ch 7 problem

SOLUTIONS TO END-OF-CHAPTER PROBLEMS
7-1

D0 = $1.50; g1-3 = 5%; gn = 10%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.50(1.05) = $1.5750.
D2 = D0(1 + g1)(1 + g2) = $1.50(1.05)2 = $1.6538.
D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.05)3 = $1.7364.
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.05)3(1.10) = $1.9101.
D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.05)3(1.10)2 = $2.1011.

7-2

D1 = $1.50; g = 6%; rs = 13%; = ?
= = = $21.43.

7-3

P0 = $22; D0 = $1.20; g = 10%; = ?; s= ?
= P0(1 + g) = $22(1.10) = $24.20.
s

= + g = + 0.10
= + 0.10 = 16.00%. s = 16.00%.

7-4

Dps = $5.00; Vps = $50; rps = ?

7-5

rps = = = 10%.
0
1

2

3

|

D0 = 2.00

|

|

D1

D2

|

D3

Step 1: Calculate the required rate of return on the stock:
rs = rRF + (rM - rRF)b = 7.5% + (4%)1.2 = 12.3%.
Step 2: Calculate the expected dividends:
D0 = $2.00
D1 = $2.00(1.20) = $2.40
D2 = $2.00(1.20)2 = $2.88
D3 = $2.88(1.07) = $3.08
Step 3: Calculate the PV of the expected dividends:
PVDiv = $2.40/(1.123) + $2.88/(1.123)2 = $2.14 + $2.28 = $4.42.
Step 4: Calculate :
= D3/(rs – g) = $3.08/(0.123 – 0.07) = $58.11.
Step 5: Calculate the PV of :
PV = $58.11/(1.123)2 = $46.08.
Step 6: Sum the PVs to obtain the stock’s price:
= $4.42 + $46.08 = $50.50.
Alternatively, using a financial calculator, input the following:
CF0 = 0, CF1 = 2.40, and CF2 = 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to
solve for NPV = $50.50.
7-6

Value of operations = Vop = PV of expected future free cash flow
Vop = = = $6,000,000.

7-7

The growth rate in FCF from 2015 to 2016 is g = ($750.00-$707.55)/$707.50 =
0.06.
HV2016 = VOp at 2016 = = $15,000.