CAPITAL BUDGETING CRITERIA

A firm with a 14% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows:

1. Calculate NPV for each project. Round your answers to the nearest cent. Do not round your intermediate calculations.
   Project M    $
   Project N    $

   Calculate IRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      %
   Project N      %

   Calculate MIRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      %
   Project N      %

   Calculate payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      years
   Project N      years

   Calculate discounted payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M      years
   Project N      years

2. Assuming the projects are independent, which one(s) would you recommend?
   -Select-Only Project M would be accepted because IRR(M) > IRR(N).Both projects would be rejected since both of their NPV's are negative.Only Project M would be accepted because NPV(M) > NPV(N).Only Project N would be accepted because NPV(N) > NPV(M).Both projects would be accepted since both of their NPV's are positive.Item 11
3. If the projects are mutually exclusive, which would you recommend?
   -Select-If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project N.If the projects are mutually exclusive, the project with the highest positive NPV is chosen. Accept Project N.If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project M.If the projects are mutually exclusive, the project with the highest positive MIRR is chosen. Accept Project M.If the projects are mutually exclusive, the project with the shortest Payback Period is chosen. Accept Project M.Item 12
4. Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?
   -Select-There is no conflict between NPV and IRR.The conflict between NPV and IRR occurs due to the difference in the size of the projects.The conflict between NPV and IRR is due to the relatively high discount rate.The conflict between NPV and IRR is due to the fact that the cash flows are in the form of an annuity.The conflict between NPV and IRR is due to the difference in the timing of the cash flows.Item 13

11.07

Katharine Rally is the vice president of operations for the ZUSH Company. She oversees

operations at a plant that manufactures components for hydraulic systems. Katharine is

concerned about the plant’s present production capability. She has reduced the decision

situation to three alternatives. The first alternative, which is fully automation, would

result in significant changes in present operations. The second alternative, which is semi-

automation, involves fewer changes in present operations. The third alternative is to make

no changes (do nothing).

As a manager of the plant management team, you have been assigned the task of

analyzing the alternatives and recommending a course of action.

a. Based on the past data, Katharine is further convinced that the capital investment,

annual revenue, useful lives, and salvage values can be considered random variables

with the following specified probability distributions. She also asks you to develop a

simulation of 50 sample points of AW values at a MARR 0f 20%/year. Interpret your

results and indicate which alternative should be selected.

Hint: Use the Random Number Generation (RNG) Data Analysis Tool package of

Microsoft Excel. The online help function explains how to initiate and use the RNG

to generate random numbers from a variety of probability distributions: normal,

uniform (continuous variable), binomial, Poisson, and discrete.

b. How do you trust the result of your simulation study? Increase the sample points to

100, 500, 1000, and 5000 and conclude that one the alternatives would be better than

the other one.

c. Statically show that one of the alternatives is more appropriate than the other one.

Hint: Apply hypothesis testing method to one of the sample point data, say the 100

sample point, data.

Alternative

--------------------------------------------------------------------------------------------

Parameter

A

B

--------------------------------------------------------------------------------------------

Capital

Normal

Normal

Investment

Mean: $300,000

Mean: $85,000

Std. dev.: $50,000

Std. dev.: $500

Annual

Normal

Normal

Revenue

Mean: $150,000

Mean: $85,000

Std. dev.: $10,000

Std. dev.: $500

Useful live

Discrete uniform

Discrete uniform

3 to 8 years with

3 to 7 years with

equal probability

equal probability

Salvage Value

Uniform

Uniform

30,000 to $60,000

$10,000 to $20000

Daily sales of bagels at a local bakery is a random variable normally distributed with a mean of $600 and a standard deviation of $60. If sales are $540, what is the value of z?

A credit card company found that its customers charge between $100 and $1,100 per month. If this random variable is uniformly distributed, the standard deviation of the monthly amount charged equals $____. Round your answer to the nearest cent.

