Solutions to End-of-Chapter 9 Problems
9-8 a.
b.
9-9 a. The preferred stock pays $8 annually in dividends. Therefore, its nominal rate of return would be:
Nominal rate of return = $8/$80 = 10%.
Or alternatively, you could determine the security’s periodic return and multiply by 4.
Periodic rate of return = $2/$80 = 2.5%.
Nominal rate of return = 2.5% 4 = 10%.
b. EAR = (1 + rNOM/4)4 – 1
= (1 + 0.10/4)4 – 1
= 0.103813 = 10.3813%.
9-11 First, solve for the current price.
= D1/(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 the stock four years from today:
= P0(1 + g)4
= $10.00(1.07)4
= $13.10796 ≈ $13.11.
9-12 a. 1.
2. = $2/0.15 = $13.33.
3.
4.
b. 1. = $2.30/0 = Undefined.
2. = $2.40/(-0.05) = -$48, which is nonsense.
These results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate.
c. No, the results of Part b show this. It is not reasonable for a firm to grow indefinitely at a rate higher than its required return. Such a stock, in theory, would become so large that it would eventually overtake the whole economy.
9-14 Calculate the dividend cash flows and place them on a time line. Also, calculate the stock price at the end of the supernormal growth period, and include it, along with the dividend to be paid at t = 5, as CF5. Then, enter the cash flows as shown on the time line into the cash flow register, enter the required rate of return as I/YR = 15, and then find the value of the stock using the NPV calculation. Be sure to enter CF0 = 0, or else your answer will be incorrect.
D0 = 0; D1 = 0; D2 = 0; D3 = 1.00; D4 = 1.00(1.5) = 1.5; D5 = 1.00(1.5)2 = 2.25; D6 = 1.00(1.5)2(1.08) = $2.43. = ?
r
s
= 15% 0 1 2 3 4 5 6
g
s
= 50%
g
s
= 50%
g
n
= 8% | | | | | | |
1.00 1.50 2.25 2.43
1/(1.15)
3
1/(1.15)
4 0.658 +34.714 =
1/(1.15)
5 0.858
18.378 36.964
$19.894 =
= D6/(rs – g) = $2.43/(0.15 – 0.08) = $34.714. This is the stock price at the end of Year 5.
CF0 = 0; CF1-2 = 0; CF3 = 1.0; CF4 = 1.5; CF5 = 36.964; I/YR = 15. With these cash flows in the CFLO register, press NPV to calculate the value of the stock today: NPV = $19.89.
9-16 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.
D1 = $2.00 (1.25)1 = $2.50 PV(D1) = $2.50/(1.12)1 = $2.2321
D2 = $2.00 (1.25)2 = $3.125 PV(D2) = $3.125/(1.12)2 = $2.4913
D3 = $2.00 (1.25)3 = $3.90625 PV(D3) = $3.90625/(1.12)3 = $2.7804
PV(D1 to D3) = $7.5...
