Answer:
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%.
