QUESTIONS ANSWERS
[Document subtitle]
FALL 2023
NAME: -------ID| 000000000000000
Question (1):
At the end of 2015, Uma Corporation is considering undertaking a major long-term
project in an effort to remain competitive in its industry. The production and sales
departments have determined the potential annual cash flow savings that could
accrue to the firm if it acts soon. Specifically, they estimate that a mixed stream of
future cash flow savings will occur at the end of the years 2016 through 2021. The
years each year. The firm estimates that its discount rate over the first 6 years will
be 7%.
The expected discount rate over the years 2022 through 2026 will be 11%. The project
managers will find the project acceptable if it results in present cash flow savings
of at least $860,000. The following cash flow savings data are supplied to the finance
department for analysis.
End of year
Cash flow savings
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
$ 110,000.00
120,000.00
130,000.00
150,000.00
160,000.00
150,000.00
90,000.00
90,000.00
90,000.00
90,000.00
90,000,00
To Do
Create spreadsheets similar to Table 5.2, and then answer the following questions.
a. Determine the value (at the beginning of 2016) of the future cash flow savings
expected to be generated by this project.
b. Based solely on one criterion set by management, should the firm undertake this
specific project? Explain.
c. What is the “interest rate risk,” and how might it influence the recommendation
made in part b? Explain.
1|Page
Answer:
End of year
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
Year (n)
1
2
3
4
5
6
7
8
9
10
11
Cash flow
$ 110,000.00
120,000.00
130,000.00
150,000.00
160,000.00
150,000.00
90,000.00
90,000.00
90,000.00
90,000.00
90,000,00
Present value End of
year 2021
81,081.08
73,046.02
65,807.22
59,285.79
53,410.62
Present value
Beginning of 2016
$ 102,803.74
104,812.65
106,118.72
114,434.28
114,077.79
99,951.33
54,027.75
48,673.65
43,850.13
39,504.62
35,589.75
$ 863,844.42
(a) First, we will discount the cash flows at the end of years 2022 through 2026 at 11% back to the
end of year 2021. Next, we will discount the cash flows at the end of years 2016 through 2021
(don't forget the present values found in the first step are now at the end of year 2021) at 7% back
to the end of year 2015. The end of year 2015 is the beginning of year 2016, which is when we want
the present value of the cash flow savings. By discounting cash flows for at the end of years 2016
through 2021 at 7%, we get PV of $863,844.42.
(b) Based solely on the criteria set by management, the firm should undertake this project as the
present value of the expected future saving total $863,844.42 which exceeds the $860,000 hurdle.
(c) The concept of interest-rate risk states that changes in the interest rates will affect the present
value of future cash flows. For this problem, if the the interest rates were to rise just 1 percentage
point, the present value of the expected savings would fall below the required $860,000 limit set
by management.
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Question (2)
Jane is considering investing in three different stocks or creating three distinct two
stock portfolios. Jane considers herself to be a rather conservative investor. She is
able to obtain forecasted returns for the three securities for the years 2015 through
2021.
The data are given in the following table.
In any of the possible two-stock portfolios, the weight of each stock in the portfolio
will be 50%. The three possible portfolio combinations are AB, AC, and BC.
Answer:
a. Calculate the expected return for each individual stock.
Year
2015
2016
2017
2018
2019
2020
2021
Expected return
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Stock A
0.1
0.13
0.15
0.14
0.16
0.14
0.12
13.43%
Stock B
0.1
0.11
0.08
0.12
0.1
0.15
0.15
11.57%
Stock C
0.12
0.14
0.1
0.11
0.09
0.09
0.1
10.71%
b. Calculate the standard deviation for each individual stock.
