Chapter 4

Question 1

Two primary forms of valuation:

Answer 1

1. Relative valuation
2. Discounted CF Analysis

Question 2

Price-to-earnings (P/E) ratio

Answer 2

One of the most common ratios used in relative valuation. Typically, the diluted EPS is used in the denominator. The price/earnings ratio of a corporation is a comparison of its current price in the market relative to its earnings per share. It’s an indication of how the market capitalizes a company’s earnings, or what the market is willing to pay for each dollar of earnings. If the market value of the stock is trading at five times its earnings and the corporation’s EPS is $3.20, it’s expected that the price per share will be $16.00. An increase of one dollar in earnings would, in turn, project an increase in the share price by $5.00.

• For companies that are particularly sensitive to cyclicality, the P/E ratio may not provide an adequate reflection of the company. If the trailing P/E is used, it may be especially high at the bottom of a cycle and excessively low at the top of a cycle. This is known as the Molodovsky Effect.
• In order to counter the Molodovsky effect, analysts often use normalized EPS. Often this just simply entails taking the average EPS over a certain period of years.

Question 3

Trailing EPS vs Leading EPS

Answer 3

Trailing EPS: Price ÷ trailing 12 months’ EPS

Leading EPS: Price ÷ projected EPS

• When comparing two companies, EPS MUST use the same time frame.
• Analysts MUST take into account nonrecurring items. Due to the effects of non-recurring items, the trailing P/E may not always be appropriate for the projection of future earnings. In such cases, it may be more pertinent to use the second method of calculating EPS called leading (forward) P/E.
• One of the drawbacks of using leading EPS is that the projections may not be accurate.

Question 4

Relative P/E

Answer 4

Investors use P/E as a proxy for earnings growth. If the perceived growth is less than the growth of a benchmark index, it will be reflected in the P/E. This is true for both a trailing P/E and forward-looking P/E. If the market multiple is 15, a company with an identical P/E is considered to have a relative P/E of 1.0.

Question 5

Trailing P/E example:
A RA is evaluating Firm A’s trailing P/E ratio. Earnings for the first 3 quarters were $0.19, $0.21, and $0.18, respectively. The earnings for the fourth quarter of the prior year were $0.16, however there was an acquisition expense of $0.08. The current price of the stock is $16.40. What is the trailing P/E ratio

Answer 5

Adjusted earnings in Q4 of prior year = $0.16 + $0.08 = $0.24
Sum of earnings = ($0.24 + $0.19 + $0.21 + $0.18) = $0.82
$16.40 ÷ $0.82 = $20

Question 6

P/E ratio example 2:
Given:
Annual dividend = $1.50
Dividend payout ratio = 40%
Dividend yield = 2%
What is the P/E ratio?

Answer 6

EPS = annual dividend ÷ payout ratio = $1.50 ÷ 0.40 = $3.75
Price = annual dividend ÷ dividend yield = $1.50 ÷ .02 = $75
$75 ÷ $3.75 = 20

Question 7

True or false: P/E is a good tool when earnings are negative?

Answer 7

False, earnings yield is a better option

Question 8

Earnings yield

Answer 8

The reciprocal of P/E. Earnings yield is good for ranking companies from least expensive to most expensive in terms of the earnings that one dollar of investment will purchase.

• A lower earnings yield (more negative) indicates which company is more overvalued.

Question 9

The Fed Stock Valuation Model (FSVM)

Answer 9

A method of valuing the overall stock market by comparing the forward earnings yield of a broad stock market index against the yield on 10-year Treasuries.

• When the 10-year yield is larger than the stock market’s forward earnings yield, the market is overvalued and if vice versa it’s undervalued.

Question 10

P/E-to-Growth (PEG) Ratio

Answer 10

A ratio that goes a step further than the P/E by addressing expectations for continued operations of the company. When using the PEG, investors will normally look for a ratio of 1.0 or less. A ratio > 1 indicates it’s overvalued, whereas a ratio < 1 indicates it’s undervalued.

Formula: P/E ratio ÷ annual growth rate of the company (in %- DO NOT convert to decimal)

• The forward growth rate can be a projection or use historical data.
• There are weaknesses of the PEG ratio. Mainly, there is an assumption that the growth rate forecast will be accurate or that the historical trend will continue. Also, if the PEG ratio is used to compare firms accross different industries, there might be other factors to consider that would justify a higher PEG ratio (ex: Aggressive investor interest in tech).
• Similar to the P/E ratio, it’s pointless if there are negative earnings.