A clothing store analyzed customer purchases over the past year and found them to be normally distributed with a mean of $110 and a standard deviation of $12. The probability that a randomly selected person spent between $87 and $138 at the store last year is ____% Round to two decimals.

A credit card company found that its customers charge between $100 and $1,100 per month. If monthly amount charged is uniformly distributed, the probability that a person charges less than $200 per month is ____%

An economics professor gives an A grade to any student scoring in the top 8.5% of her Principles of Economics class. If the scores are normally distributed with a mean of 70% and a standard deviation of 5%, the minimum grade a student must score to receive a grade of A is _____%. Round to two decimal places.

A random survey of adult Canadians indicated that the mean number of hours spent watching television per week was 9 with a standard deviation of 1.5 hours. If hours watching television per week is a normally distributed variable, the probability of randomly selecting a Canadian adult and finding that they watch somewhere between 10 and 12 hours of television per week is ____%. Round your answer to 2 decimal places.

The mean cholesterol level of 40 to 60-year-old women surveyed in a particular country was found to be 5 mmol/l with a standard deviation is 1 mmol/l. About 4% of all women in this age category would have a cholesterol level below _____ mmol/l? Leave two decimal places in your answer.

Suppose a train arrives at a stop every 30 minutes between 5 a.m. and 11:30 p.m. The time that a passenger will wait for the train is uniformly distributed from 0 to 30 minutes. The probability a passenger will wait more than 25 minutes is ____%. Round your answer to 2 decimal places.

You have estimated the effects of the age of children, women’s age in years, years of schooling, unemployment rate in the county of residence, and whether the woman lives in metropolitan area on the woman’s probability of being in labor force. In Table 2, column 1 shows the coefficients from the linear probability model, column 2 shows the coefficients from a probit model, and column 3 shows the coefficients from a logit model.

1. Interpret coefficients on variables: # kids < 6 years and # kids 6-18 from column 1.

2. Calculate probability of being in the labor force when woman has 1 child that is less than 6 years old using columns 1, 2 and 3, holding everything else constant.

3. Calculate probability of being in the labor force when woman has 2 children that are less than 6 years old using columns 1, 2 and 3, holding everything else constant.

4. Compute the differences in probabilities when number of children that are less than 6 years old increases from 1 to 2 for each model. Compare the differences in the probabilities between these 3 models.

5. Interpret Pseudo R^2 from column 2.

6. Table 2. Estimation results

   	(1)	(2)	(3)
   	=1 if in lab frce, 1975	=1 if in lab frce, 1975	=1 if in lab frce, 1975
   	Coeff./Std. err.	Coeff./Std. err.	Coeff./Std. err.
   # kids < 6 years	-0.307***	-1.467***	-0.883***
   	(0.036)	(0.195)	(0.112)
   # kids 6-18	-0.017	-0.089	-0.053
   	(0.014)	(0.067)	(0.040)
   woman's age in years	-0.013***	-0.061***	-0.037***
   	(0.003)	(0.013)	(0.008)
   years of schooling	0.044***	0.206***	0.124***
   	(0.008)	(0.038)	(0.023)
   unemployment rate in	-0.004	-0.018	-0.011
   county of residence	(0.006)	(0.026)	(0.016)
   =1 if live in metro area	-0.030	-0.129	-0.074
   	(0.037)	(0.171)	(0.104)
   Constant	0.727***	1.093	0.661
   	(0.165)	(0.781)	(0.473)
   R-squared/Pseudo R-2	0.1248	0.0980	0.0978
   N. of cases	753.0000	753.0000	753.0000

7. p < 0.05, ^**p < 0.01, ^***p < 0.001

Suppose a geyser has a mean time between eruptions of 79 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes. Complete parts ​(a) through ​(e) below.

The probability that a randomly selected time interval is longer than 89 minutes is approximately ____. ​(Round to four decimal places as​ needed.)

​(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 89 ​minutes?

The probability that the mean of a random sample of 13 time intervals is more than 89 minutes is approximately ____. ​(Round to four decimal places as​ needed.)

