The blue stair-step line depicts the value of future stock dividends. The orange stair-step line depicts the present value of those future dividends discounted by rs for a stock with initial dividend D0 = $1.15 and an anticipated growth rate of g = 4%. Use the slider to change rs and observe the corresponding changes in the equilibrium price of the stock. \large \hat P_0 = \sum_{t=1}^{\infty} PV D_t = \frac {D_0 (1+g)} {r_s - g} = \frac {\$1.15(1+0.04)} {0.08 - 0.04} = \$29.90P^0=∑t=1∞PVDt=rs−gD0(1+g)=0.08−0.04$1.15(1+0.04)=$29.90 1. If rs increases to 10%, what would be the value of the constant growth stock? (Note: D0 is $1.15 and the expected constant growth rate g = 4%.) $29.90 $19.93 $10.87 Undetermined 2. When rs increases from, say, 8% to 10%, the value of the constant growth stock: Increases because the interest rate is higher. Decreases because its dividends are being discounted at a higher rate. Remains the same because it is a "constant growth" stock. Might either increase or decrease. 3. Move the slider so that rs is 12%. If the stock were selling on the market for $15.50, would you buy it? (Note: D0 is $1.15 and the expected growth consstant rate g = 4%.) Yes, it is a bargain. No, the stock is overvalued, as the expected stock price is only $14.95. Not enough information to determine whether it would be a good buy. 4. The slider for rs is limited to a minimum of 4.1% so that rs is always greater than g. Move the slider to the minimum and observe how the present value of the stock changes. Must rs be greater than g? No reason rs needs to be greater than g because the formula adjusts the value of the stock appropriately. Yes, because if rs were not greater than g, then the graph would be too large to display easily. Yes, because if rs = g, then the formula divides by zero, producing an infinite value.

The blue stair-step line depicts the value of future stock dividends. The orange stair-step line depicts the present value of those future dividends discounted by rs for a stock with initial dividend D0 = $1.15 and an anticipated growth rate of g = 4%. Use the slider to change rs and observe the corresponding changes in the equilibrium price of the stock. \large \hat P_0 = \sum_{t=1}^{\infty} PV D_t = \frac {D_0 (1+g)} {r_s - g} = \frac {\$1.15(1+0.04)} {0.08 - 0.04} = \$29.90P^0=∑t=1∞PVDt=rs−gD0(1+g)=0.08−0.04$1.15(1+0.04)=$29.90 1. If rs increases to 10%, what would be the value of the constant growth stock? (Note: D0 is $1.15 and the expected constant growth rate g = 4%.) $29.90 $19.93 $10.87 Undetermined 2. When rs increases from, say, 8% to 10%, the value of the constant growth stock: Increases because the interest rate is higher. Decreases because its dividends are being discounted at a higher rate. Remains the same because it is a "constant growth" stock. Might either increase or decrease. 3. Move the slider so that rs is 12%. If the stock were selling on the market for $15.50, would you buy it? (Note: D0 is $1.15 and the expected growth consstant rate g = 4%.) Yes, it is a bargain. No, the stock is overvalued, as the expected stock price is only $14.95. Not enough information to determine whether it would be a good buy. 4. The slider for rs is limited to a minimum of 4.1% so that rs is always greater than g. Move the slider to the minimum and observe how the present value of the stock changes. Must rs be greater than g? No reason rs needs to be greater than g because the formula adjusts the value of the stock appropriately. Yes, because if rs were not greater than g, then the graph would be too large to display easily. Yes, because if rs = g, then the formula divides by zero, producing an infinite value.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

See similar textbooks

Exploring Finance: Constant Growth Stock.

Constant Growth Stock

Conceptual Overview: Explore how the value of a stock changes as a function of the discount interest rate.

The blue stair-step line depicts the value of future stock dividends. The orange stair-step line depicts the present value of those future dividends discounted by r_s for a stock with initial dividend D₀ = $1.15 and an anticipated growth rate of g = 4%. Use the slider to change r_s and observe the corresponding changes in the equilibrium price of the stock.

\large \hat P_0 = \sum_{t=1}^{\infty} PV D_t = \frac {D_0 (1+g)} {r_s - g} = \frac {\$1.15(1+0.04)} {0.08 - 0.04} = \$29.90P^0=∑t=1∞PVDt=rs−gD0(1+g)=0.08−0.04$1.15(1+0.04)=$29.90

1. If r_s increases to 10%, what would be the value of the constant growth stock? (Note: D₀ is $1.15 and the expected constant growth rate g = 4%.)

$29.90
$19.93
$10.87
Undetermined

2. When r_s increases from, say, 8% to 10%, the value of the constant growth stock:

Increases because the interest rate is higher.
Decreases because its dividends are being discounted at a higher rate.
Remains the same because it is a "constant growth" stock.
Might either increase or decrease.

3. Move the slider so that r_s is 12%. If the stock were selling on the market for $15.50, would you buy it? (Note: D₀ is $1.15 and the expected growth consstant rate g = 4%.)

Yes, it is a bargain.
No, the stock is overvalued, as the expected stock price is only $14.95.
Not enough information to determine whether it would be a good buy.

4. The slider for r_s is limited to a minimum of 4.1% so that r_s is always greater than g. Move the slider to the minimum and observe how the present value of the stock changes. Must r_s be greater than g?

No reason r_s needs to be greater than g because the formula adjusts the value of the stock appropriately.
Yes, because if r_s were not greater than g, then the graph would be too large to display easily.
Yes, because if r_s = g, then the formula divides by zero, producing an infinite value.

Dividend ($1)
30-
25-
20
15
10-
05-
00
10
15
20
Years
rs = 8
10
15
20

Definition Video Definition Point where the demand and supply curves intersect. At the equilibrium price the quantity supplied of a good is equal to the quantity demanded. When the market is not in equilibrium, market surplus or market shortage occurs. The region that is above the price equilibrium indicates market surplus and the region below the price equilibrium indicates market shortage. Video

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