Question 11

True or false: If a company has historically traded at 15 times earnings, and is currently trading at 12 times earnings, it might signal a buying opportunity?

Answer 11

True. This is an example of an undervalued stock.

Question 12

PEG ratio example:
Given:
Market cap = $440mm
NI = $40mm
TA = $400mm
TL = $150mm
Dividend payout ratio = 50%
What is the PEG ratio?

Answer 12

P/E ratio = Market cap ÷ NI = 440 ÷ 40 = 11
ROE = 40mm ÷ (400mm - 150mm = 250mm) = 16%
Growth rate = [ (1 - dividend payout ratio) * ROE ] = [ (1 - 0.50) * 0.16 ] = 8%
PEG ratio = 11 ÷ 8 = 1.375

Question 13

How to calculate the price target from the PEG ratio

Answer 13

PEG ratio * growth rate = P/E ratio
P/E * next year’s EPS = price target

Question 14

Rule of 72

Answer 14

To find the growth rate, take 72 ÷ # of years it will take earnings to double

Question 15

Compound annual growth rate

Answer 15

Formula: ((ending value ÷ beginning value)^(1 ÷ # of years)) - 1

Question 16

Avg. Annual growth rate

Answer 16

The average growth rate for a period of time

Question 17

Annual growth rate calculation

Answer 17

((ending value ÷ beginning value) - 1) * 100

Question 18

Price-to-Cash flow (P/CF)

Answer 18

Measures the price per unit of CF. CF in this context means FCF: CFO - CAPEX.

The free CF yield is equal to the recipracol of the P/CF.

Question 19

Price-to-sales

Answer 19

Useful for evaluating firms w/ negative earnings, having low margins, or are start-ups. This ratio can be used to mitigate differences in a firm’s capital structure and leverage. Also, this ratio IS NOT influenced by a firm’s accounting decisions.

Formula: Market cap ÷ Sales/revenue

• This ratio can vary substantially by industry.

Question 20

Price-to-book (P/B)

Answer 20

This is a less volatile # that P/E. P/B is a common metric for financial sector stocks since they hold large amts of liquid assets.

Formula: Price ÷ BVPS

• If P/B is < 1 it means that the firm is selling below its BV and theoretically below its liquidation value.
• Some investors will avoid any companies that trade above 2X BV.

Question 21

How to calculate BV

Answer 21

Shareholders’ equity ÷ # of shares of stock outstanding

Question 22

Enterprise value (EV)

Answer 22

The EV is the real tangible price that a company can be purchased. However, EV IS NOT necessarily the price a buyer is willing to pay or a buyer is willing to accept.

Formula: Market cap of CS and PS + debt + capital leases + minority interet - cash & cash equivalents
OR
equity value + net debt

• Cash & cash equivalents are added back since the purchaser will acquire these and thus considered a reduction to the acquisition cost.
• If a firm has cash and no debt OR cash > debt, the EV < market cap.
• If a firm has no cash, the EV is the MV of the stock + MV of debt.
• If a firm has cash < debt, the EV > market cap

Question 23

Equity value calculation

Answer 23

(EV + cash) - (long-term debt + short-term debt)

Question 24

EBITDA

Answer 24

EBITDA allows for firms w/ different amts of interest, taxes, and D&A to be compared.

Question 25

EV-to-EBITDA

Answer 25

When comparing this ratio between two companies, a lower ratio could signal an undervalued firm and if vice versa it could be overvalued.

Question 26

How to calculate the EV of a company after an acquisition

Answer 26

1. To calculate the new market cap: take (the $ amt of the acquisition funded by equity ÷ purchaser's stock price). This value is the new amount of shares added to the shares outstanding. 2. Multiply #1 * market price per share to get the market cap 3. #2 + net debt (debt - cash) of both companies 4. #3 + the $ amt of debt that was used to fund the acquisition.