Stock A
Year
Return
Expected
return
Deviation
Deviation^2
2015
2016
2017
2018
2019
2020
2021
10%
13%
15%
14%
16%
14%
12%
13.43%
13.43%
13.43%
13.43%
13.43%
13.43%
13.43%
-3.43%
-0.43%
1.57%
0.57%
2.57%
0.57%
-1.43%
0.00117551
0.00001837
0.00024694
0.00003265
0.00066122
0.000032
0.00020408
0.00237143
Standard deviation = 1.99%
Stock B
Year
Return
Expected
return
Deviation
Deviation^2
2015
2016
2017
2018
2019
2020
2021
10%
11%
8%
12%
10%
15%
15%
11.57%
11.57%
11.57%
11.57%
11.57%
11.57%
11.57%
-1.57%
-0.57%
-3.57%
0.43%
-1.57%
3.43%
3.43%
0.00024694
0.00003265
0.00127551
0.00001837
0.00024694
0.00117551
0.00117551
0.00417143
Standard deviation = 2.64%
Stock C
Year
Return
Expected
return
Deviation
Deviation^2
2015
2016
2017
2018
2019
2020
2021
12%
14%
10%
11%
9%
9%
10%
10.71%
10.71%
10.71%
10.71%
10.71%
10.71%
10.71%
1.29%
3.29%
-0.71%
0.29%
-1.71%
-1.71%
-0.71%
0.00016531
0.00107959
0.00005102
0.00000816
0.00029388
0.00029388
0.00005102
0.00194286
Standard deviation = 1.80%
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c. Calculate the expected returns for portfolios AB, AC, and BC.
d. Calculate the standard deviations for portfolios AB, AC, and BC
Portfolio AB
Return
Weight
Year
2015
2016
2017
2018
2019
2020
2021
Stock A
Stock B
Stock A
Stock B
Expected
Return
10.00%
13.00%
10.00%
11.00%
0.5
0.5
0.5
0.5
10.0%
12.0%
15.00%
14.00%
16.00%
8.00%
12.00%
10.00%
0.5
0.5
0.5
0.5
0.5
0.5
11.5%
13.0%
13.0%
14.00%
12.00%
15.00%
15.00%
0.5
0.5
0.5
0.5
14.5%
13.5%
87.5%
Expected Return = 12.58%
Year
Return
Expected
return
Deviation
Deviation^2
2015
2016
2017
2018
2019
2020
2021
10%
12%
12%
13%
13%
15%
14%
12.5%
12.5%
12.5%
12.5%
12.5%
12.5%
12.5%
-2.500%
-0.500%
-1.000%
0.500%
0.500%
2.000%
1.000%
0.062500%
0.002500%
0.010000%
0.002500%
0.002500%
0.040000%
0.010000%
0.130000%
Standard deviation = 1.47%
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Portfolio AC
Return
Weight
Year
2015
2016
2017
2018
2019
2020
2021
Stock A
Stock C
Stock A
Stock C
Expected
Return
10.00%
13.00%
12%
14%
0.5
0.5
0.5
0.5
11.0%
13.5%
15.00%
14.00%
16.00%
10%
11%
9%
0.5
0.5
0.5
0.5
0.5
0.5
12.5%
12.5%
12.5%
14.00%
12.00%
9%
10%
0.5
0.5
0.5
0.5
11.5%
11.0%
84.5%
Expected Return = 12.07%
Year
Return
Expected
return
Deviation
Deviation^2
2015
2016
2017
2018
2019
2020
2021
11%
14%
13%
13%
13%
12%
11%
12.1%
12.1%
12.1%
12.1%
12.1%
12.1%
12.1%
-1.071%
1.429%
0.429%
0.429%
0.429%
-0.571%
-1.071%
0.011480%
0.020408%
0.001837%
0.001837%
0.001837%
0.003265%
0.011480%
0.052143%
Standard deviation = 0.93%
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Portfolio BC
Return
Weight
Year
2015
2016
2017
2018
2019
2020
2021
Stock B
Stock C
Stock B
Stock C
Expected
Return
10.00%
11.00%
12%
14%
0.5
0.5
0.5
0.5
11.0%
12.5%
8.00%
12.00%
10.00%
10%
11%
9%
0.5
0.5
0.5
0.5
0.5
0.5
9.0%
11.5%
9.5%
15.00%
15.00%
9%
10%
0.5
0.5
0.5
0.5
12.0%
12.5%
78.0%
Expected Return = 11.14%
Year
Return
Expected
return
Deviation
Deviation^2
2015
2016
2017
2018
2019
2020
2021
11%
13%
9%
12%
10%
12%
13%
11.1%
11.1%
11.1%
11.1%
11.1%
11.1%
11.1%
-0.143%
1.357%
-2.143%
0.357%
-1.643%
0.857%
1.357%
0.000204%
0.018418%
0.045918%
0.001276%
0.026990%
0.007347%
0.018418%
0.118571%
Standard deviation = 1.41%
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e. Would you recommend that Jane invest in the single stock A or the portfolio
consisting of stocks A and B? Explain your answer from a risk–return viewpoint.
