2,000,000 0.592 1,184,161 5 4,000,000 0.519 2,077,475 - 10,000,000 - 5,193,687 - 10,000,000 - 5,193,687 6 4,000,000 0.456 1,822,346 6,000,000 2,733,519 4,000,000 1,822,346 7 3,000,000 0.400 1,198,912 6,000,000 2,397,824 4,000,000 1,598,549 8 1,000,000 0.351 350,559 6,000,000 2,103,354 4,000,000 1,402,236 9 0.308 6,000,000 1,845,048 4,000,000 1,230,032

10 0.270 6,000,000 1,618,463 4,000,000 1,078,975

Worth of the project NPV - 2,571,539 5,504,521 1,938,452 -

0.3 0.3 0.4

1,651,356 581,536 -

- 2,571,539 Worth of the option (NPV) 2,232,892

Worth of the project with option - 338,647

Conclusion: While the option's value raises the worth of the project, it does not entirely set off the initial project's negative NPV.Therefore, we still would rejected the project.

Prob1-The probability distribution of the possible net present values for project X has an expected value of $20,000 and a standard deviation of $10,000. Assuming a normal distribution, calculate the probability that the net present value will be zero or less,that it will be greater than $30,000; and that it will be less than $5,000.

Ans1-Probability of NPV σ = X - NPV

σ

Zero or Less = 0 - 20000 -20,000 -2.010,000 10,000

30,000 or more = 30000 -20000 10,000 1.010,000 10,000

5,000 or more = 5000 - 20000 -15,000 -1.510,000 10,000

From Table C, these standardized differences corresponds to the probabilities of 0.228, 0.1577, and 0.668 respectively.

Prob2-The Dewitt Corporation has determined the following decrease probability distributionsfor the net cash flows generated by a contemplated project.

Period 1 Period 2 Period 3

Probability Cash Flows Probability Cash Flows Probability 0.10 1,000 0.20 1,000 0.30 1,000 0.20 2,000 0.30 2,000 0.40 2,000 0.30 3,000 0.40 3,000 0.20 3,000 0.40 4,000 0.10 4,000 0.10 4,000

a- Assume that probability distribution of cash flows for future periods are independent.Also, assume that risk-free rate is 7 percent. If the initial outlay of $5,000, determine themean net present value.b- Determine the standard deviation about the mean.c- if total distribution is approximately normal and assumed continuous, what is the probability that the net present value being zero or less?d- What is the probability that net present value will be greater than zero?e- What is the probability that the profitability index will be 1.00 or less?f- What is the probability that the profitability will be greater than 2.00?

Ans2a- Calculation of NPVPeriod 1

Probability Cash Flows Exp. Val0.10 1,000 100.00 0.20 2,000 400.00 0.30 3,000 900.00 0.40 4,000 1,600.00

3,000.00

Period 2Probability Cash Flows Exp. Val

0.20 1,000 200.00 0.30 2,000 600.00 0.40 3,000 1,200.00 0.10 4,000 400.00

2,400.00

Period 3Probability Cash Flows Exp. Val

0.30 1,000 300.00 0.40 2,000 800.00 0.20 3,000 600.00 0.10 4,000 400.00

2,100.00

Period Cash Flows DF PV0 - 5,000 1.00 - 5,000 1 3,000 0.93 2,804 2 2,400 0.87 2,096 3 2,100 0.82 1,714

Cash Flows

NPV 1,614

Ans2b-Calculation of Standard DeviationSince, the Cash flows over the period are independent and not dependent, formula for calculating the standard deviation would be different and would be as follows:

σ =

Period 1Probability Cash Flows CF - Mean Sq(CF - Mean) Sq(CF - Mean) X Prob

0.10 1,000 - 2,000.00 4,000,000.00 400,000.00 0.20 2,000 - 1,000.00 1,000,000.00 200,000.00 0.30 3,000 - - - 0.40 4,000 1,000.00 1,000,000.00 400,000.00

1,000,000.00

1000Period 2

Probability Cash Flows CF - Mean Sq(CF - Mean) Sq(CF - Mean) X Prob0.20 1,000 - 1,400.00 1,960,000.00 392,000.00 0.30 2,000 - 400.00 160,000.00 48,000.00 0.40 3,000 600.00 360,000.00 144,000.00 0.10 4,000 1,600.00 2,560,000.00 256,000.00

840,000.00

917Period 3

Probability Cash Flows CF - Mean Sq(CF - Mean) Sq(CF - Mean) X Prob0.30 1,000 - 1,100.00 1,210,000.00 363,000.00 0.40 2,000 - 100.00 10,000.00 4,000.00 0.20 3,000 900.00 810,000.00 162,000.00 0.10 4,000 1,900.00 3,610,000.00 361,000.00

