Accountant Ian Somnia's infamous napping at work has given rise to a challenge from colleague I. M. Tarde. At the company retreat, the two will take turns trying to stay awake during a sequence of 5-minute company training films. The probability that Somnia will fall asleep during a given film is 0.8, while the probability that Tarde does is 0.7. The first one to stay awake (as determined by a panel of alert judges) wins a $1000 bonus. If Somnia and Tarde alternate watching films, with Somnia going first, what are the chances that Tarde wins the bonus? (Hint: A typical sequence of films for which Tarde wins the bonus is NNNY, where N = “not awake” and Y = “awake.”)

Better Mousetraps has developed a new trap. It can go into production for an initial investment in equipment of $5.7 million. The equipment will be depreciated straight-line over 6 years, but, in fact, it can be sold after 6 years for $671,000. The firm believes that working capital at each date must be maintained at a level of 10% of next year’s forecast sales. The firm estimates production costs equal to $1.80 per trap and believes that the traps can be sold for $8 each. Sales forecasts are given in the following table. The project will come to an end in 6 years, when the trap becomes technologically obsolete. The firm’s tax bracket is 40%, and the required rate of return on the project is 11%.

Suppose the firm can cut its requirements for working capital in half by using better inventory control systems. By how much will this increase project NPV? (Do not round your intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

What is Reeby Sports worth per share? We will value the company using George
Reeby's forecasts.
The spreadsheet accompanying this solution sets out a forecast in the same
general format as Table 4.5. Historical results from 2011 to 2016 are also shown.Earnings
per share (EPS)equals return on equity (ROE) times starting book value per share
(BVPS). EPS is divided between dividends and retained earnings, depending on the
dividend payout ratio.BVPS grows as retained earnings are reinvested.
The keys to Reeby Sports’ future value and growth are profitability (ROE) and
the reinvestment of retained earnings. Retained earnings are determined by dividend
payout. The spreadsheet sets ROE at 15% for the six years from 2018 to 2022. If Reeby
Sports will lose its competitive edge by 2022, then it cannot continue earning more than
its10% cost of capital. Therefore ROE is reduced to 10%startingin 2023.1
The payout ratio is set at .30 from 2018 onwards. Notice that the long-term
growth rate, which settles inafter 2023, is ROE × ( 1 – dividend payout ratio) = .10 × (1 -
.30) = .07.
The spreadsheet allows you to vary ROE and the dividend payout ratio separately
for 2018-2022 and for 2023-2024.2But let’s start with the initial input values. To
calculate share value, we have to estimate a horizon value at H = 2022 and add its PV to
the PV of dividends from 2017 to 2022. Using the constant-growth DCF formula,
PV = 0.71 = 23.72 H .10- .07
The PV of dividends from 2017 to 2022 is $3.43 at the start of 2017, so share value is:3
6
PV = 3.43+ 23.72 = $16.82
(1.1)
The spreadsheet also calculates the PV of dividends through 2024 and the horizon
value at 2024. Notice that the PV at the start of 2017 remains at $16.82. This makes sense, since the value of a firm should not depend on the investment horizon chosen to calculate
PV. (If you calculate a value that does depend on the horizon, you have made a mistake.)
We have reduced ROE to the 10% cost of capital after 2022, assuming that Reeby
Sports will have exhausted valuable growth opportunities by that date. With PVGO = 0,
PV = EPS/r.4So we could discard the constant-growth DCF formula and just divide EPS
in 2023 by the cost of capital:
PVH = 2.37 = $23.72 .10
This PVis identical to the PV from the constant-growth DCF formula. It doesn’t matter
how fast a company grows after the horizon date H if it only earns its cost of capital.
How much of Reeby Sports’ value is due to PVGO?You can check by setting
ROE = .10 for 2018 and all later years.You should get PV = $13.82. Thus PVGO = 16.82
– 13.82 = $3.00 per share for investments made in 2017onward.
George Reeby has also identified a "comparable," Molly Sports. We could use its
P/E ratio of 13.1 to calculate horizon value in 2022 and PV at the start of 2017. Using
the original inputs for ROE, EPS in 2023 is 2.37.5
H
6
PV 13.1 2.37 $31.05
PV 3.43 31.05 $20.96
(1.10)
= ´ =
= + =
We couldalso use Molly’s P/E ratio to calculate Reeby Sports’ PV at the start of 2017
directly from 2017 EPS:
PV = 13.1 ´ 2.03 = $26.59

The Question is ?
Both values based on Molly’s P/E are higher than our DCF calculations. Is Molly
significantly more profitable than Reeby Sports, or does our spreadsheet understate
Reeby Sports’ prospects?
What if Reeby Sports could continue to earn ROE = .15 for two extra years, until
2024?You can check by changing ROE for 2023-2024 from .10 to .15. (The ROE for
2025 and 2026 is hard-wired at .10.)You should get NPV of $18.04, somewhat higher
than our original DCF calculations, but not enough for Reeby Sports to match Molly’s P/E.You may wish to experiment to find inputs that generate P/E = 13 for Reeby Sports
at the start of 2017. Do you think these inputs are reasonable?