Stock A
Portfolio B
Return
Risk
CV
13.43%
12.50%
1.99%
1.47%
14.80%
11.78%
Stock A, by itself, has an expected return of 13.43% with a standard deviation of 1.99%.
Investing in the portfolio with a standard deviation 1.47%.
So there is both a lower amount of risk and return in the portfolio, she needs to find the
coefficient of variation (CV). Here we can see the CV of variation of the portfolio is less
than stock A alone so the portfolio of AB should be recommended.
f. Would you recommend that Jane invest in the single stock B or the portfolio
consisting of stocks B and C? Explain your answer from a risk–return viewpoint.
Stock B
Portfolio BC
Return
Risk
CV
11.57%
11.14%
2.64%
1.41%
22.79%
12.62%
Stock B, by itself, has an expected return of 11.57% with a standard deviation of 2.64%.
Investing in the portfolio comprised of stocks B and C delivers a lower return of 11.14% and
is associated with a standard deviation of 1.41%. So once again both the return and risk of
the portfolio are lower.
Considering the CV, however, Jane, can determine that the portfolio BC is preferable to
stock B alone because the CV of is lower for the portfolio.
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Question 3 Integrative case 2 Tuck :
a. (1) On what financial goal does Stanley seem to be focusing? Is it the correct goal?
Why or why not?
Increase in net profits over the period from 2009 to 2015 indicates that Stanely is focus on
maximizing profits. The way in which he is deciding on employing a software designer also
reflects the financial goals. Wealth maximization needs a long-term prospective, along with
risk and cash flows whereas profit maximization does not integrate the factors in the
management decision process. Hence, Stanley is using the correct financial goal.
(2) Could a potential agency problem exist in this firm? Explain.
Stanley owns 40% of the outstanding equity, there is no potential for problems at Track
Software. An agency problem exists when managers place personal goals instead of
corporate goals.
b. Calculate the firm’s earnings per share (EPS) for each year, recognizing that the
number of shares of common stock outstanding has remained unchanged since the
firm’s inception. Comment on the EPS performance in view of your response in part
a.
Year
Net profit after taxes
EPS (NPAT/100,000 shares)
2009
(50,000)
0
2010
(20,000)
0
2011
15,000
0.15
2012
35,000
0.35
2013
40,000
0.40
2014
43,000
0.43
2015
48,000
0.48
Earnings per share have steadily increased. This verifies that Stanley is focusing on the goal
of profit maximization.
c. Use the financial data presented to determine Track’s operating cash flow (OCF)
and free cash flow (FCF) in 2015. Evaluate your findings in light of Track’s current
cash flow difficulties.
