The shares of ABC Inc.,traded at $65 after its financial statements were published atthe end of year 2021.The balance sheet reported a book value per share (BPS)of$24.50.The income statement reported an earnings per share of(EPS)of$3. A dividendper share(DPS)of $1.50 was distributed for 2021.Analysts are forecasting an EPS of$3.60 for 2022 and$4.80 for 2023.Assume a fixed dividend payout ratio.The requiredreturn of equity is 10 percent.1.Calculate the intrinsic value per share in early 2022 with a forecast that residualearnings will grow at the long-term GDP growth rate of 4% after 2023.(5 marks)2.What is the forecast of the long-term residual earnings growth rate after 2023 that isimplicit in the market price?(4 marks)3.Based on the residual earnings model,calculate the market implied forecast of EPSfor 2024 and 2025.(6 marks)
Question
The shares of ABC Inc.,traded at 24.50.The income statement reported an earnings per share of(EPS)of1.50 was distributed for 2021.Analysts are forecasting an EPS of4.80 for 2023.Assume a fixed dividend payout ratio.The requiredreturn of equity is 10 percent.1.Calculate the intrinsic value per share in early 2022 with a forecast that residualearnings will grow at the long-term GDP growth rate of 4% after 2023.(5 marks)2.What is the forecast of the long-term residual earnings growth rate after 2023 that isimplicit in the market price?(4 marks)3.Based on the residual earnings model,calculate the market implied forecast of EPSfor 2024 and 2025.(6 marks)
Solution
- Calculate the intrinsic value per share in early 2022 with a forecast that residual earnings will grow at the long-term GDP growth rate of 4% after 2023.
The intrinsic value per share can be calculated using the Residual Earnings Model. The formula is:
Intrinsic Value = Book Value + Present Value of Residual Earnings
Residual Earnings = EPS - (Required Return * Book Value)
First, we need to calculate the Residual Earnings for 2022 and 2023:
For 2022: Residual Earnings = 24.50) = $1.10
For 2023: Residual Earnings = 24.50) = $2.30
Next, we calculate the present value of these residual earnings:
For 2022: PV = 1.00
For 2023: PV = 1.90
Then, we calculate the present value of all future residual earnings, assuming a growth rate of 4%:
PV of future Residual Earnings = Residual Earnings for 2023 * (1 + growth rate) / (required return - growth rate) = 42.20
Finally, we add the book value and the present value of residual earnings to get the intrinsic value:
Intrinsic Value = 1.00 + 42.20 = $69.60
- What is the forecast of the long-term residual earnings growth rate after 2023 that is implicit in the market price?
The implicit growth rate can be calculated by rearranging the formula for the intrinsic value:
Growth Rate = (Residual Earnings for 2023 * (1 + growth rate) / (Intrinsic Value - Book Value - PV of Residual Earnings for 2022 and 2023)) + required return = (65 - 1.00 - $1.90)) + 0.10 Solving this equation for g will give the implicit growth rate.
- Based on the residual earnings model, calculate the market implied forecast of EPS for 2024 and 2025.
The EPS for 2024 and 2025 can be calculated using the formula:
EPS = (Residual Earnings + (Required Return * Book Value)) / (1 + growth rate)
For 2024 and 2025, we would need to know the book value for those years, which is not provided in the question. Therefore, we cannot calculate the EPS for 2024 and 2025.
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