宏观经济 习题Chap009
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Estimate future dividends in the foreseeable future. Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.
9-5
Constant Growth Example
Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for? P0 = .50(1+.02) / (.15 - .02) = $3.92
D 0(1+ g1) D 0(1+ g1)2 iv iv
…
0 1 2
N
D 0(1+ g1) iv
D N (1+ g2) iv = D 0(1+ g1)N (1+ g2) iv
…
N N+1
…
9-9
Case 3: Differential Growth
We can value this as the sum of: a T-year annuity growing at rate g1
. . .
D N = D N−1(1+ g1) = D 0(1+ g1)N iv iv iv
D N+1 = D N (1+ g2) = D 0(1+ g1) (1+ g2) iv iv iv
N
. . .
9-8
Case 3: Differential Growth
Dividends will grow at rate g1 for N years and grow at rate g2 thereafter
E PS $5 P= = =$31.25 0 R .16
So, NPVGO must be: $75 - $31.25 = $43.75
9-19
Retention Rate and Firm Value
An increase in the retention rate will:
Reduce the dividend paid to shareholders Increase the firm’s growth rate
9-2
9.1 The PV of Common Stocks
The value of any asset is the present value of its expected future cash flows. Stock ownership produces cash flows from:
$2.16
0 1
$2.62 $2.33 $2.52+ .12−.04
2 3
$2.16 $2.33 $2.52+$32.75 P= + + =$28.89 0 2 3 1.12 (1.12) (1.12) $2.62
P= 3 .08
=$32.75
9-14
9.2 Estimates of Parameters
D 1 = D 2 = D 3 =⋯ iv iv iv
• Since future cash flows are constant, the value of a zero
growth stock is the present value of a perpetuity:
D 1 iv D 2 iv D 3 iv P= + + +⋯ 0 3 1 2 (1+ R) (1+ R) (1+ R) D iv P= 0 R
(1.12)
P=$5.58+$23.31
P =$28.89
9-13
With Cash Flows
$2(1.08) $2(1.08)
0 1 2
2
$2(1.08) $2(1.08) (1.04)
3
3
…
3 4
The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.
Chapter 9
Stock Valuation
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
Understand how stock prices depend on future dividends and dividend growth Be able to compute stock prices using the dividend growth model Understand how growth opportunities affect stock values Understand the PE ratio Understand how stock markets work
The value of a firm depends upon its growth rate, g, and its discount rate, R.
Where does g come from? g = Retention ratio × Return on retained earnings
9-6
Case 3: Differential Growth
Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. To value a Differential Growth Stock, we need to:
9-16
Using the DGM to Find R
Start with the DGM:
D ( +g ) D 0 1 1 P = = 0 R- g R- g Rearrange and solve for R: D ( +g ) D 0 1 R= +g = 1 +g P P 0 0
9-17
9.3 Growth Opportunities
Growth opportunities are opportunities to invest in positive NPV projects. The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends plus the net present value of the growth opportunities. EPS P= + NPVG O R
9-10
Case 3: Differential Growth
Consolidating gives:
D T+1 iv C (1+ g1)T R− g2 P= 1− + T T R− g1 (1+ R) (1+ R)
Or, we can “cash flow” it out.
9-1
Chapter Outline
9.1 9.2 9.3 9.4 9.5 The Present Value of Common Stocks Estimates of Parameters in the Dividend Discount Model Growth Opportunities Price-Earnings Ratio The Stock Markets
. . .
3
Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:
D 1 iv P= 0 R− g
Dividends Capital Gains
Valuation of Different Types of Stocks
Zero Growth Constant Growth Differential Growth
9-3
Case 1: Zero Growth
Assume that dividends will remain at the same level forever
ቤተ መጻሕፍቲ ባይዱ
9-7
Case 3: Differential Growth
• Assume that dividends will grow at rate g1 for N
years and grow at rate g2 thereafter.
D 1 = D 0(1+ g1) iv iv
D 2 = D 1(1+ g1) = D 0(1+ g1)2 iv iv iv
9-11
A Differential Growth Example
A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%.
9-15
Where Does R Come From?
The discount rate can be broken into two parts.
The dividend yield The growth rate (in dividends)
In practice, there is a great deal of estimation error involved in estimating R.
9-12
With the Formula
$2(1.08)3(1.04) $2×(1.08) (1.08)3 .12−.04 P= 1− + 3 3 .12−.08 (1.12) (1.12)
($32.75) P =$54×[1−.8966] + 3
9-4
Case 2: Constant Growth
Assume that dividends will grow at a constant rate, g, forever, i.e.,
D 1 = D 0(1+ g) iv iv
D 2 = D 1(1+ g) = D 0(1+ g)2 iv iv iv D 3 = D 2(1+ g) = D 0(1+ g) iv iv iv
(1+ g1)T C P= 1 A − T R−g1 (1+R)
plus the discounted value of a perpetuity growing at rate g2 that starts in year T+1
D T+1 iv R− g 2 P = B T (1+ R)
9-18
NPVGO Model: Example
Consider a firm that has forecasted EPS of $5, a discount rate of 16%, and is currently priced at $75 per share.
