Homework and Assigned Reading

Security Analysis (FIN 40610)

Professor Zambrana
Lecture 6 – Relative Valuation

Lecture 6 deals with relative valuation or multiples. We will start with a basic discussion of multiples
and how to interpret them. We will then describe specific multiples in more detail focusing on their
definitions, their distributions, and the fundamental characteristics that drive variation in the multiple
across firms. We will focus our attention on P/E and EV/EBITDA multiples, but the concepts we discuss
can be applied to any other multiple, including PEG ratios, book value multiples, and revenue multiples.

Homework:
Complete the homework problems on the attached pages and compare your solutions to the answer
key available on Canvas.

Required and Related Reading:

The table below describes the required reading from the McKinsey book. I recommend reviewing all
end-of-chapter review questions associated with the required McKinsey readings. You should focus on
the topics covered in class and your course notes in both the readings and review questions.
For those who want to gain a deeper knowledge of valuation, I have listed additional related readings
from the McKinsey and Damodaran books.

Required Reading:

Book Chapter Topic

McKinsey Ch. 18 Using Multiples

Optional Related Reading:

Book Chapter Topic

Damodaran Ch. 17 An Overview of Relative Valuation
Damodaran Ch. 18 Earnings Multiples
Damodaran Ch. 19 Book Value Multiples
Damodaran Ch. 20 Revenue Multiples and Sector-Specific Multiples

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 Problem Set #6
1. A firm has $600 market value of equity and $300 market value of debt. The firm also has $100 in
nonconsolidated subsidiaries and $50 in excess cash. If the firm’s expected EBITDA is $100, what is
the Enterprise Value-to-EBITDA ratio?
a. 7.5x
b. 9.0x
c. 11.0x
d. 6.9x
Since EBITDA represents earnings from the firm's core operations, the EV calculation is adjusted to
exclude items (like nonconsolidated subsidiaries) that do not contribute directly to these operations.
EV=Market Value of Equity + Market Value of Debt − Cash and Cash Equivalents − Value of
Nonconsolidated Subsidiaries
EV = 600 + 300 – 50 – 100 = 750
EV/EBITDA = 750/100=7.5x

2. Suppose that a company has no debt, non-operating assets nor excess cash. The EV/EBITDA ratio
for the company is 11.2 and growth is estimated to be 3.5%. Additionally, the firm has tax rate of
20%, D&A of $500m, interest income $50m, and net income $14,360 m. What is the value of the PEG
ratio?
a. 2.67x
b. 4.1x
c. 3.75x
d. 6.86x
EBITDA=Pre-tax Income - Interest Income After Tax + D&A = [14,360 / (1-0.2)] - 50 + 500
= 17,950 - 50 + 500 = 18,400
E = EV = EV/EBITDA x EBITDA = 206,080
P/E ratio = 206,080/14,360 = 14.35x
PEG Ratio = PE ratio / g = 14.35/ 3.5 = 4.1x

3. Do you agree with the following statement: Future value creation for the firm comes from growth
greater than the cost of capital?
a. Yes, because the benefits of growth need to be greater than the cost of capital for a firm to create
value.
b. Yes, because growth will always drive value.
c. No, because value typically isn’t created when the cost of capital is less than growth.
d. No, because return on capital needs to be greater than the cost of capital in order to create value.
D. Growth by itself does not guarantee value creation. A firm can grow by reinvesting in its business,
but if the return on capital (ROC) from that reinvestment is less than the cost of capital (CoC), the firm
destroys value rather than creating it. Value creation occurs when the firm’s return on capital exceeds
the cost of capital.

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4. Choose the best answer: All else equal, the PE ratio will be lower for firms with:
a. Lower cost of equity
b. Higher ROE and higher required reinvestment
c. Lower expected growth
d. Lower expected growth, assuming ROE > cost of equity
C. Higher expected growth in earnings leads to a higher P/E ratio because investors are willing to pay
more for future earnings potential. Conversely, lower expected growth reduces the P/E ratio.

5. Suppose that a company has Cap Ex=$2,390, D&A=$900, change in WC=$1,267, EBIT=$15,482,
Retained Earnings = 2010, and Net Income=$7,236. Additionally, their tax rate is 22.4%, Book value
of debt and equity are $25,225 and $67,834 respectively. Currently the risk-free rate is 1.76%, and
their estimated beta is 1.15. The market is returning 6.56%, currently.
a. Using the fundamental growth calculation, what is the forward PE ratio for this company?