890,000.00

943

Sum of 1000^2 917^2 943^2(1.07)^(1 X 2) (1.07)^(2 X 2) (1.07)^(2 X 3)

= 1000000 840889 8892491.1449 1.31079601 1.500730351849

= 873,439 641,510 592,544

= 2,107,493

= 1452

Ans2c- Probability of NPV Zero or LessProbability of NPV σ = X Value

σ

Zero or Less = 0 - 16141,452

1,6141,452

Standard Deviation = 1.1

Probability = 0.134

Ans2d- Probability of NPV greater than Zero

= 1 - Probability of NPV Zero or Less

= 1- 0.134

0.866

Ans2e- The probability that the profitability index will be 1.00 or less

Profitability index is 1 when NPV is Zero, thus, the probability that theprofitability index is 1 is 0.134

Ans2e- The probability that the profitability will be greater than 2.00

If Profitability Index is 2, then NPV is 0 + 5,000 = 5,000

Therefore, NPV = 5000 - 1614

1,452

3,3861,452

Standard Deviation 2.3

Probability 0.01 or 1 Percent

Prob3-Ponape Lumber Company is evaluating a new saw with a life of 2 years. The sawcosts $3,000 and future after tax cash flows depend on the demand for the company'sproduct. The probability tree of possible future cash flows associated with the new saw is:

Year 1 Year 2

Cash Flows Cash Flows Branch

0.3 1000 10.4 1500 0.4 1500 2

0.3 2000 3

0.4 2000 40.6 2500 0.4 2500 5

0.2 3000 6

a- What are the joint probabilities of occurrence of various branches?

b- if the risk-free rate is 10 percent, what are the mean and standard deviation of the probability distribution possible net present values?

c- Assuming a normal distribution, What is the probability that the actual net present value will be zero or less?

Ans3a-Year 1 Year 2

Cash Flows Cash Flows Branch

0.3 1000 1 0.120.4 1500 0.4 1500 2 0.16

0.3 2000 3 0.12

0.4 2000 4 0.240.6 2500 0.4 2500 5 0.24

0.2 3000 6 0.12

Mean NPV YearsYear 0 1 2

DF 10% 1.000 0.909 0.826Branch NPV Con. Prob Mean NPV

1 - 3,000 1,364 826 - 810 0.12 - 97 2 - 3,000 1,364 1,240 - 397 0.16 - 63 3 - 3,000 1,364 1,653 17 0.12 2 4 - 3,000 2,273 1,653 926 0.24 222 5 - 3,000 2,273 2,066 1,339 0.24 321 6 - 3,000 2,273 2,479 1,752 0.12 210

Initial Probability

Conditional probability

Initial Probability

Initial Probability

Conditional probability

Joint Probabilities

Mean NPV 595

Standard Deviation

A B C = (A -B) E F = D X EBranch Net C.F Mean NPV Con. Prob

1 - 810 595 - 1,405 1,973,909 0.12 236,869 2 - 397 595 - 992 983,539 0.16 157,366 3 17 595 - 579 334,677 0.12 40,161 4 926 595 331 109,282 0.24 26,228 5 1,339 595 744 553,241 0.24 132,778 6 1,752 595 1,157 1,338,706 0.12 160,645

754,047

Square Root 868 Ans3a-

The probability of NPV zero or less = 0 - NPV

σ

0 - 595868

-595868

-0.6854839

After checking from table C, we find -0.68548 falls between .65 and .70These standard deviation correspond to areas under the curve of .2578 & .2420, respectively

Where,0.68548 = Standardized deviation

0.65 = Lower Standard Deviation0.7 = Higher Standard Deviation

0.2578 = Area of the lower standard deviation0.242 = Area of the higher standard deviation

Applying interpolation method, we have

.2578 - (.2578-.2420) X ((.68548 - .65) / (.7 - .65))

0.246588 X 100 24.66%

Conclusion: Thus, there is approximately 25 percent probability that actual return will be zero or less

D = C2

Prob4-Xonic Graphic is evaluating a new technology for its reproduction equipment. The technology will have a 3-year lifeand cost $1,000. its impact on cash flows is subject to risk. Management estimates that there is 50-50 chance that technology will either save the company $1,000 in the first year or save it nothing at all. if nothing at all, savings in the last 2 years would be zero. Even worse, in the second year, an additional outlay of $300 may be required to convert back to original process, for the new technology may result in less efficiency. Management attaches a 40 percent probability to this occurrence, given the fact that new technology "bombs out" in the first year. If the technology proves it self, the second-year cash flows may be either $1,800, $1,400 or $1,000 with probabilities of 0.2, 0.6 and 0.2, respectively. In the third-year cash flows are expected to be $200 greater or $200 less than the cash flows in the period 2, with an equal chance of occurrence. (Again these cash flows depend on the cash flows in the period 1 being $1,000). All cash flows are after tax.

a- set up a probability tree to depict the foregoing cash flow probabilities.b- Calculate a net present value for each three-year possibility, using a risk-free rate of 5 percent.c- What is the risk of the project?