HYPOTHESIS TESTING SUMMARY ACTIVITY

Part 1: Overview of the Hypothesis Test for the Population Proportion Answer the following questions:

1) The general form of the test statistic for the hypothesis test for a population proportion is shown below. Label the different components of the test statistic.

2) For the following situations, state the null and alternative hypothesis. Then determine whether the alternative hypothesis is one-sided or two-sided.

a) A toy manufacturer claims that 23% of the 14-year-old residents of a certain city own a skateboard. A sample of fifty 14-year-olds shows that nine own a skateboard. Is there enough evidence to show that the percentage has changed?

b) At a large university, a study found that 25% of the students who commute travel more than 14 miles to campus. Recently, the university built more housing closer to campus so they believe that the proportion has decreased.

c) For students who first enrolled in two-year public institutions in fall 2007, the proportion who earned a bachelor’s degree within 6 years was 0.399. The president of Joliet Junior College believes that the proportion of students who enroll in her institution have a higher completion rate.

3) Use the information in question 2a (toy manufacturer) to answer the following questions.

a) Calculate the test statistic and draw a diagram with a normal curve to represent the sampling distribution of ??� in the context of this situation.

b) If the sample size of the survey was increased, would the test statistic increase or decrease? Would it give us more or less evidence against H0 ?

A larger and more modern main post office is to be constructed at a new location in​ Davis, California. Growing suburbs caused a shift in the population density from where it was 40 years​ ago, when the current facility was built. Annette​ Werk, the​ postmaster, asked her assistants to draw a grid map of the seven points where mail is picked up and delivered in bulk. The coordinates and trips per day to and from the seven mail source points and the current main post​ office, M, are shown in the following table. M will continue to act as a mail source point after relocation.  

a. Calculate the center of gravity as a possible location for the new facility. ​(Enter your responses rounded to the nearest whole​ number.)

The center of gravity​ "X" coordinate​ =

The center of gravity​ "Y" coordinate​ =

b. Compare the​ load-distance scores for the location in part​ (a) and the current​ location, using rectilinear distance. ​(Round all intermediate calculations to the nearest whole​ number.)

The​ load-distance score to​ "M" is

​ (Enter your response as an​ integer.)

The​ load-distance score to the center of gravity is

​(Enter your response rounded to the nearest whole​ number.)

Greenwork Accessories assembles a computer networking device from kits of imported components. You have been asked to develop a quarterly and annual operating budget and pro- forma income statements for 2016. You have obtained the following information: 20 points

Beginning-of-year balances

Desired end-of-quarter balances

Fixed cost per quarter

Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                                                $40,000.00

Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                                                 10,000.00

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                                                $50,000.00

Selling and administrative costs

Variable cost per unit. . . . . . . . . . . . . . . . . . . . . . .. . . . . . .

Fixed costs per quarter:

$6.00

Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                                    $20,000.00

Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   5,000.00

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                                    $25,000.00

Sales Forecast

Quarter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     First      Second       Third        Fourth

Unit sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      2,400      1,500             2,000         3,100

Additional information

All cash payments except purchases are made quarterly as incurred.

All borrowings occur at the start of the quarter.

All repayments on borrowings occur at the end of the quarter.

All interest on borrowed funds is paid at the end of each quarter.

Borrowings and repayments may be made in any amount.

Required – 20 points

A sales budget for each quarter and the year.

A production budget for each quarter and the year.

c.   A purchases budget for each quarter and the year.

d.   A manufacturing cost budget for each quarter and the year.

e.   A selling and administrative expense budget for each quarter and the year.

f.    A cash budget for each quarter and the year.

g.   A pro-forma contribution income statement for each quarter and the year.

Works Accessories assembles a computer networking device from kits of imported components. You have been asked to develop a quarterly and annual operating budget and pro- forma income statements for 2016. You have obtained the following information:

Beginning-of-year balances

Desired end-of-quarter balances

Fixed cost per quarter

Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             $40,000.00

Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .              10,000.00

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .            $50,000.00

Selling and administrative costs

Variable cost per unit. . . . . . . . . . . . . . . . . . . . . . .. . . . . . .