ROE = 7236/67834=0.10667
Ke = 1.76+1.15(6.56-1.76)=7.28%
g = retention rate x ROE = 2010/7236 x 0.10667 = 2.96%
𝑔𝑔
�1−� ��
𝑅𝑅𝑅𝑅𝑅𝑅
𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑃𝑃/𝐸𝐸 = 𝑘𝑘𝑒𝑒 −𝑔𝑔
= (1 – 0.02963/0.10667) / (0.0728-0.02963) = 16.73x

b. If the company has $2,876 million of excess cash and marketable securities, $100 million
impairment charge and earned $224 million in investments, what is the adjusted PE for this
company? Assume the BV equity = MV equity.

Adjusted Equity Value = BV Equity − Excess Cash and Marketable Securities = 67834 – 2876= 64,958
Adjusted Net Income = Reported Net Income + After-Tax Impairment Charge − After-Tax Investment
Income = 7236 + 100 (1-0.224) – 224 (1-0.224) = 7,139.776

𝑃𝑃 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 64958

𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 = = = 9.1𝑥𝑥
𝐸𝐸 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑁𝑁𝑁𝑁𝑁𝑁 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 7139.776

6. Suppose a company has a current share price of $24.50 and 1,189 million shares outstanding. The
company’s net income is $1494.5 million, and its debt is $16,050 million. The cost of equity is
10.42%, the market return is 7.3%, and the risk-free rate is 0.8%. The company’s long-term growth
is expected to be 26.3%. Assume the BV equity (debt) = MV equity (debt). The regression
coefficients for estimating the forward P/E based on several firm characteristics are as follows:

Coefficient Beta
Intercept -0.245
Market Cap 0.001

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 Beta -4.262
Long-term growth 6.560
ROE 0.012
Debt to Capital ratio 0.961

a. Determine the expected P/E ratio using the above information.

Market Cap = 24.5*1189=29130.5

Beta = (Ke – rf) / (Rm-rf) = (10.42-0.8) / (7.3-0.8) = 1.48
ROE = 1494.5/29130.5= 5.13%
D/C= 16,050/(16,050+29130.5)=35.5%
Expected P/E =−0.245+0.001(29130.5)−4.262(1.48)+6.56(0.263)+0.012(0.0513)+0.961(0.355)
=24.64x

b. What share price would the firm need to trade at in order to justify a P/E of 25x?

Given the net income of 1494.5 and the 1189 of shares outstanding, the price that justify a PE of 25x for
an EPS of 1494.5/1189=1.257, is 25 x 1.257 = $31.42

7. The following are the projected cash flows to the firm over the next five years, where an estimated
cost of equity=12% and cost of capital=9.94%. The 5-year projection for EBITDA is $567 million.
The current EV/EBITDA ratio is 10.2x, the current stock price is $5.17, debt is $1,924.77 and market
cap is $2,585 million.

Year CF Firm
1 340.0
2 357.0
3 374.85
4 393.59
5 413.27
Terminal Value 6,000

a. Using the DCF perpetuity growth method, what is the estimated share price?

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b. Using the DCF EV/EBITDA exit multiple method, what is the estimated share price?

5
8. For the most recent year, Apple reported net income of $57,215 million and diluted EPS of $12.73
per share. Weighted-average shares outstanding were 4,459.1 million and weighted-average
diluted shares were 4,495.3 million. The firm reported cash and investments totaling $192,844
million and non-operating income of $4,718 million. Assuming a tax rate of 15% and a stock price
of $373 per share, calculate the P/E ratio for Apple before and after adjusting for non-operating
assets.

P/E = 373/12.73 = 29.3

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Adj P/E = Adj Equity Value / Adjusted Net Income
= [(4,495.3 x 373) – 192,844] / [57,215 – (4,718 x (1-0.15))]
= 1,483,902.9 / 53,204.7 = 27.89

9. Which of the following statements is INCORRECT?

A. P/E ratios are difficult to interpret for firms with negative earnings.
B. P/E ratios are affected by capital structure and by non-operating income.
C. P/E ratios measure equity value relative to earnings available to all claimholders.
D. P/E ratios, by construction, mix capital structures and non-operating items with expectations of
operating performance.
E. None of the above.

P/E Ratios measure equity value relative to equity earnings

10. Which of the following statements is INCORRECT when adjusting the PE ratio?
A. Add the equity value associated with employee stock options.
B. Subtract the value of non-operating assets from the market value of equity.
C. Remove the after-tax value of investment income from the net income.
D. Add back the after-tax value of unusual charges to the net income.
E. None of the above