XYZ Corp. reported a per share book value of $12 in its balance sheet on December 31,2019. Analysts are forecasting consensus earnings per share of $1.80 for 2020 and $2.40for 2021. The required return for common equity is 10 percent. The dividend payout isexpected to be 50 percent of earnings.a) Calculate the intrinsic value per share in early 2020 with a forecast that residualearnings will grow at a long-term GDP growth rate of 4% after 2021.
Question
XYZ Corp. reported a per share book value of 1.80 for 2020 and $2.40for 2021. The required return for common equity is 10 percent. The dividend payout isexpected to be 50 percent of earnings.a) Calculate the intrinsic value per share in early 2020 with a forecast that residualearnings will grow at a long-term GDP growth rate of 4% after 2021.
Solution 1
To calculate the intrinsic value per share, we can use the Residual Income Model. This model is based on the idea that the intrinsic value of a stock is equal to the current book value per share plus the present value of future residual earnings.
Here are the steps to calculate the intrinsic value per share:
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Calculate the Residual Earnings for 2020 and 2021:
Residual Earnings = EPS - (Required Return * Book Value per Share)
For 2020: Residual Earnings = 12) = 1.20 = $0.60
For 2021: Residual Earnings = 12) = 1.20 = $1.20
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Calculate the present value of these residual earnings:
PV of 2020 Residual Earnings = 0.545
PV of 2021 Residual Earnings = 0.991
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Calculate the Residual Earnings for 2022 and beyond:
Residual Earnings in 2022 = 2021 Residual Earnings * (1 + Growth Rate) = 1.248
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Calculate the present value of these residual earnings:
PV of 2022 and beyond Residual Earnings = 1.248 / (0.10 - 0.04) = $20.80
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Calculate the intrinsic value per share:
Intrinsic Value per Share = Book Value per Share + PV of 2020 Residual Earnings + PV of 2021 Residual Earnings + PV of 2022 and beyond Residual Earnings
Intrinsic Value per Share = 0.545 + 20.80 = $34.336
So, the intrinsic value per share in early 2020 is approximately $34.336.
Solution 2
To calculate the intrinsic value per share, we can use the Residual Income Model. This model is based on the idea that the intrinsic value of a stock is equal to the current book value per share plus the present value of future residual incomes, discounted at the appropriate cost of equity.
Here are the steps to calculate the intrinsic value per share:
-
Calculate the Residual Earnings for 2020 and 2021:
Residual Earnings = (EPS - (Book Value per Share * Cost of Equity)) * (1 - Dividend Payout Ratio)
For 2020: Residual Earnings = (12 * 10%)) * (1 - 50%) = $0.30
For 2021: Residual Earnings = (12 * 10%)) * (1 - 50%) = $0.60
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Calculate the present value of these Residual Earnings:
PV of 2020 Residual Earnings = 0.27
PV of 2021 Residual Earnings = 0.49
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Calculate the Residual Earnings for 2022 and beyond, assuming a growth rate of 4%:
Residual Earnings in 2022 = 0.624
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Calculate the present value of these future Residual Earnings, using the Gordon Growth Model:
PV of future Residual Earnings = Residual Earnings in 2022 / (Cost of Equity - Growth Rate) = 10.40
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Finally, calculate the intrinsic value per share:
Intrinsic Value per Share = Book Value per Share + PV of 2020 Residual Earnings + PV of 2021 Residual Earnings + PV of future Residual Earnings
Intrinsic Value per Share = 0.27 + 10.40 = $23.16
So, the intrinsic value per share in early 2020 is $23.16.
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