Fixed costs per quarter:

$6.00

Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $20,000.00

Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   5,000.00

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $25,000.00

Sales Forecast

Quarter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     First      Second       Third        Fourth

Unit sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         2,400      1,500             2,000         3,100

Additional information

All cash payments except purchases are made quarterly as incurred.

All borrowings occur at the start of the quarter.

All repayments on borrowings occur at the end of the quarter.

All interest on borrowed funds is paid at the end of each quarter.

Borrowings and repayments may be made in any amount.

(a) A sales budget for each quarter and the year.

(b) A production budget for each quarter and the year.

c.   A purchases budget for each quarter and the year.

d.   A manufacturing cost budget for each quarter and the year.

e.   A selling and administrative expense budget for each quarter and the year.

f.    A cash budget for each quarter and the year.

g.   A pro-forma contribution income statement for each quarter and the year.

Hooper Chemical Company, a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process, is examining a plastics firm to add to its operations. Before the acquisition, the normal expected outcomes for the firm were as follows: Outcomes ($ millions) Probability Recession $ 40 0.2 Normal economy 60 0.1 Strong economy 80 0.7

Compute the expected value, standard deviation, and coefficient of variation prior to the acquisition. (Do not round intermediate calculations. Enter your dollar answers in millions rounded to 2 decimal places (e.g., $12,300,000 should be entered as "12.30"). Round the coefficient of variation to 3 decimal places.)

Suppose the following data represent the ratings​ (on a scale from 1 to​ 5) for a certain smart phone​ game, with 1 representing a poor rating. Complete parts​ (a) through​ (d) below. Stars Frequency 1 2963 2 2372 3 4696 4 4393 5 10 comma 585 ​(a) Construct a discrete probability distribution for the random variable x. Stars​ (x) ​P(x) 1 nothing 2 nothing 3 nothing 4 nothing 5 nothing ​(Round to three decimal places as​ needed.) ​(b) Graph the discrete probability distribution. Choose the correct graph below. A. 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 has five vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 1, 0.42; 2, 0.18; 3, 0.19; 4, 0.1; 5, 0.12. B. 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 five vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 1, 0.12; 2, 0.1; 3, 0.19; 4, 0.18; 5, 0.42. C. 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 five vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 1, 0.1; 2, 0.18; 3, 0.12; 4, 0.19; 5, 0.42. D. 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 A histogram has a horizontal axis labeled from 0 to 4 in intervals of 1 and a vertical axis labeled from 0 to 0.5 in intervals of 0.1 five vertical lines positioned on the horizontal axis tick marks. The approximate heights of the vertical lines are as follows, with the horizontal coordinate listed first and the line height listed second: 1, 0.19; 2, 0.18; 3, 0.42; 4, 0.12; 5, 0.1. ​(c) Compute and interpret the mean of the random variable x. The mean is nothing stars. ​(Round to one decimal place as​ needed.) Which of the following interpretations of the mean is​ correct? A. As the number of experiments​ decreases, the mean of the observations will approach the mean of the random variable. B. The observed value of an experiment will be less than the mean of the random variable in most experiments. C. The observed value of an experiment will be equal to the mean of the random variable in most experiments. D. As the number of experiments​ increases, the mean of the observations will approach the mean of the random variable. ​(d) Compute the standard deviation of the random variable x. The standard deviation is nothing stars. ​(Round to one decimal place as​ needed.)

4. The Transactional Records Access Clearinghouse at Syracuse University reported data showing the chance of an Internal Revenue Service (IRS) audit. The data in file IRSAudit.xlsx show the average adjusted gross income reported (in $ thousands) and the percent of the returns that were audited for 20 selected IRS districts.

1. Use XLSTAT to create a scatterplot with average adjusted gross income reported on the horizontal axis and percent of the returns that were audited on the vertical axis. Include the fitted simple linear regression line on the plot and include the plot in your answer. What does the scatterplot indicate about the relationship between the average adjusted gross income reported and the percent of the returns that were audited?

Hint: Select Visualizing data > Scatter plots, select cells B1:B21 for X and select cells C1:C21 for Y. Click “Options” and check “Regression lines.”

2. Use XLSTAT to estimate a simple linear regression model using least squares. Report the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported.

Hint: Select Modeling data > Linear regression, select cells C1:C21 for “Y / Dependent variables: Quantitative” and select cells B1:B21 for “X / Explanatory variables: Quantitative.”

3. Is there a significant linear relationship between the two variables based on a significance level α=0.05α=0.05?

Hint: You can use either a t-test or an F-test to answer this question. In your answer state the hypotheses, test statistic, p-value, decision, and conclusion.

4. Use the estimated regression equation to predict the percent audited for a district with an average adjusted gross income of $35,000.