Question 27

EV-to-net sales

Answer 27

This ratio measure the economic value of a firm and its use to generate sales. By using this ratio, the RA eliminates the effects of different methods of calculating operating expenses (ex: lease accounting, capitalizing expenses, etc.) Net sales = revenue - trade discounts - returns & allowances - excise taxes

Question 28

Value of the firm calculation

Answer 28

CF to the firm ÷ (1 + WACC)

Question 29

Value of the equity calculation

Answer 29

CF to equity ÷ (1 + COE)

Question 30

Cost of capital

Answer 30

The required rate of return necessary to enter into and finance corporate projects. It's the opportunity cost of entering into business decisions.

Question 31

How to calculate cost of debt

Answer 31

Interest ÷ Principal ## Footnote * Add IB fees, legal fees, accounting fees, and/or printing costs to the denominator.

Question 32

How to calculate cost of PS

Answer 32

Preferred dividend ÷ price of PS

Question 33

True or false: Interest and dividends are after-tax entries?

Answer 33

False, interest expense is a pre-tax entry, whereas dividends are after-tax entries.

Question 34

How to determine how much to increase EBIT when dealing w/ PS

Answer 34

1. Preferred dividend ÷ (1 - tax rate %) 2. #1 * amt of PS issued 3. Increase EBIT by #2 to cover the cost of the preferred dividend OR (Proceeds * after-tax cost of debt) ÷ (1 - tax bracket %) Proceeds = Amt of PS issued * after-tax cost of PS/debt | This is a PS adjustment when calculating earnings available to common ## Footnote * If we don't do this, earnings available to common shareholders will be higher for debt than PS.

Question 35

After-tax cost of debt

Answer 35

Pre-tax cost of debt * (1 - tax rate %)

Question 36

Two primary methods of calculating COE:

Answer 36

1. CAPM 2. DGM

Question 37

CAPM

Answer 37

Formula: k = Rf + (β * market risk premium)

Question 38

DGM

Answer 38

k = (D1 ÷ P0) + g ## Footnote * If the company invests the amount that it didn’t pay in dividends, and doesn’t earn the required rate of return (7.0%), the value of the stock should decrease

Question 39

True or false: If a company is going to create equity through a new issue of common stock, the cost of capital will be higher than through RE?

Answer 39

True, since there are underwriting fees associated w/ the distribution of the new issue, COE goes up.

Question 40

How to calculate cost of capital for a new issue?

Answer 40

[ D1 ÷ (P0 * (1 - F)) ] + g - F = underwriting fee

Question 41

WACC formula

Answer 41

WACC = wd * rd * (1-T) + we * re + wps * rps | * Be careful if the exam gives pre-tax cost of debt!!!!

Question 42

How to calculate debt and equity weights given a D/E ratio? Ex: 40% D/E with $40MM in debt and $100MM in equity.

Answer 42

Total capital = $100MM + $40MM = $140MM Debt % of Capital = $40MM ÷ $140MM = 28.57% Equity % of Capital = $100MM ÷ $140MM = 71.43%

Question 43

True or false: If a company issued additional debt, the WACC would decline since the cost of debt is generally cheaper than the cost of equity. In addition, if a company replaced debt with preferred stock, the WACC would increase since there’s a tax shield (tax advantage) associated with debt?

Answer 43

True

Question 44

Free CF

Answer 44

CFs that are not required to be reinvested into operating activities in order to purchase new equipment or maintain present production capacity.

Question 45

FCFF

Answer 45

The CFO available to providers of capital (bondholders and stockholders) after operating expenses have been covered. Operating expenses include working capital (investments in inventory), fixed capital (investment in new or maintenance costs on existing equipment), and the payment of taxes. Formula: (EBIT * (1 - T)) + D&A - CAPEX - increases in WC

Question 46

FCFE

Answer 46

The cash available to stockholders after funding capital requirements and expenses associated with debt financing. Formula: NI + D&A - CAPEX - increases in WC

Question 47

PV of FCFF

Answer 47

FCFF ÷ (1 + WACC)^t ## Footnote * By using free cash flow to the firm and the weighted average cost of capital, we derive a value for both the debt and equity holders of the company

Question 48

PV of FCFE

Answer 48

FCFE ÷ (1 + COE) OR FCFF - MV of debt | To get equity value per share, divide by shares outstanding

Question 49

Terminal value

Answer 49

The projected CFs for the indefinite future. For relative valuation, just multiply EV/EBITDA by the last projected CF Formula in DCF analysis: Expected CF ÷ (discount rate - terminal growth rate)

