ABC Company is not expected to pay any dividends for the next 3 years. Beginning 4 years from today, investors expect to receive a dividend of $2 per share for 3 years and then a dividend of $3 per share for each of the next 4 years. Then dividends are expected to grow at 4% per year forever. If investors require a 15% return, what is the price per share? Do not use excel. Need to understand this writing out PVIF functions.
Year |
Dividend |
||
1 |
D1= |
$0 |
|
2 |
D2= |
$0 |
|
3 |
D3= |
$0 |
|
4 |
D4= |
$2 |
|
5 |
D5= |
$2 |
|
6 |
D6= |
$2 |
|
7 |
D7= |
$3 |
|
8 |
D8 |
$3 |
|
9 |
D9= |
$3 |
|
10 |
D10 |
$3 |
|
11 |
D11 |
$3.12 |
(3*1.04) |
12 |
$3.24 |
(3.12*1.04) |
|
13 |
$3.37 |
(3.24*1.04) |
P10=Price in year 10=D11/(R-g)=Present Value in year 10 of future cash flows from year 11 to perpetuity.
R=Required Return=15%=0.15
g= 4%=0.04
P10=3.12/(0.15-0.04)=$28.36
Current Price Per Share =P0=Present Value of future cash flows
Present Value (PV) of Cash Flow:
(Cash Flow)/((1+i)^N)
i=Discount Rate=Required rate of return=15%=0.15
N=Year of Cash Flow
Cash Flows and Present value of cash flows are given below:
N |
A |
PV=A/(1.15^N) |
||
Year |
Cash Flow |
|||
1 |
D1 |
$0 |
$0 |
|
2 |
D2 |
$0 |
$0 |
|
3 |
D3 |
$0 |
$0 |
|
4 |
D4 |
$2 |
1.143506491 |
(2/(1.15^4) |
5 |
D5 |
$2 |
0.994353471 |
(2/(1.15^5) |
6 |
D6 |
$2 |
0.864655192 |
(2/(1.15^6) |
7 |
D7 |
$3 |
1.12781112 |
(3/(1.15^7) |
8 |
D8 |
$3 |
0.980705322 |
(3/(1.15^8) |
9 |
D9 |
$3 |
0.852787236 |
(3/(1.15^9) |
10 |
D10 |
$3 |
0.741554118 |
(3/(1.15^10) |
10 |
P10 |
$28.36 |
7.010158266 |
(28.36/1.15^10) |
SUM |
$13.72 |
Price Per Share =Sum of PV of future cash flows=$13.72
Current Price per share=P0= |
$13.72 |
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