Question

Sawchuck Consulting has been profitable for the last 5 years, but it has never paid a dividend. Management has indicated that it plans to pay a $0.25 dividend 3 years from today, then to increase it at a relatively rapid rate for 2 years, and then to increase it at a constant rate of 8.00% thereafter. Management's forecast of the future dividend stream, along with the forecasted growth rates, is shown below. Assuming a required return of 11.00%, what is your estimate of the stock's current value?

Year	0	1	2	3	4	5	6	7
Growth rate	NA	NA	NA	NA	95%	47.5%	8.00%	8.00%
Dividends	$0.000	$0.000	$0.000	$0.25	$0.49	$0.72	$0.78	$0.84

Use the rounded values of dividends (as given in the table above) for your subsequent calculations.

Select the correct answer.

a. $81.24

b. $-7.96

c. $-24.18

d. $16.36

e. $65.02

Answer 1

Step 1: The Present value of the stock is calculated using the time value of money concept.

We discount the future dividends to their present values.

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Step 2: The given data is

Years	0	1	2	3	4	5
Growth Rate					95%	47.50%
Dividends	0	0	0	0.25	0.49	0.72

From year 6 onwards, the dividend grow at a constant rate of 8% forever(perpetuity)

So, Dividend for year 6 is (D6) =Dividend of 5th year * (1 + growth rate)

D6 = 0.72 *(1+0.08) = $0.78

Step 3: The value of stock in year 5 (P5) is given as -

P5 = D6/(Required Return - growth rate from year 6 onwards)

P5 = 0.78/(0.11 - 0.08)

P5 = $26

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Step 3: The cash inflows after calculating the value of stock in perpetuity looks like this -

Years	0	1	2	3	4	5	5
Cash flow	0	0	0	0.25	0.49	0.72	26

The Present value of these cash flows with discount rate as the rate of return = 11% are

Present Value for Year 1 = 0

Present Value for Year 2 = 0

Present Value for Year 3 = Cash flow/(1+discount rate)^3 = 0.25/(1+0.11)^3 = $0.18

Present Value for Year 4 = Cash flow/(1+discount rate)^4 = 0.49/(1+0.11)^4 =$0.32

Present Value for Year 5 = Cash flow/(1+discount rate)^5 = 0.72/(1+0.11)^5 =$0.43

Present Value for Year 5 = Cash flow/(1+discount rate)^5 = 26/(1+0.11)^5 = $15.43

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Step 4: The Present Value of the Stock = Sum of Present values of the cash flows calculated in step 3

The Present Value of the Stock = 0.18 + 0.32 + 0.43 + 15.43 = $16.36

OPTION (d) IS CORRECT