Introduction to Corporate Finance, Fourth Edition. Chapter 7: Equity Valuation

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1 Chater 7: Equity Valuation Multile Choice Questions 6. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) A D 0 $2.00. D 1 $2.00 ( ) $2.13 RF + Ris Premium 4% + 7.5% 11.5% P 0 $2.13/( ) $ Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) C Payout ratio D 0 /EPS 0 $1.5/$3 1/2 50% ROE NI/E EPS/BVPS $3/$36 1/ % g (1 ayout ratio) ROE (retention ratio) ROE (1 1/2) 8.33% 4.17% Practice Problems Basic 16. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Level of difficulty: Basic Exected dividend, required rate of return, and the constant dividend growth rate. 19. Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 Level of difficulty: Basic Solving these questions involves the algebraic maniulation of the referred share valuation formula. Preferred Shares in Canada Required Dividends Co. Price Par value Dividend rate return aid er share A $5.00 $100 8% 5% $5.00 P s 0.08 $62.50 B $60 $50 3% $ % $50.00 $60 D 0.03 D $1.80 Solutions Manual 1 Chater 7

2 C $70 $75 $8.00 $ % D $50 $50 $7.00 $50 14% $ % $75.00 $ % D.14*50 $7.00 E $150 $30 7% $ % $30.00 $150 D 0.07 D $10.50 F $9.50 $100 4% $9.50 P s 9.5% 0.04 $100 $9.50 $ G $18 $18 7% 9% $18.00 P s 9% 0.07 Par $ Par $200 H $18 $0.90 5% 6% D 6% $18 Par 0.05 Par $15 D $ Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Level of difficulty: Basic a. Assuming the dividend is aid annually: P! D! + P! 1 +! D! + P! ! P! % b.! D! + P! P! % c. P! D! + P! 1 +! P! P! 1 +! D! $41.60 d. Solutions Manual 2 Chater 7

3 P 1 48(1+.18) 4 $52.64 Intermediate 31. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) No, my broer is incorrect. Debt: bans are not immune from failure and default and therefore some ris will always exist. In fact, in 1985 two Alberta-based bans, the Northlands Ban and the Canadian Commercial Ban, failed. Preferred stoc: there are generally no voting rights associated with referred stoc. Common stoc: there is no legal obligation to ay a dividend and the failure to ay a dividend on common stoc does not trigger banrutcy. The fact that the firm has aid a dividend of $2.50 er year for the ast 18 years is irrelevant. 38. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) The easiest way to solve this roblem is to use Excel. Year Growth Stoc rice at Present value of Dividend rate end of year 7 each cash flow % % % % % % % % Discount rate: 12% Price of stoc in year 0: $ The rice of the stoc today is $48.98 The Excel formulas: A B C D E Solutions Manual 3 Chater 7

4 1 Year Growth rate Dividend Stoc rice at end of year 7 Present value of each cash flow A (1+B3)*C2 (C3+D3)/(1+C$12)^A3 4 1+A (1+B4)*C3 (C4+D4)/(1+C$12)^A4 5 1+A (1+B5)*C4 (C5+D5)/(1+C$12)^A5 6 1+A (1+B6)*C5 (C6+D6)/(1+C$12)^A6 7 1+A (1+B7)*C6 (C7+D7)/(1+C$12)^A7 8 1+A (1+B8)*C7 (C8+D8)/(1+C$12)^A8 9 1+A (1+B9)*C8 C10/(C12-B10) (C9+D9)/(1+C$12)^A A (1+B10)*C Discount rate: Price of stoc in year 0: SUM(E3:E9) 42. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) a. Current share rice of Dillon Mechanical: P! D!! g $15 P! P! 1 +! 15! 1.15! $8.58 b. Current share rice of Sterling: P! D!! g D! 1.02! g $47.08 c. PVGO of Dillon Mechanical: P! EPS!! + PVGO PVGO PVGO!"##$% The negative PVGO suggests that Dillon s growth is destroying value d. PVGO of Sterling: P! EPS!! + PVGO Solutions Manual 4 Chater 7