Ans4a- Requirement A Requirement BDF 1 0.952 0.907 0.864

Period 0 Period 1 Period 2 Period 3 OverallCash Flow Cond. Prob Cash Flow Cond. Prob Cash Flow Cond. Prob Cash Flow Cond. Prob Cash Flow Joint Prob. NPV Exp. Val

0.5 0 0.4 -300 1.0 0 0.2 - 1,272 - 254

0.6 0 1.0 0 0.3 - 1,000 - 300 -1000 -1000

0.5 800 0.05 1,550 78 0.2 1000

0.5 1200 0.05 1,896 95

0.5 1000 0.5 1200 0.15 2,259 339 0.6 1400

0.5 1600 0.15 2,604 391

0.5 1600 0.05 2,967 148 0.2 1800

0.5 2000 0.05 3,313 166

661

Ans4c- Risk of the project = σJoint Prob. NPV Mean NPV (NPV -Mean NPV)^2 X Prob

0.20 (1,272) 661 747,672 0.30 (1,000) 661 828,051 0.05 1,550 661 39,525 0.05 1,896 661 76,217 0.15 2,259 661 382,778 0.15 2,604 661 566,280 0.05 2,967 661 265,835 0.05 3,313 661 351,478

3,257,837

Square Root 1805

Conclusion: Thus, the distribution of possible probability distribution of possible net present values is very wide. In turn, this is due to a 50 percent probability of zero outcome or less.

Prob5-The Hume Corporation is faced with several possible investment projects. For each, the totalcash out flow required will occur in the initial period. The cash outflow, expected net presentvalues, and standard deviations are as follows:( All projects are discounted at risk-free rate of 8 percent, and it is assumed that distributionof their possible net present values are normal.)

Project Cost Net Present Value σA 100,000 10,000 20,000 B 50,000 10,000 30,000 C 200,000 25,000 10,000 D 10,000 5,000 10,000 E 500,000 75,000 75,000

a- Determine the coefficient of variations for each of these projects. (use cost plus net present value in the denominator of the coefficient.)

b- Ignoring sizes, do you find some projects clearly dominated by others?

c- May size be ignored?

d- What is the probability that each of these projects will have a net present value greater than 0 ?

e- What decision rule would you suggest for adoption of projects within this context? Which (if any)of the forgoing projects would be adopted under your rule?

Ans5a- Coefficient of Variations

Project Cost Plus NPV σ Co of Var.A 110,000 20,000 0.18B 60,000 30,000 0.50C 225,000 10,000 0.04D 15,000 10,000 0.67E 575,000 75,000 0.13

Ans5b- Domination of one project by other(s)A project is dominated by the other if its Cov. of Var. is greater than that of other.

Project A Dominated by project E & CProject B Dominated by project A, C, and EProject C Dominated by None of the others.Project D Dominated by all the projectsProject E Dominated by Project C

Ans5c- Size of the projectSize can not be ignored in a Realistic System

Ans5d- Probability of Project greater than zero

Project NPV/σ Prob of Zero Prob > 0A 0.50 0.3085 0.692B 0.33 0.37 0.630C 2.50 0.0062 0.994D 0.50 0.3085 0.692E 1.00 0.1577 0.842

Ans5e- Decision rule suggestion for adoption of projectsAlthough most people would prefer project C. However,No solution may be recommended.

Prob6-The Windop Company will invest in two of three possible proposals, the cash flows ofwhich are normally distributed. The expected net present value (discounted at riskfree rate) and the standard deviation of each proposal are given as follows:

Proposals 1 2 3Expected net present value 10000 8000 6000Standard deviation 4000 3000 4000

Assume the following correlation coefficients for each possible combination, which two proposals dominate?