OCF = EBIT- Taxes + Depreciation
OCF=$89 - 12 + 11 = $88
FCF=OCF-Net fixed asset investment - Net current asset investment
FCF=$88 - 15 - 47 = 26
NFAI = Change in net fixed assets + depreciation
NFAI = (132 - 128) + 11 = 15
NCAI = Change in current assets - change in (accounts payable + accruals)
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NCAI = 59 - (10+2) = 47
The OCF is large enough to provide the cash needed for the needed investment in both
fixed assets and the increase in networking capital. The firm still has $26,000 available to
pay investors.
d. Analyze the firm’s financial condition in 2015 as it relates to (1) liquidity, (2)
activity, (3) debt, (4) profitability, and (5) market, using the financial statements
provided in Tables 2 and 3 and the ratio data included in Table 5. Be sure to evaluate
the firm on both a cross-sectional and a time-series basis. e. What recommendation
would you make to Stanley regarding hiring a new software developer? Relate your
recommendation here to your responses in part a.
Actual
Industry average
1- liquidity Ratio
Net Working capital
2014
$21.000
2015
$58.000
2015
$96.000
Current ratio
1.06
1.16
1.82
Actual
Industry average
2- Activity Ratio
2014
2015
2015
Inventory turnover
10.40
5.39
12.45
Average collection
period
Total asset turnover
29.6 days
35.3 days
20.2 days
2.66
2.80
3.92
Actual
Industry average
3- Debt Ratio
Debt ratio
2014
0.78
2015
0.73
2015
0.55
Times interest earned
3.0
3.1
5.6
Gross profit margin
32.1%
33.5%
42.3%
Net profit margin
3.0%
3.1%
4.0%
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TS: Time Series
CS: Cross sectional
TS: improving.
CS: Poor
TS: improving.
CS: Poor
TS: Time Series
CS: Cross sectional
TS: Deteriorating
CS: Poor
TS: Deteriorating
CS: Poor
TS: improving.
CS: Poor
TS: Time Series
CS: Cross sectional
TS: Decreasing.
CS: Poor
TS: stable.
CS: Poor
TS: Improving
CS: Poor
TS: stable
CS: fair
Actual
Industry average
4- Profitability Ratio
Return on total assets
(ROA)
Return on Equity
(ROE)
2014
80%
2015
8.7%
2015
15.6%
36.4%
31.6%
34.7%
Actual
Industry average
5- Market Ratio
Price /Earning (P/E)
2014
5.2
2015
11.0
2015
7.1
Market /Book (M/B)
2.1
1.74
2.2
TS: Time Series
CS: Cross sectional
TS: improving.
CS: Poor
TS: Deteriorating.
CS: fair
TS: Time Series
CS: Cross sectional
TS: improving.
CS: poor
TS: Deteriorating.
CS: fair
Analysis of Track Software based on ratio data:
1. Liquidity – Track software liquidity is shown by the current ratio, net working capital
and acid-test ratio has slightly improved or stable but overall it is below the industry
average.
2. Activity – Inventory turnover has decreased considerably and much worse than the
industry average. The average collection period has also decreased and worse than the
industry average. Total asset turnover has improved slightly but it is below the industry
norm.
3. Debt – It has improved slightly from 2014 but greater than the industry average. The
times interest earned ratio is stable and provides reasonable cushion for the company and
is below the industry average.
4. Profitability – the firm’s gross, operating and net margins have slightly improved in
2014 but remain low compared to industry. Return on total assets has improved but half
the industry average.
5- Market- Overall, the company's financial ratios have shown some mixed trends. The P/E
ratio has improved, while the M/B ratio has deteriorated. The company is still undervalued
compared to the industry average based on its P/E ratio.
e. What recommendation would you make to Stanley regarding hiring a new
software developer? Relate your recommendation here to your responses in part a.
Since Stanley focused on profit maximization, the ability of a new product would increase
Track Software's sales and results in greater profits over the long-term. Hence, Stanley
should make all the effort possible to find the cash in hiring a new software developer.