Question 50

Enterprise value

Answer 50

(CF1 ÷ (1 + WACC)^1) + (CF2 ÷ (1 + WACC)^2) ... (CFn ÷ (1 + WACC)^n) OR [ CF * (1 + g) ] ÷ (discount rate - growth rate) OR Net present value = Annual CF in perpetuity ÷ WACC

Question 51

Valuation using DDM

Answer 51

P0 = (D1 ÷ (1 + k)) + (D2 ÷ (1+k)^2) ... + (dn ÷ (1 + k)^n) - k = the discount rate consistent with the uncertainty of the dividend estimates. ## Footnote * DDMs are less sensitive to short-term fluctuations of value than other DCFs

Question 52

Valuation using DDM if no expected growth

Answer 52

P0 = D1 ÷ k In the constant growth case, k = (d1 + g) ÷ P0 In the constant growth case, P0 = d1 ÷ (k - g) g = b * roe b - retention rate = (1 - payout ratio)

Question 53

Main challenges presented with DDMs

Answer 53

1. What DDM should be used for a given company 2. What method will be used to forecast dividends 3. What discount rate should be used to discount CFs to PV

Question 54

True or false: FCF analysis may also be used to calculate the amount of additional leverage or borrowing a company can incur?

Answer 54

True

Question 55

Economic profit

Answer 55

Different than accounting profit because it takes into account cost of capital- not only profit from operations but also profit above the expected returns on CAPEX. Economic profit also incorporates market expectation and opportunity cost. ## Footnote * IF economic profit is > the cost of capital, value is created and if vice versa, value is destroyed.

Question 56

Marginal revenue formula

Answer 56

△TR ÷ △Q

Question 57

Marginal cost formula

Answer 57

△TC ÷ △Q ## Footnote * If MR > MC, economic value is created * If MR < MC, economic value is destroyed

Question 58

Sum-of-the-parts analysis

Answer 58

A process of valuing a company by determining what its aggregate divisions would be worth if they were spun off or acquired by another company. Valuation is typically done by taking the current income of each segment and multiplying each respective income by the projected growth rate for the segment to the power of whatever time period. Then, sum the projected income of each segment together. Multiply this number by what similar companies sell in comparison to the NI (ex: 15X NI). Then, discount that number into present terms using ROE as the discount rate. ## Footnote * When using a sum-of-the-parts analysis it may be necessary to use different valuation metrics for each business unit. For example, you might use 6.0 times EBITDA for one unit, 1.5 times revenue for another unit, and 13.0 times earnings for a third unit. By adding the value of all three units, subtracting the net debt, and allowing for any non-operating adjustments, the research analyst could calculate the equity value of the firm. In some instances, you would use a DCF analysis with some businesses and a relative valuation with others

Question 59

What to look for when determining what ratios to use in relative valuation:

Answer 59

1. P/E: Growth, payout, risk 2. P/B: Growth, payout, risk, ROE 3. P/S: Growth, payout, risk, net margin 4. EV/EBIT: Growth, some reinvestment needs, leverage, risk 5. EV/EBITDA: Growth, greater reinvestment needs, leverage, risk 6. EV/S: Growth, net CAPEX needs, leverage, risk, operating margin 7. EV/B: Growth, leverage, risk, and return on capital 8. EV/EBITDAR: Companies that depend on leases (ex: restaurants and retail) | R in EBITDAR stands for restructuring

Question 60

Typical multiples used for certain sectors

Answer 60

1. Cyclical industries → Relative P/E (w/ normalized earnings) 2. High tech, High growth → PEG 3. High tech, no earnings → P/S or EV/S 4. Heavy infrastructure → EV/EBITDA 5. REIT → P/CF or FFO 6. Financials → P/BV, EV/B OR P/Net TBV 7. Retail → P/S or EV/Sales

Question 61

When is it appropriate to use DCFs?

Answer 61

1. When CFs are positive 2. When CFs can be estimated reliably in future periods 3. When the benchmark for risk (Treasuries) have a positive correlation to the stock price

Question 62

When is it appropriate to use DDMs

Answer 62

When all of #61 applies, and the dividends considered CFs are positive and can be accurately forecasted.

