This year Shoreline Light and Gas(SL&G) paid its stockholders an annual dividend of $3 a share. A major brokerage firm recently put out a report on SL&G stating that,in its opinion, the company's annual dividends should grow at the rate of 10% per year for each of the next five years and then level off and grow at the rate of 6% a year therafter.
a. use the variable growth DVM and a required rate of return of 12%,to find the minimum price you shhould be willing to pay for this stock.
b. Redo the SL&G problem in part a, this time assuming that after year 5, dividends stop growing altogether (for year 6 and beyond g=0) . Use all other information given to find stocks intrinsic value.
c. contrast your two answers and comment on your findings.How important is growth to this valuation?
How to do it
To solve this problem, we need to use the Dividend Valuation Model (DVM) formula:
D1 / (r - g)
where:
D1 = next year's dividend
r = required rate of return
g = growth rate
Given information:
- Current year's dividend = $3
- Dividends are expected to grow by 10% per year for the next 5 years, and then grow at 6% per year thereafter.
- Required rate of return (r) = 12%
a. Minimum price willing to pay for the stock:
To find the intrinsic value of the stock, we need to calculate the present value of future dividends. Let's calculate the value after 5 years, when the dividend growth rate levels off at 6%.
Year 1: D1 = $3 * (1 + 10%) = $3.30
Year 2: D2 = $3.30 * (1 + 10%) = $3.63
Year 3: D3 = $3.63 * (1 + 10%) = $3.99
Year 4: D4 = $3.99 * (1 + 10%) = $4.39
Year 5: D5 = $4.39 * (1 + 10%) = $4.83
After year 5, dividends grow at 6% annually. We will use the formula:
D5 * (1 + g) / (r - g)
where g = 6% and D5 = $4.83.
Intrinsic value = (4.83 * (1 + 6%)) / (12% - 6%)
= 5.12 / 6%
= $85.33 (rounded to 2 decimal places)
Therefore, the minimum price you should be willing to pay for this stock is $85.33.
b. Assuming no growth after year 5:
Following the same approach as in part a, we need to calculate the intrinsic value based on no growth (g = 0) beyond year 5.
Intrinsic value = (4.83 / (12% - 6%)
= 4.83 / 6%
= $80.50 (rounded to 2 decimal places)
Therefore, the intrinsic value of the stock, assuming no growth after year 5, is $80.50.
c. Comparison and comments on findings:
In part a, when assuming dividends continue to grow at a rate of 6% beyond year 5, the intrinsic value of the stock is $85.33. However, in part b, when assuming no growth beyond year 5 (g = 0), the intrinsic value decreases to $80.50.
From this analysis, we can observe that growth is a significant factor in determining the valuation of the stock. Assuming a growth rate of 6% leads to a higher intrinsic value than assuming no growth. This suggests that investors heavily consider the growth potential of a company when valuing its stock.
Note: The above calculations assume that the dividends are paid at the end of each year.
a. To find the minimum price that you should be willing to pay for the stock using the variable growth Dividend Discount Model (DVM) and a required rate of return of 12%, you need to calculate the present value of the expected future dividends and the stock's intrinsic value.
The formula for the variable growth DVM is:
Intrinsic Value = D1 / (r - g)
Where:
D1 = Expected dividend for the next year
r = Required rate of return
g = Expected growth rate of dividends
Given that the annual dividends grow at a rate of 10% for the next five years and then level off and grow at 6% thereafter, and the annual dividend is $3, we can calculate the intrinsic value:
D1 = $3 * (1 + 0.10) = $3.30 (expected dividend for the next year)
r = 12% (required rate of return)
g = 10% for the first five years, and 6% afterwards
So, for the first five years, we can calculate the present value of the expected future dividends using the formula for the present value of a growing annuity:
PV of Dividends (Years 1-5) = D1 * (1 - (1 + g)^-n) / (r - g)
Where:
n = number of years of growth (here, 5)
For the period after year 5, where the dividend growth rate levels off at 6%, we can use the formula for the present value of a perpetuity:
PV of Dividends (Year 6 and beyond) = D6 / (r - g)
Plug in the values and calculate the present values:
PV of Dividends (Years 1-5) = $3.30 * (1 - (1 + 0.10)^-5) / (0.12 - 0.10)
PV of Dividends (Years 1-5) ≈ $11.22
PV of Dividends (Year 6 and beyond) = $3.30 * (1 + 0.06) / (0.12 - 0.06)
PV of Dividends (Year 6 and beyond) ≈ $34.65
Finally, calculate the intrinsic value by summing up the present values:
Intrinsic Value = PV of Dividends (Years 1-5) + PV of Dividends (Year 6 and beyond)
Intrinsic Value ≈ $11.22 + $34.65
Intrinsic Value ≈ $45.87
Therefore, the minimum price you should be willing to pay for this stock is approximately $45.87.
b. To redo the SL&G problem assuming that after year 5, dividends stop growing altogether (g = 0), we need to recalculate the present value of the expected future dividends.
Using the same formula as in part a, we have:
PV of Dividends (Years 1-5) = $3.30 * (1 - (1 + 0.10)^-5) / (0.12 - 0.10)
PV of Dividends (Years 1-5) ≈ $11.22
PV of Dividends (Year 6 and beyond) = D6 / (r - g)
PV of Dividends (Year 6 and beyond) = $3.30 / (0.12 - 0)
PV of Dividends (Year 6 and beyond) ≈ $27.50
Calculate the intrinsic value by summing up the present values:
Intrinsic Value = PV of Dividends (Years 1-5) + PV of Dividends (Year 6 and beyond)
Intrinsic Value ≈ $11.22 + $27.50
Intrinsic Value ≈ $38.72
Therefore, the intrinsic value of the stock, assuming no growth after year 5, is approximately $38.72.
c. Comparing the two answers from parts a and b, we can see that assuming no growth after year 5 results in a lower intrinsic value for the stock ($38.72 compared to $45.87). This shows that growth is indeed important in determining the valuation of the stock.
The difference in intrinsic value between the two scenarios ($45.87 - $38.72 = $7.15) indicates that the additional growth in dividends after year 5 contributes to an increase in the stock's value.
Overall, growth plays a significant role in the valuation of this stock. Higher expected growth rates in dividends lead to higher intrinsic values. However, it is important to consider that as time goes on, the impact of future dividends on the intrinsic value decreases, and thus the effect of growth on valuation diminishes.