Consider a stock with current year dividend equal to $2.00 per share. You believe the dividend will grow 15% per year for 10 years and 4% per year thereafter. The required equity rate of return (and your hurdle rate) is 10%. What is the fair price of the stock? Assuming the market price of the stock is $70, what is the expected return?

a. Fair price of the stock = $79.82

b. The expected return is 7.29%

Explanation:

a. What is the fair price of the stock?

Note: See the attached file for the calculation of present values (PV) of dividends for year 1 to 10.

From the attached excel file, we have:

Previous year dividend in year 1 = Current year dividend = $2

Total of dividends from year 1 to year 10 = $25.74793130208810

Year 10 dividend = $8.09111547141582

Therefore, we have:

Year 11 dividend = Year 10 dividend * (100% + Dividend growth rate in year 11) = $8.09111547141582 * (100% + 4%) = $8.41476009027245

Share price at year 10 = Year 11 dividend / (Required equity rate of return - Perpetual dividend growth rate) = $8.41476009027245 / (10% - 4%) = $140.246001504541

PV of share price at year 10 = Price at year 10 / (100% + required equity rate of return)^Number of years = $140.246001504541 / (100% + 10%)^10 = $54.0709047493998

Therefore, we have:

Fair price of the stock = Total of dividends from year 1 to year 10 + PV of share price at year 10 = $25.74793130208810 + $54.0709047493998 = $79.82

b. Assuming the market price of the stock is $70, what is the expected return?

This can be calculated using the dividend discount model formula as follows:

P = D1 / (r - g) (1)

Where,

P = Market price of the stock = $70

D1 = Next dividend = Current dividend * (100% + Dividend growth rate in perpetuity) = $2 * (100% + 4%) = $2.30

r = Expected return = ?

g = Dividend growth rate in perpetuity = 4%, or 0.04

Substituting the values into equation (1) and solve for r, we have:

70 = 2.30 / (r - 0.04)

70(r - 0.04) = 2.30

70r - 2.80 = 2.30

70r = 2.30 + 2.80

70r = 5.10

r = 5.10 / 70

r = 0.0729, or 7.29%

Therefore, the expected return is 7.29%.

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