Proposals 1 2 3 1 and 2 1 and 3 2 and 3Correlation Coefficient 1.0 1.0 1.0 0.6 0.4 0.7

Expected net present value NPVAns6- Proposal 1 & 2 10000 8000 18000

Proposal 1 & 3 10000 6000 16000

Proposal 2 & 3 8000 6000 14000

Standard deviation =

σ Proposal 1 & 2 =

= 6277

σ Proposal 1 & 3 =

= 6693

σ Proposal 2 & 3 =

= 6465

NPV SDProject-1 18,000 6,277 Project-2 16,000 6,693 Project-3 14,000 6,465

Conclusion: Proposal 1 & 2 have both highest NPV and lowest standard deviation, therefore,these dominate in all other proposals' combination

(σ1^2 + (2 X (σ1 X σ2) X 0.6) + σ2^2)^(1/2)

(4000^2 + (2 X (4000 X 3000) X 0.6) + 3000^2)^(1/2)

(4000^2 + (2 X (4000 X 4000) X 0.4) + 4000^2)^(1/2)

(3000^2 + (2 X (3000 X 4000) X 0.7) + 4000^2)^(1/2)

Prob8-The Ferret Company is considering a new location. If it constructs an officeand 100 cages, the cost will be $100,000 and the project is likely to producenet cash flows of $17,000 per year for 15 years, after which the leasehold on land expires and there will be no residual value. The company's requiredrate of return is 18 percent. If the location proves favorable, Ferret pet willbe able to expand by 100 cages at the end of 4 years. The cost per cage would be $200 With the new cages, incremental cash flows of $17,000 per year for years 5 through 15 would be expected. The company believes there is a 50-50chance that the location will prove to be a favorable one.

a- if the initial project favorable?

b- What is the value of the option? The worth of the project with the option? Is it acceptable?First Approach Second Approach

Ans8a- Ans8a-Year Cash Flows DF 18% PV Year Cash Flows DF 18% PV

0 -100000 1.000 - 100,000 0 -100000 1.000 - 100,000 1 17000 0.847 14,407 17000 5.092 86,557 2 17000 0.718 12,209 3 17000 0.609 10,347 NPV - 13,443 14 17000 0.516 8,768 5 17000 0.437 7,431 Conclusion: Initially project is unacceptable since, NPV is negative6 17000 0.370 6,297 7 17000 0.314 5,337 Ans8b-8 17000 0.266 4,523 Option Valuation:9 17000 0.225 3,833

10 17000 0.191 3,248 Year Cash Flows DF 18% PV11 17000 0.162 2,753 4 -20000 0.516 - 10,316 12 17000 0.137 2,333 5 - 15 17000 2.402 40,826 13 17000 0.116 1,977 14 17000 0.099 1,675 NPV 30,510 0.515 17000 0.084 1,420 The Worth of the project with the Option:

NPV - 13,443 NPV X 0.5 + NPV X 0.5

- 13,443 + 30,510 X 0.5

1,812

Conclusion: The value of the option enhances the worth of the project and make it acceptable

1 - 15 .

Prob10- ABC Corporation is ordering a special purpose piece of machinery costing $9,000 with a useful life of 2 years, after which there is no expected salvage value. The possible incremental net cash flows are:

Year 1 Year 2

Probability Cash Flow 2,000 0.3

6,000 0.3 3,000 0.5 4,000 0.2

4,000 0.3 7,000 0.4 5,000 0.4

6,000 0.3

6,000 0.2 8,000 0.3 7,000 0.5

8,000 0.3

The company’s required rate of investment for this project is 8 percent.

a- Calculate the mean of the probability distribution of the possible net present values.

b- Suppose now that the possibility of abandonment exists and that the abandonment

the company abandons the project if it is worth while to do so. Compare your calculations with those in part a. What are the implications.

Ans10a-Year 1 Year 2

Probability Cash Flow 2,000 0.3 0.09

6,000 0.3 3,000 0.5 0.15 4,000 0.2 0.06

4,000 0.3 0.12 7,000 0.4 5,000 0.4 0.16

6,000 0.3 0.12

6,000 0.2 0.06 8,000 0.3 7,000 0.5 0.15

8,000 0.3 0.09

1.00

Cash Flow

Conditional Probability

value of the project at the end of year 1 is $4,500. Calculate the new mean NPV, assuming

Cash Flow

Conditional Probability

Joint probabilities

Year 0 1 2

DF 1.000 0.926 0.857Net C.F Mean NPV

Branch 1 - 9,000 6,000 2,000 - 9,000 5,556 1,715 - 1,730 0.09 - 155.68

2 - 9,000 6,000 3,000 - 9,000 5,556 2,572 - 872 0.15 - 130.86

3 - 9,000 6,000 4,000 - 9,000 5,556 3,429 - 15 0.06 - 0.91

4 - 9,000 7,000 4,000 - 9,000 6,481 3,429 911 0.12 109.30

5 - 9,000 7,000 5,000 - 9,000 6,481 4,287 1,768 0.16 282.91

6 - 9,000 7,000 6,000 - 9,000 6,481 5,144.0 2,626 0.12 315.06

7 - 9,000 8,000 6,000 - 9,000 7,407 5,144 3,551 0.06 213.09

8 - 9,000 8,000 7,000 - 9,000 7,407 6,001 4,409 0.15 661.32

9 - 9,000 8,000 8,000 - 9,000 7,407 6,859 5,266 0.09 473.95

Mean Net Present Value 1.00 1768

Ans10b- Project worth = NPV without abandonment option + Value of abandonment Option

