Question

Show the solution, please

Sharon Myers expects the $3.20 current dividend for CatTrak, Inc. (CAT) to grow at an initial rate of 18%, decreasing at a constant rate to 4% over a 12 year period. After year 12, she expects the dividend growth rate to be 4%. The required rate of return for CAT is 10%. What is the value per share of CAT? (Enter your answer to the nearest $0.01. Leave the $ sign off. In other words, if your answer is $55.55, enter 55.55 for your answer.)

Answer 1

Sol:

Current dividend expected = 3.20

CAT initial growth rate = 18%

Growth rate to decline at a constant rate to 4% over 12 years peariod.

After 12 years dividend growth rate expected to be 4%

Required rate of return = 10%

To determine value per share of CAT

Present value of dividends will be constant decrease over 12 year = (18% - 4%) / 12 = 1.1667%

Present value of dividends:

YEAR	GROWTH RATE	DIVIDEND	PRESENT VALUE OF DIVIDEND
Formula	Previous growth rate - constant decrease	Previous dividend*(1 + growth rate)	Dividend/(1+10%)^n
1	18%	3.7760	3.4327
2	16.83%	4.4116	3.6460
3	15.67%	5.1028	3.8338
4	14.50%	5.8427	3.9906
5	13.33%	6.6217	4.1115
6	12.17%	7.4273	4.1925
7	11.00%	8.2443	4.2306
8	9.83%	9.0550	4.2242
9	8.67%	9.8397	4.1730
10	7.50%	10.5777	4.0781
11	6.33%	11.2476	3.9422
12	5.17%	11.8286	3.7690
	Present value of dividend		47.6244

Present value of Share price in year 12:

Share price in year 12 = Dividend in year 12 * (1+growth rate) / (Required rate - Growth rate)

Share price in year 12 = 11.8286*(1+4%) / (10% - 4%)

Share price in year 12 = 11.8286*(1.04) / (0.06) = 205.03

Share price in year 12 = 205.03

Value per share of CAT

Value per share of CAT = Present value of dividends + Present value of Share price in year 12

Value per share of CAT = 47.6244 + (205.03 / (1+10%)^12)

Value per share of CAT = 47.6244 + (205.03 / (1.10)^12)

Value per share of CAT = 47.6244 + 65.33 = 112.95

Therefore per share value of CAT will be 112.95