Question 63

M&A valuation

Answer 63

When one company agrees to purchase another, the acquiring company may use cash, its common stock, or a combination of the two. If the acquisition is made in stock, a research analyst would need to understand the concept of the exchange ratio. Ex: Firm A agrees to acquire Firm B for a 20% premium using common stock. Firm A's EPS is $3 and its P/E ratio is 16X. Firm B's EPS is $1.25 and its P/E ratio is 20X. From these, we know that firm A trades at $48 and Firm B trades at $25.

Question 64

Exchange ratio formula

Answer 64

[ (EPS of acquiree * P/E ratio of acquiree) * any premium/discount ] ÷ (EPS of acquirer * P/E of acquirer)

Question 65

How to determine whether an acquistion is accretive or dilutive?

Answer 65

Sum of the net incomes of the two companies ÷ total number of shares of the acquirer, including the additional shares issued to fund the transaction. Ex: Firm A agrees to acquire Firm B for a 20% premium using common stock. Firm A's EPS is $3 and its P/E ratio is 16X. Firm B's EPS is $1.25 and its P/E ratio is 20X. From these, we know that firm A trades at $48 and Firm B trades at $25. Firm B has $2mm shares outstanding and Firm B has $900m shares outstanding. Firm A's NI is $6mm while Firm B's NI is $1.125MM. The total acquistion cost is $30 * 900,000 shares outstanding = $27MM. This will require $27MM ÷ 48 = 562,500 shares to be issued by Firm A to pay for the transaction. This will bring the total shares outstanding to (2MM + 562,500) = 2.5625MM. The new EPS for the firm is ($6MM + $1.125MM) = $7.125MM ÷ 2.5625MM = $2.78. Since the original EPS was $3.00, and now it's $2.78, the transaction is immediately dilutive.

Question 66

How to determine the # of shares that the smaller firm in a merger will own?

Answer 66

Number of shares created ÷ Total number of shares after the merger If a transaction is a combo of cash and stock, in order to find the % of ownership multiply the exchange ratio by the % of the offer in the stock. If only cash is used: The additional interest expense needs to be deducted from EBIT in order to calculate the revised NI.

Question 67

Stock transaction vs cash transaction example: Firm A Revenue - $1,000 Operating income $98 Interest expense - $10 Taxes - $34 NI = $54 Shares outstanding - 60 Firm B Revenue - $900 Operating income $92 Interest expense - $7 Taxes - $32 NI = $53 Shares outstanding - 30 (i) Firm B has agreed to be acquired by Firm A. The terms of the acquisition require the issuance of 1.5 shares of Company A common stock for each share of Company B. What’s the effect on the EPS of Firm A following the acquisition? (ii). If Firm A agrees to acquire Firm B for $250MM cash, raised by issuing 7% debentures, what’s the accretive effect on Firm B’s EPS, assuming no change in the tax rate for the company? Assume a 38.6% tax rate.

Answer 67

(i). EPS before transaction: $54 ÷ 60 = $0.9 EPS after transaction: 1.5 * 30 = 45 new shares that must be issued. 45 + 60 = 105. ($54 + $53) ÷ 105 = $1.02. It's immediately accretive (ii). Interest expense for debt raised = $250mm * 0.07 = $17.5mm Combined revenue = $1,000 + $900 = $1,900 Combined operating income = $98 + $92 = $190 Combined interest expense = $10 + $7 + $17.5 = $34.5 Combined taxes = ($190 - $34.5) * (1 - .386) = $59.83 NI = ($190 - $34.5) - $59.83 ~ $95.5 EPS: $95.5 ÷ 60 = $1.59. It's immediately accretive.

Question 68

True or false: An acquisition is considered accretive to shareholder value if the return on invested capital (ROIC) > the weighted average cost of capital (WACC)?

Answer 68

True

Question 69

Example: How enterprise value is affected by M&A Prior to transaction: Firm A: CS outstanding = 2.4MM Market value = $20.00 Debt outstanding = $52MM Cash & Cash equivalents= $16.5MM Firm B: CS outstanding= 2MM Market value = $11.00 Debt outstanding = $10MM Cash & cash equivalents = $5MM Firm A agrees to purchase Firm B for $20MM. The terms of the acquisition are: $6MM of Firm A's CS (based on the MV of $20 per share); $4MM of newly issued Firm A 6.0% debentures; $10MM cash to Firm B shareholders, obtained from Firm A's revolving credit line; and $10MM in assumed debt of Firm B. What is the new enterprise value if Firm A stock is trading at $23.00 after the acquisition is complete?