The value of the project at the end of year 1 is $4,500.00 0.926 $4,167 DF 1.000 0.926 0.857

Branch 1 - 9,000 10,500 - 9,000 9,722 - 722 0.30 216.67

2 - - - - 0.15 -

3 - - - - 0.06 -

4 - 9,000 7,000 4,000 - 9,000 6,481 3,429 911 0.12 109.30

5 - 9,000 7,000 5,000 - 9,000 6,481 4,287 1,768 0.16 282.91

6 - 9,000 7,000 6,000 - 9,000 6,481 5,144.0 2,626 0.12 315.06

7 - 9,000 8,000 6,000 - 9,000 7,407 5,144 3,551 0.06 213.09

8 - 9,000 8,000 7,000 - 9,000 7,407 6,001 4,409 0.15 661.32

9 - 9,000 8,000 8,000 - 9,000 7,407 6,859 5,266 0.09 473.95

Mean Net Present Value 2272

Conclusion: The present value of the abandonment value at the end of year 1 is $4,167. Therefore, the project would be abandoned if the period 1 cash flows turned out to be $6,000. ( The mean of present value for period 2 is lower than the abandonment value.) It would not be worthwhile to abandon the project if either of the other year outcomes occurred. The present value of cash flows are the same as in part a's solution except for the main branch which has a mean NPV of $723.

Thus, the mean net present value is increased when the probability of abandonment is considered in the evaluation.

Prob10- ABC Corporation is ordering a special purpose piece of machinery costing $9,000 with a useful life of 2 years, after which there is no expected salvage value. The possible incremental net cash flows are:

Year 1 Year 2

Cash Flow Probability Cash Flow 2,000 0.3

6,000 0.3 3,000 0.5 4,000 0.2

4,000 0.3 7,000 0.4 5,000 0.4

6,000 0.3

6,000 0.2 8,000 0.3 7,000 0.5

8,000 0.3

The company’s required rate of investment for this project is 8 percent.

a- Calculate the mean of the probability distribution of the possible net present values.

b- Suppose now that the possibility of abandonment exists and that the abandonment

the company abandons the project if it is worth while to do so. Compare your calculations with those in part a. What are the implications.

Ans10a-Year 1 Year 2

Cash Flow Probability Cash Flow 2,000 0.3 0.09

6,000 0.3 3,000 0.5 0.15 4,000 0.2 0.06

4,000 0.3 0.12 7,000 0.4 5,000 0.4 0.16

6,000 0.3 0.12

6,000 0.2 0.06 8,000 0.3 7,000 0.5 0.15

8,000 0.3 0.09

1.00

Conditional Probability

value of the project at the end of year 1 is $4,500. Calculate the new mean NPV, assuming

Conditional Probability

Joint probabilities

Branches Year DF 1 2 3 4 5

0 1.000 - 9,000 - 9,000 - 9,000 - 9,000 - 9,000 1 0.926 6,000 6,000 6,000 7,000 7,000 2 0.857 2,000 3,000 4,000 4,000 5,000

NPV - 1,730 - 872 - 15 911 1,768 Joint Prob. 0 0.15 0.06 0.12 0.16

Mean NPV - 156 - 131 - 1 109 283

Ans10b- Project worth = NPV without abandonment option + Value of abandonment Option

Branches Year DF 1 2 3 4 5

0 1.000 - 9,000 - 9,000 - 9,000 1 0.926 10,500 7,000 7,000 2 0.857 4,000 5,000

NPV 722 - - 911 1,768 Joint Prob. 0.3 0.12 0.16

Mean NPV 217 - - 109 283

$4,500.00 0.926 $4,167

Conclusion: The present value of the abandonment value at the end of year 1 is $4,167. Therefore, the project would be abandoned if the period 1 cash flows turned out to be $6,000. ( The mean of present value for period 2 is lower than the abandonment value.) It would not be worthwhile to abandon the project if either of the other year outcomes occurred. The present value of cash flows are the same as in part a's solution except for the main branch which has a mean NPV of $723.

Thus, the mean net present value is increased when the probability of abandonment is considered in the evaluation.