A company is currently running at a loss, but A expected to report EPS of 10 cents and payout 50% of earnings as a dividend in 2 years. Once profitable, earnings and dividend will grow at 15% for 5 years (year 3-7). From year 8, growth will slow to 4%. If A’s required return is 20%. What are A shares worth today?
Question
A company is currently running at a loss, but A expected to report EPS of 10 cents and payout 50% of earnings as a dividend in 2 years. Once profitable, earnings and dividend will grow at 15% for 5 years (year 3-7). From year 8, growth will slow to 4%. If A’s required return is 20%. What are A shares worth today?
Solution
To calculate the value of the shares today, we need to calculate the present value of the dividends that will be paid in the future.
Step 1: Calculate the dividends for the first 2 years. Since the company is running at a loss, no dividends will be paid. So, the dividends for year 1 and 2 are 0.
Step 2: Calculate the dividends for years 3-7. The EPS for year 2 is 10 cents and the company pays out 50% as dividends. So, the dividend for year 2 is 10 * 0.5 = 5 cents. This will grow at 15% for the next 5 years.
Year 3 dividend = 5 * 1.15 = 5.75 cents Year 4 dividend = 5.75 * 1.15 = 6.61 cents Year 5 dividend = 6.61 * 1.15 = 7.60 cents Year 6 dividend = 7.60 * 1.15 = 8.74 cents Year 7 dividend = 8.74 * 1.15 = 10.05 cents
Step 3: Calculate the dividends for years 8 and onwards. The dividend for year 7 will grow at 4% indefinitely.
Year 8 dividend = 10.05 * 1.04 = 10.45 cents
Step 4: Calculate the present value of these dividends. The formula for present value is D / (1 + r)^t, where D is the dividend, r is the required return, and t is the time in years.
PV of dividends for years 3-7 = 5.75 / (1 + 0.2)^3 + 6.61 / (1 + 0.2)^4 + 7.60 / (1 + 0.2)^5 + 8.74 / (1 + 0.2)^6 + 10.05 / (1 + 0.2)^7
Step 5: Calculate the present value of the dividends for year 8 and onwards. This is a perpetuity, so the formula is D / r, where D is the dividend and r is the required return.
PV of dividends for years 8 and onwards = 10.45 / (0.2 - 0.04) / (1 + 0.2)^7
Step 6: The value of the shares today is the sum of the present value of the dividends for years 3-7 and the present value of the dividends for year 8 and onwards.
Value of shares today = PV of dividends for years 3-7 + PV of dividends for years 8 and onwards
This is the theoretical value of the shares today, assuming that all the projections and assumptions hold true.
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