​(c) What is the probability that a random sample of 24 time intervals between eruptions has a mean longer than 89 ​minutes?

The probability that the mean of a random sample of 24 time intervals is more than 89 minutes is approximately _____. (Round to four decimal places as needed.)

(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result. Fill in the blanks below.

If the population mean is less than 89 ​minutes, then the probability that the sample mean of the time between eruptions is greater than 89 minutes _____▼ (Increase -or- decrease) because the variability in the sample mean _____▼(Increase -or- decrease) as the sample size _____▼ (decreases / increases).

(e) What might you conclude if a random sample of 24 time intervals between eruptions has a mean longer than 89 ​minutes? Select all that apply.

A.The population mean must be more than 79​, since the probability is so low.

B.The population mean may be less than 79.

C.The population mean must be less than 79​, since the probability is so low.

D.The population mean is 79​, and this is an example of a typical sampling result.

E.The population mean is 79​, and this is just a rare sampling.

F.The population mean may be greater than 79.

G. The population mean cannot be 79​, since the probability is so low.

Thank you!

Suppose the data to the right represent the survival data for a certain ship that sank. , The males are adult males and the females are adult females. Complete parts (a) through (j).

(a) If a passenger is selected at random, what is the probability that the passenger survived?

nothing

(Round to three decimal places as needed.)

(b) If a passenger is selected at random, what is the probability that the passenger was female?

nothing

(Round to three decimal places as needed.)

(c) If a passenger is selected at random, what is the probability that the passenger was female or a child?

nothing

(Round to three decimal places as needed.)

(d) If a passenger is selected at random, what is the probability that the passenger was female and survived?

nothing

(Round to three decimal places as needed.)

(e) If a passenger is selected at random, what is the probability that the passenger was female or survived?

nothing

(Round to three decimal places as needed.)

(f) If a female passenger is selected at random, what is the probability that she survived?

nothing

(Round to three decimal places as needed.)

(g) If a child passenger is selected at random, what is the probability that the child survived?

nothing

(Round to three decimal places as needed.)

(h) If a male passenger is selected at random, what is the probability that he survived?

nothing (Round to three decimal places as needed.)

(i) Do you think the adage "women and children first" was adhered to on this ship?

A. No, because the survival rate for men was about the same as the survival rates for women and children.

B. No, because the survival rate for men was higher than the survival rates for women and children.

C. Yes, because the survival rate for men was much lower than the survival rates for women and children.

(j) Suppose two females are randomly selected. What is the probability both survived?

(Round to three decimal places as needed.)

C.

Yes, because the survival rate for men was much lower than the survival rates for women and children.

(j) Suppose two females are randomly selected. What is the probability both survived?

(Round to three decimal places as needed.)

According to a survey in a​ country, 35​% of adults do not own a credit card. Suppose a simple random sample of 500 adults is obtained. Complete parts​ (a) through​ (e) below.

​(a) Determine the mean of the sampling distribution of

mu Subscript ModifyingAbove p with caret Baseline equals

μp=___

​(Round to two decimal places as​ needed.)

​(b) Determine the standard deviation of the sampling distribution of

sigma Subscript ModifyingAbove p with caret equals

σp=___

​(Round to three decimal places as​ needed.)

(c) What is the probability that in a random sample of 500 ​adults, more than 38​% do not own a credit​ card?

The probability is ____ .

​(Round to four decimal places as​ needed.)

Interpret this probability.

If 100 different random samples of 500 adults were​ obtained, one would expect ___ to result in more than 38​% not owning a credit card.

​(Round to the nearest integer as​ needed.)

(d) What is the probability that in a random sample of 500 adults, between 33​% and 38​% do not own a credit​ card?

The probability is ___.

​(Round to four decimal places as​ needed.)

Interpret this probability.

If 100 different random samples of 500 adults were​ obtained, one would expect __ to result in between 33​% and 38​% not owning a credit card.

​(Round to the nearest integer as​ needed.)