We can calculate the value of the firm as a cash cow.
9-5
Constant Growth Example
Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for? P0 = .50(1+.02) / (.15 - .02) = $3.92
D 0(1+ g1) D 0(1+ g1)2 iv iv
…
0 1 2
N
D 0(1+ g1) iv
D N (1+ g2) iv = D 0(1+ g1)N (1+ g2) iv
…
N N+1
…
9-9
Case 3: Differential Growth
We can value this as the sum of: a T-year annuity growing at rate g1
. . .
D N = D N−1(1+ g1) = D 0(1+ g1)N iv iv iv
D N+1 = D N (1+ g2) = D 0(1+ g1) (1+ g2) iv iv iv
N
. . .
9-8
Case 3: Differential Growth
Dividends will grow at rate g1 for N years and grow at rate g2 thereafter
E PS $5 P= = =$31.25 0 R .16
So, NPVGO must be: $75 - $31.25 = $43.75
9-19
Retention Rate and Firm Value
An increase in the retention rate will:
Reduce the dividend paid to shareholders Increase the firm’s growth rate
9-2
9.1 The PV of Common Stocks
The value of any asset is the present value of its expected future cash flows. Stock ownership produces cash flows from:
$2.16
0 1
$2.62 $2.33 $2.52+ .12−.04
2 3
$2.16 $2.33 $2.52+$32.75 P= + + =$28.89 0 2 3 1.12 (1.12) (1.12) $2.62
P= 3 .08
=$32.75
9-14
9.2 Estimates of Parameters
D 1 = D 2 = D 3 =⋯ iv iv iv
• Since future cash flows are constant, the value of a zero
growth stock is the present value of a perpetuity:
D 1 iv D 2 iv D 3 iv P= + + +⋯ 0 3 1 2 (1+ R) (1+ R) (1+ R) D iv P= 0 R
(1.12)
P=$5.58+$23.31
P =$28.89
9-13
With Cash Flows
$2(1.08) $2(1.08)
0 1 2
2
$2(1.08) $2(1.08) (1.04)
3
3
…
3 4
The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.
Chapter 9
Stock Valuation
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
Understand how stock prices depend on future dividends and dividend growth Be able to compute stock prices using the dividend growth model Understand how growth opportunities affect stock values Understand the PE ratio Understand how stock markets work
The value of a firm depends upon its growth rate, g, and its discount rate, R.
Where does g come from? g = Retention ratio × Return on retained earnings
9-6
Case 3: Differential Growth
Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. To value a Differential Growth Stock, we need to:
9-16
Using the DGM to Find R
Start with the DGM:
D ( +g ) D 0 1 1 P = = 0 R- g R- g Rearrange and solve for R: D ( +g ) D 0 1 R= +g = 1 +g P P 0 0
9-17
9.3 Growth Opportunities
Growth opportunities are opportunities to invest in positive NPV projects. The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends plus the net present value of the growth opportunities. EPS P= + NPVG O R
9-10
Case 3: Differential Growth
Consolidating gives:
D T+1 iv C (1+ g1)T R− g2 P= 1− + T T R− g1 (1+ R) (1+ R)
Or, we can “cash flow” it out.
9-1
Chapter Outline
9.1 9.2 9.3 9.4 9.5 The Present Value of Common Stocks Estimates of Parameters in the Dividend Discount Model Growth Opportunities Price-Earnings Ratio The Stock Markets
. . .
3
Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:
D 1 iv P= 0 R− g
Dividends Capital Gains
Valuation of Different Types of Stocks
Zero Growth Constant Growth Differential Growth
9-3
Case 1: Zero Growth
Assume that dividends will remain at the same level forever
ቤተ መጻሕፍቲ ባይዱ
9-7
Case 3: Differential Growth
• Assume that dividends will grow at rate g1 for N
years and grow at rate g2 thereafter.
D 1 = D 0(1+ g1) iv iv
D 2 = D 1(1+ g1) = D 0(1+ g1)2 iv iv iv
9-11
A Differential Growth Example
A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%.
9-15
Where Does R Come From?
The discount rate can be broken into two parts.
The dividend yield The growth rate (in dividends)
In practice, there is a great deal of estimation error involved in estimating R.
9-12
With the Formula
$2(1.08)3(1.04) $2×(1.08) (1.08)3 .12−.04 P= 1− + 3 3 .12−.08 (1.12) (1.12)
($32.75) P =$54×[1−.8966] + 3
9-4
Case 2: Constant Growth
Assume that dividends will grow at a constant rate, g, forever, i.e.,
D 1 = D 0(1+ g) iv iv
D 2 = D 1(1+ g) = D 0(1+ g)2 iv iv iv D 3 = D 2(1+ g) = D 0(1+ g) iv iv iv
(1+ g1)T C P= 1 A − T R−g1 (1+R)
plus the discounted value of a perpetuity growing at rate g2 that starts in year T+1
D T+1 iv R− g 2 P = B T (1+ R)
9-18
NPVGO Model: Example
Consider a firm that has forecasted EPS of $5, a discount rate of 16%, and is currently priced at $75 per share.
We can calculate the value of the firm as a cash cow.