11 | P a g e
f. Track Software paid $5,000 in dividends in 2015. Suppose that an investor
approached Stanley about buying 100% of his firm. If this investor believed that by
owning the company, he could extract $5,000 per year in cash from the company in
perpetuity, what do you think the investor would be willing to pay for the firm if
the required return on this investment is 10%?
If the investor believes they can extract $5,000 per year in cash from the company in
perpetuity, the value of the firm can be calculated using the perpetuity formula:
Value of the firm = Cash flow per year / Required return
Value of the firm = $5,000 / 0.10
Value of the firm = $50,000
g. Suppose that you believed that the FCF generated by Track Software in 2015 could
continue forever. You are willing to buy the company in order to receive this
perpetual stream of free cash flow. What are you willing to pay if you require a 10%
return on your investment?
FCF = OCF – Net fixed asset investment (NFAI) – Net current asset investment
OCF = [EBIT * (1 – T)] +Depreciation
NFAI = Change in net fixed assets + Depreciation
NCAI = Change in current assets – Change in (accounts payable + accruals)
OCF = [89,000 * (1-20%)] + 11,000
OCF = 82,200
NFAI = 4,000 + 11,000 = 15,000
NCAI = 59,000 – (2,000 + 10,000)
NCAI = 59.000 – 12,000 = 47,000
FCF = 82, 200 – 15,000 – 47,000
FCF = 20,200
12 | P a g e
Question 4: Integrative Case 3 / Encore International
In the world of trendsetting fashion, instinct and marketing savvy are prerequisites to
success. Jordan Ellis had both. During 2015, his international casual-wear company, Encore,
rocketed to $300 million in sales after 10 years in business. His fashion line covered the
young woman from head to toe with hats, sweaters, dresses, blouses, skirts, pants,
sweatshirts, socks, and shoes. In Manhattan, there was an Encore shop every five or six
blocks, each featuring a different color. Some shops showed the entire line in mauve, and
others featured it in canary yellow. Encore had made it. The company’s historical growth
was so spectacular that no one could have predicted it. However, securities analysts
speculated that Encore could not keep up the pace. They warned that competition is fierce
in the fashion industry and that the firm might encounter little or no growth in the future.
They estimated that stockholders also should expect no growth in future dividends.
Contrary to the conservative securities analysts, Jordan Ellis believed that the company
could maintain a constant annual growth rate in dividends per share of 6% in the future,
or possibly 8% for the next 2 years and 6% thereafter. Ellis based his estimates on an
established long-term expansion plan into European and Latin American markets.
Venturing into these markets was expected to cause the risk of the firm, as measured by
the risk premium on its stock, to increase immediately from 8.8% to 10%. Currently, the
risk-free rate is 6%. In preparing the long-term financial plan, Encore’s chief financial
officer has assigned a junior financial analyst, Marc Scott, to evaluate the firm’s current
stock price. He has asked Marc to consider the conservative predictions of the securities
analysts and the aggressive predictions of the company founder, Jordan Ellis. Marc has
compiled the following 2015 financial data to aid his analysis.
Data item 2015
Earnings per share (EPS)
Price per share of common stock
Book value of common stock equity
Total common shares outstanding
Common stock dividend per share
value
$6.25
$40.00
$60,000,000
2,500,000
$4.00
TO do
a. What is the firm’s current book value per share?
b. What is the firm’s current P/E ratio?
c. (1) What is the current required return for Encore stock?
(2)
What will be the new required return for Encore stock assuming that the firm
expands into European and Latin American markets as planned?
d. If the securities analysts are correct and there is no growth in future dividends, what will
be the value per share of the Encore stock? (Note: Use the new required return on the
company’s stock here.)
e. (1) If Jordan Ellis’s predictions are correct, what will be the value per share of Encore
stock if the firm maintains a constant annual 6% growth rate in future dividends? (Note:
Continue to use the new required return here.)
13 | P a g e
(2)
f.