5 PVGO PVGO!"#$%&'( 7.08 The ositive PVGO suggests that Sterling s growth oortunities are creating value. 46. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Time line: a. Calculating g 2 D 5 ( ) 4 ( 1+ g 2 ) P 4 D 1+ g 0 1 c g 2 c g ( )4 ( 1+ g 2 ) g g g g g 2 or : g % ( ) b. Calculating rice of TelTec 5 years from now: P 5 P 4 ( 1+ g 2 ) $ $10.84 Alternatively : You can also use the following formula to get the same answer D 6 ( ) 4 ( 1+ g 2 ) 2 P 5 D 0 1+ g 1 c g c. Current rice of TelTec will be the resent value of the $10 rice in year 4 lus the resent value of all the dividends aid in years 1 through 4. The ayments in year 1 through 4 reresent a growing annuity, therefore, using the resent value of a growing annuity formula: D P g 1 c g 1 1+ c P Excel 4 + P 4 ( ) 4 1+ c ( ) 4 $7.32 Solutions Manual 5 Chater 7

49. Section: Aendix 7B Additional Multiles or Relative Value Ratios Learning Objective: 7.7 PayoutD 0 /EPS 0 $4/$6 0.6667, Retention ratio (b) 1 Payout ratio 1 0.6667 0.3333 D/E0.

6 49. Section: Aendix 7B Additional Multiles or Relative Value Ratios Learning Objective: 7.7 PayoutD 0 /EPS 0 $4/$ , Retention ratio (b) 1 Payout ratio D/E0.6, leverage ratio A/E(D+E)/E(0.6+1)/11.6 ROE Net rofit margin Asset turnover leverage ratio 15% % g b ROE % 10% EPS 1 EPS 0 (1 + g) $6 1.1 $ % + 10% 13.5% Leading P/E ayout/( g) /( ) P 0 leading P/E EPS $6.60 $ Section: 7.2 Preferred Share Valuation Learning Objective: 7.2 The required rates of return for the two stocs: Dillon: $70 D 0.07 * % Sherwood: $45 D 0.04 * % As the ris-free rate is the same for both firms, the only way Sherwood can have a higher required return is if the ris remium is higher. A higher ris remium reflects a higher level of ris; therefore, Sherwood is the risier referred stoc. Solutions Manual 6 Chater 7

7 53. Section: 7.4 Using Multiles to Value Shares Learning Objective: 7.4 There are two roblems with Prime s analyst s statement: first, a constant P/E ratio imlies a constant growth over time the growth could be zero, ositive or negative. The more imortant roblem with the statement is that WX is only a good investment if its return is greater than or equal to the required rate of return. If the investment earns less than its required rate of return, then by definition, it is a bad investment regardless of the growth rate of the earnings. 56. Section: 7.3 Common Share Valuation: The Dividend Discount Model (DDM) Begin by determining the sustainable growth rate for the three eriods: Years 1 to 5, g 1 1% (1 0.05) % Years 6 to 10: g 2 15% (1 0.10) 81.00% Years 11 to : g 2 5% (1 0.50) 3.50% Year Growth rate Dividend Stoc rice at end of year 10 Present value of each cash flow % % % % % % % % % % % Discount rate: 15% Price of stoc in year 0: $ Solutions Manual 7 Chater 7

1 < = α σ +σ < 0. Using the parameters and h = 1/365 this is N ( ) = If we use h = 1/252, the value would be N ( ) =

1 < = α σ +σ < 0. Using the parameters and h = 1/365 this is N ( ) = If we use h = 1/252, the value would be N ( ) = Chater 6 Value at Risk Question 6.1 Since the rice of stock A in h years (S h ) is lognormal, 1 < = α σ +σ < 0 ( ) P Sh S0 P h hz σ α σ α = P Z < h = N h. σ σ (1) () Using the arameters and h = 1/365 this