Download Notes on Stock Theorem - Financial Management I | FIN 340 and more Assignments Financial Management in PDF only on Docsity!
9-3 P 0 = $20; D 0 = $1.00; g = 6%; Pˆ 1 = ?; rs =?
Pˆ 1 = P 0 (1 + g) = $20(1.06) = $21.20.
ˆrs = 0
1 P
D
- 0.06 = 11.30%. rs = 11.30%.
9-4 a. The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at the end of Year 2.
b. 0 1 2 3 | | | | 1.25 1.50 1.80 1.
The horizon, or terminal, value is the value at the horizon date of all dividends expected thereafter. In this problem it is calculated as follows:
c. The firm’s intrinsic value is calculated as the sum of the present value of all dividends during the supernormal growth period plus the present value of the terminal value. Using your financial calculator, enter the following inputs: CF 0 = 0, CF 1 = 1.50, CF 2 = 1.80 + 37.80 = 39.60, I/YR = 10, and then solve for NPV = $34.09.
9-8 a. $ 125.
- 08
r
D
V
p
p p = = =
b. $ 83. 33.
- 12
Vp = =
$ 5 [ 1 ( 0. 05 )]
r g
D ( 1 g) r g
D
Pˆ
s
0 s
1 (^0) − − = + = =
9-11 First, solve for the current price.
Pˆ 0 = D 1 /(rs – g) = $0.50/(0.12 – 0.07) = $10.00.
If the stock is in a constant growth state, the constant dividend growth rate is also the capital gains yield for the stock and the stock price growth rate. Hence, to find the price of
rs = 10% gs = 20% gs = 20% gn = 5%
the stock four years from today:
Pˆ 4 = P 0 (1 + g) 4
= $10.00(1.07)^4 = $13.10796 ≈ $13.11.
9-13 a. ri = rRF + (rM – rRF)bi.
rC = 7% + (11% – 7%)0.4 = 8.6%.
rD = 7% + (11% – 7%)(-0.5) = 5%.
Note that rD is below the risk-free rate. But since this stock is like an insurance policy because it “pays off” when something bad happens (the market falls), the low return is not unreasonable.
b. In this situation, the expected rate of return is as follows:
ˆrC = D 1 /P 0 + g = $1.50/$25 + 4% = 10%.
However, the required rate of return is 8.6%. Investors will seek to buy the stock, raising its price to the following:
$ 32. 61.
- 086 0. 04
$ 1. 50 PˆC = −
=
At this point, 4 % 8. 6 % $ 32. 61
ˆrC = + = , and the stock will be in equilibrium.
9-18 The value of any asset is the present value of all future cash flows expected to be generated from the asset. Hence, if we can find the present value of the dividends during the period preceding long-run constant growth and subtract that total from the current stock price, the remaining value would be the present value of the cash flows to be received during the period of long-run constant growth.
D 1 = $2.00 × (1.25)^1 = $2.50 PV(D 1 ) = $2.50/(1.12)^1 = $2. D 2 = $2.00 × (1.25)^2 = $3.125 PV(D 2 ) = $3.125/(1.12)^2 = $2. D 3 = $2.00 × (1.25)^3 = $3.90625 PV(D 3 ) = $3.90625/(1.12)^3 = $2.
Σ PV(D 1 to D 3 ) = $7.
Therefore, the PV of the remaining dividends is: $58.8800 – $7.5038 = $51.3762. Compounding this value forward to Year 3, we find that the value of all dividends received during constant growth is $72.18. [$51.3762(1.12)^3 = $72.1799 ≈ $72.18.] Applying the constant growth formula, we can solve for the constant growth rate:
Pˆ 3 = D 3 (1 + g)/(rs – g) $72.18 = $3.90625(1 + g)/(0.12 – g)
This is the total firm value. Now find the market value of its equity.
MVTotal = MVEquity + MVDebt $10,000,000,000 = MVEquity + $3,000,000, MVEquity = $7,000,000,000.
This is the market value of all the equity. Divide by the number of shares to find the price per share. $7,000,000,000/200,000,000 = $35.00.
9-23 a. Old rs = rRF + (rM – rRF)b = 6% + (3%)1.2 = 9.6%.
New rs = 6% + (3%)0.9 = 8.7%.
Old price: (^) $ 58. 89.
- 096 0. 06
$ 2 ( 1. 06 ) r g
D ( 1 g) r g
D Pˆ s
0 s
1 (^0) − = − =
= −
=
New price: (^) $ 44. 26.
- 087 0. 04
$ 2 ( 1. 04 ) Pˆ 0 = −
=
Since the new price is lower than the old price, the expansion in consumer products should be rejected. The decrease in risk is not sufficient to offset the decline in profitability and the reduced growth rate.
b. POld = $58.89. PNew = r 0. 04
s −^
Solving for rs we have the following:
r 0. 04
s − $2.08 = $58.89(rs) – $2. $4.4356 = $58.89(rs) rs = 0.07532.
Solving for b: 7.532% = 6% + 3%(b) 1.532% = 3%(b) b = 0.5107.
Check: rs = 6% + (3%)0.5107 = 7.532%.
Pˆ 0 =
Therefore, only if management’s analysis concludes that risk can be lowered to b = 0.5107, should the new policy be put into effect.