If Jordan Ellis’s predictions are correct, what will be the value per share of Encore
stock if the firm maintains a constant annual 8% growth rate in dividends per share over
the next 2 years and 6% thereafter?
Compare the current (2015) price of the stock and the stock values found in parts a, d,
and e. Discuss why these values may differ. Which valuation method do you believe
most clearly represents the true value of the Encore stock?
Answer:
a. What is the firm’s current book value per share?
= $ 24
The Current book value per share =
b. What is the firm’s current P/E ratio?
The Current P/E ratio =
c.
(1) What is the current required return for Encore stock?
Givens:
•
•
The Current risk premium is 8.8%
the risk-free rate is 6%
Then
The Current Required Rate of Return (RRR) = Current Risk-Free rate + Current Risk Premium
= 6% + 8.8
= 14.8%
(2) What will be the new required return for Encore stock assuming that the firm expands into
European and Latin American markets as planned?
Given (With the assumption of expand):
•
•
The Risk Premium is 10%
The Risk – Free is 6% Then:
The New Required Rate of Return (RRR) = Risk- Free rate + The New Risk Premium
= 6% + 10%
= 16%
d. If the securities analysts are correct and there is no growth in future dividends, what will be the
value per share of the Encore stock? (Note: Use the new required return on the company’s stock here.)
Given:
14 | P a g e
• Form (2C) - The New Required Rate of Return (RRR) = 16%
• Common stock dividend per share $4.00 then
Using Zero Growth Dividends
The Present Value Per Share =
= $25
e.
(1) If Jordan Ellis’s predictions are correct, what will be the value per share of Encore stock if the firm
maintains a constant annual 6% growth rate in future dividends? (Note: Continue to use the new
required return here.)
Given:
•
Constant annual growth (g) = 6%
•
a constant annual growth rate in dividends per share of 6%
•
Form (2C) - The New Required Rate of Return (RRR) = 16%
•
Common stock dividend per share $4.00 then
Using Constant Growth
The Present Value Per Share P0
(2) If Jordan Ellis’s predictions are correct, what will be the value per share of Encore stock if the firm
maintains a constant annual 8% growth rate in dividends per share over the next 2 years and 6%
thereafter?
Given:
•
•
•
•
Constant annual growth next 2 Year (g) = 8%
Constant annual growth thereafter (g) = 6%
Form (2C) - The New Required Rate of Return (RRR) = 16%
2015 Common stock dividend per share (D0) $4.00
Then
Using Variable Growth
𝐷�1�=�𝐷�0(1�+�8%)1�=�4(1.08)1 = 4.32
𝐷�2�=�𝐷�0(1�+�8%)2�=�4(1.08)2= 4.67
𝐷�3�=�𝐷�2(1�+�6%)1�=�4.67(1.06)1= 4.95
15 | P a g e
PV = 3.72+3.47+36.77 = $43.96
f. Compare the current (2015) price of the stock and the stock values found in parts a, d, and e.
Discuss why these values may differ. Which valuation method do you believe most clearly represents
the true value of the Encore stock?
Valuation Method
Per Share
Price per share of common stock
$40
The Current book value
$24
Using Zero Growth Dividends
$25
Using Constant Growth
$42.4
Using Variable Growth
$43.96
The Values Different Because: It has differences on dividends growth.
•
BV per share: Can’t be used as stock valuation, except comparing it with peers and using
it as P/B multiples.
•
Zero Growth: the most conservative method, but lacks of reality sense therefore not good
method.
•
Constant and variable Growth: Both methods have similar stock price target, but variable
is more realistic since it measures shift up or down due to the changing expectations.
valuation method I believe most clearly represents the true value of the Encore stock
Based on the computation, the book value has no relevance to the true value of the firm. Of the
remaining methods, the most conservative estimate of value is given by the zero-growth model.
Wary the analyst should advise paying no more than $25 per share.
16 | P a g e