Answer 69

1. Combined CS: 2.4MM + ($6MM ÷ $20) = 2.7MM 2. Combined debt outstanding: $52MM + $10MM + $4MM + $10MM = $76MM 3. Combined cash & cash equivalents: $16.5MM + $5.5MM = $21.5MM 4. Market cap = $2.7MM * 23 = $62.1MM 5. #4 + net debt (#2 - #3) = $116.6MM

Question 70

How do employee stock options affect M&A transactions?

Answer 70

Most companies will use the proceeds from the exercised options to repurchase shares in the opern market at the current market price. Any differential in the # of shares will be made up through treasury stock.

Question 71

Employee stock options' affect on M&A transactions example: Current shares outstanding = $6mm Number of options: 300m at a strike price of $25 AND 200m at a strike price of $50 Current stock price = $30 per share

Answer 71

(300m * $25) = $7.5mm $7.5MM ÷ $30 = 250m shares bought back The difference between the # of shares repurchased and the # of shares granted through the exercise of options equals (300m - 250m) = 50m. This difference is issued from the firm's treasury stock account, which will bring the # of shares outstanding to $6,050M | * the 200m options won't be exercised since they're out-the-money

Question 72

True or false: Transaction value = enterprise value?

Answer 72

True

Question 73

How to calculate goodwill after the transaction is complete?

Answer 73

Offer value - net tangible assets → This amount will be added to the acquirer's existing goodwill to calculate the new total goodwill Net tangible assets = Total assets - liabilities - existing goodwill - intangibles

Question 74

True or false: In a strong-dollar environment, U.S. companies will be more attractive takeover candidates by foreign acquirers?

Answer 74

False, they will be less attractive since foreign buyers will have less buying power.

Question 75

Common stockholders' equity formula

Answer 75

Net worth - preferred stockholders' equity

Question 76

True or false: Effecting a stock buyback will decrease ROE?

Answer 76

False, it'll increase ROE

Question 77

True or false: If a company effects a stock buyback, it'll decrease the firm's outlook for internal growth?

Answer 77

False, effecting a buyback will cause income to be spread over fewer shares which will increase the firm's outlook for internal growth.

Question 78

Events that will affect the P/E ratio

Answer 78

* Projected growth rate of a company/industry: If a firm is expected to grow rapidly, it justifies a higher P/E ratio. * Litigation * Capital structure change by a company * Cost of capital: a relatively small difference in beta will cause a pronounced difference in the cost of capital.

Question 79

Example: Firm A has a P/E ratio of 34 and normally trades at a premium of 150% to the S&P 500 Index. The historic range of the firm's P/E is 20-35. If the S&P 500 Index has an average P/E of 18, which of the following descriptions best characterizes the company? A. It appears to be underpriced B. It's a growth company w/ accelerated earnings C. It's in a mature, cyclical industry D. It's expected that the earnings of the company are decelerating

Answer 79

B. The high P/E ratio shows that the company is growing rapidly. Firms in mature industry typically show little growth.

Question 80

P/E ratio formula 2

Answer 80

Dividend payout ratio ÷ dividend yield EPS = annual dividend ÷ payout ratio Price = annual dividend ÷ dividend yield

Question 81

Dividend yield formula

Answer 81

Dividend payout ratio * earnings yield

Question 82

Sustainable growth rate formula

Answer 82

(1 - dividend payout ratio) * ROE

Question 83

Example: Enterprise value = $1.2B Stock price = $40 Shares outstanding = 19MM Employee stock options ($25 stock price) = 6MM Debt = $250MM How to compute the equity value per share

Answer 83

1. Use the treasury stock method to determine the new # of outstanding shares: (6MM * $25) = 150MM 2. #1 ÷ $40 = 3.75MM 3. The difference between (6MM - #2 = 2.25MM shares) will be issued. 4. Equity value = $1.2B - $250MM = $950MM 5. $950MM ÷ (19MM + 2.25MM) 21.25MM = $45