Arena Distributors is a new company and currently pays no dividends. The company has just reported earnings of $1.5 per share and its earnings are expected to grow at a 15 percent annual rate over the next four years. Following this four-year high growth period earnings will grow at 5 percent per year forever. Starting at the end of year 5, Arena will distribute 20 percent of the previous year’s earnings in the form of dividends. The required rate of return is 10 percent (EAR). Calculate the value of Arena’s share.
$8.57
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To calculate the value of Arena's share, we can use the dividend discount model (DDM) formula:
\[ P = \frac{D_1}{(1 + r)^1} + \frac{D_2}{(1 + r)^2} + \frac{D_3}{(1 + r)^3} + \frac{D_4}{(1 + r)^4} + \frac{D_5}{(1 + r)^5} + \frac{D_6}{r - g} \]
Where:
- P is the value of Arena's share
- D1, D2, D3, D4, D5 are the dividends expected to be paid in years 1, 2, 3, 4, 5, respectively
- D6 is the dividend expected to be paid starting from year 6 (continuous growth rate)
- r is the required rate of return (10% or 0.10 in decimal form)
- g is the growth rate of dividends after year 5 (5% or 0.05 in decimal form)
First, we need to calculate the future dividends for years 1 to 5 using the given earnings growth rate of 15%:
Year 1 dividend (D1) = Earnings per share * (1 - Payout ratio)
= $1.5 * (1 - 0)
= $1.5
Year 2 dividend (D2) = D1 * (1 + g)
= $1.5 * (1 + 0.15)
= $1.725
Year 3 dividend (D3) = D2 * (1 + g)
= $1.725 * (1 + 0.15)
= $1.98375
Year 4 dividend (D4) = D3 * (1 + g)
= $1.98375 * (1 + 0.15)
= $2.28181
Year 5 dividend (D5) = D4 * (1 + g)
= $2.28181 * (1 + 0.15)
= $2.62309
Next, we need to calculate the dividend in year 6 (D6) using the perpetual growth formula:
D6 = D5 * (1 + g)
= $2.62309 * (1 + 0.05)
= $2.75424
Now, we can substitute these values into the DDM formula:
P = \(\frac{\$1.5}{(1 + 0.10)^1} + \frac{\$1.725}{(1 + 0.10)^2} + \frac{\$1.98375}{(1 + 0.10)^3} + \frac{\$2.28181}{(1 + 0.10)^4} + \frac{\$2.62309}{(1 + 0.10)^5} + \frac{\$2.75424}{0.10 - 0.05}\)
P = \$1.36364 + \$1.48763 + \$1.54507 + \$1.46814 + \$1.27003 + \$55.0848
P = \$62.2193
Therefore, the value of Arena's share is approximately \$62.22.
To calculate the value of Arena's share, we can use the dividend discount model (DDM) and the concept of present value. The DDM states that the value of a stock is equal to the present value of all future dividends.
Step 1: Calculate the dividends for the first 4 years.
Since Arena currently pays no dividends, we need to project the earnings and calculate the dividends for the next four years.
Year 1: Dividend = Earnings x Dividend Payout Ratio
Dividend Payout Ratio = 20% (given)
Dividend Year 1 = $1.5 x 20% = $0.3
Year 2: Dividend = Earnings x Dividend Payout Ratio
Dividend Year 2 = ($1.5 x 1.15) x 20% = $0.345
Year 3: Dividend = Earnings x Dividend Payout Ratio
Dividend Year 3 = ($1.5 x 1.15^2) x 20% = $0.397
Year 4: Dividend = Earnings x Dividend Payout Ratio
Dividend Year 4 = ($1.5 x 1.15^3) x 20% = $0.456
Step 2: Calculate the dividend in perpetuity after year 4.
Starting from year 5, Arena will distribute 20% of the previous year’s earnings as dividends, which will grow at a 5% annual rate forever. We can calculate the dividend using the Gordon Growth Model.
Dividend Year 5 = Dividend Year 4 x (1 + Dividend Growth Rate)
Dividend Growth Rate = 5% (given)
Dividend Year 5 = $0.456 x (1 + 5%) = $0.479
Step 3: Calculate the present value of future dividends.
Now, we can calculate the present value of all the future dividends using the required rate of return (10% EAR) to discount the future cash flows.
PV = Dividend Year 1 / (1 + 10%)^1 + Dividend Year 2 / (1 + 10%)^2 + Dividend Year 3 / (1 + 10%)^3 + Dividend Year 4 / (1 + 10%)^4 + Dividend Year 5 / (1 + 10%)^5
PV = $0.3 / (1 + 10%)^1 + $0.345 / (1 + 10%)^2 + $0.397 / (1 + 10%)^3 + $0.456 / (1 + 10%)^4 + $0.479 / (1 + 10%)^5
Step 4: Calculate the terminal value of the stock at the end of year 4.
The terminal value represents the discounted value of all future dividends beyond year 5.
Terminal Value = Dividend Year 5 / (Required Rate of Return - Dividend Growth Rate)
Terminal Value = $0.479 / (10% - 5%)
Step 5: Calculate the present value of the terminal value.
Just like before, we need to discount the terminal value to its present value.
PV Terminal = Terminal Value / (1 + Required Rate of Return)^4
Step 6: Calculate the total present value of all future dividends.
We can now sum the present value of future dividends and the present value of the terminal value to get the total present value.
Total Present Value = PV + PV Terminal
Step 7: Calculate the value of Arena's share.
Finally, we need to divide the total present value by the number of outstanding shares to get the value of Arena's share.
Value of Arena's Share = Total Present Value / Number of Outstanding Shares
By following these steps, inputting the calculated values, and knowing the number of outstanding shares, you will be able to determine the value of Arena's share.