(e) Would it be unusual for a random sample of 500 adults to result in 165 or fewer who do not own a credit​ card? Why? Select the correct choice below and fill in the answer box to complete your choice.

​(Round to four decimal places as​ needed.)

A.The result is unusual because the probability that ModifyingAbove p with caretp is less than or equal to the sample proportion is ___ ​, which is less than​ 5%.

B.The result is notunusual because the probability that ModifyingAbove p with caretp is less than or equal to the sample proportion is ___, which is greater than​ 5%.

C.The result is not unusual because the probability that ModifyingAbove p with caretp is less than or equal to the sample proportion is ___​, which is less than​ 5%.

D.The result is unusual because the probability that ModifyingAbove p with caretp is less than or equal to the sample proportion is ___​, which is greater than​ 5%.

QUESTION 1)

Which of the following statements is correct?

Group of answer choices:

a) Logistic regression extends the idea of linear regression to the situation where the OUTCOME variable is categorical

b) Logistic regression extends the idea of linear regression to the situation where a PREDICTOR variable is categorical

c) Linear regression extends the idea of logistic regression to the situation where a PREDICTOR variable is categorical

d) Linear regression extends the idea of logistic regression to the situation where the OUTCOME variable is categorical

QUESTION 2)

Which statement is correct with regard to describing the odds of belonging to class 1 in a binary classification model?

Group of answer choices:

a) The ratio of the probability of belonging to class 1 to the probability of belonging to class 0

b) The probability of belonging to class 1

c) The ratio of the probability of belonging to class 0 to the probability of belonging to class 1

d) The probability of belonging to class 0

QUESTION 3)

What is the range for the value of Log Odds, or as it's called the logit?

Group of answer choices:

a) -  to +

b) 0 to +

c) 0 to 1

d) -1 to +1

QUESTION 4)

What is the interpretation of “log odds = 0” in a binary classification model?

Group of answer choices:

a) The probability of belonging to class 1 is zero

b) The probability of belonging to class 1 is undeterminable

c) The probability of belonging to class 1 is almost zero

d) The probability of belonging to class 1 is 0.5

QUESTION 5)

Which of the following statements is NOT a difference between Linear and Logistic Regression?

Group of answer choices:

a) Linear regression is more suitable for explanatory purpose, while logistic regression is more suitable for predictive purpose

b) In linear regression, the relationship between Y and the beta coefficients is non-linear. Whereas in logistic regression, the relationship between Y and the beta coefficients is linear.

c) Linear regression is more suitable for predictive purpose, while logistic regression is more suitable for explanatory purpose

d) In linear regression, the relationship between Y and the beta coefficients is linear. Whereas in logistic regression, the relationship between Y and the beta coefficients is non-linear.

Thank you so much for the help! (Data Analytics)

6.5 - 6) 7) and 8)

Suppose x has a distribution with μ = 11 and σ = 9.

(a) If a random sample of size n = 36 is drawn, find μ_x, σ_x and P(11 ≤ x ≤ 13). (Round σ_x to two decimal places and the probability to four decimal places.)

(b) If a random sample of size n = 65 is drawn, find μ_x, σ_x and P(11 ≤ x ≤ 13). (Round σ_x to two decimal places and the probability to four decimal places.)

(c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is  ---Select--- smaller than the same as larger than part (a) because of the  ---Select--- larger same smaller sample size. Therefore, the distribution about μ_x is

Question 7 )

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 84 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean μ = 84 tons and standard deviation σ = 0.7 ton.

(a) What is the probability that one car chosen at random will have less than 83.5 tons of coal? (Round your answer to four decimal places.)
__________________

(b) What is the probability that 39 cars chosen at random will have a mean load weight x of less than 83.5 tons of coal? (Round your answer to four decimal places.)
____________________

Question 8) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 2 inches.

(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of twenty-five 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.

The probability in part (b) is much higher because the mean is smaller for the x distribution.    

The probability in part (b) is much higher because the mean is larger for the x distribution.

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.