Residual Income at Corvane AG: A One-Time Gain and a Clean Surplus Break
Analyst Tomas Brix values Corvane AG with a single-stage residual income model. Beginning book value per share is EUR 25.00, reported EPS EUR 3.00 and dividends EUR 1.20. Reported EPS includes a EUR 0.60 after-tax gain on the sale of a warehouse that Brix judges non-recurring; he expects operating EPS of EUR 2.40 to persist. Corvane also reports a EUR 0.50 per share loss in other comprehensive income from foreign currency translation, and 2% of shares were issued mid-year at market price. The cost of equity is 10%. Brix holds the dividend payout ratio at its current level and assumes residual income grows at the implied sustainable rate in perpetuity.
1. Compute the justified P/B and value per share using (a) reported EPS and (b) Brix's adjusted EPS. Explain the main driver of the difference.
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(a) Reported. ROE = 3.00/25.00 = 12%; payout = 1.20/3.00 = 40%; g = (1 - 0.40)(0.12) = 7.2%. Residual income = 3.00 - (0.10 x 25.00) = 0.50. V = 25.00 + 0.50/(0.10 - 0.072) = 25.00 + 17.86 = EUR 42.86; P/B = 1.71.
(b) Adjusted. ROE = 2.40/25.00 = 9.6%; the dividend is held at 1.20, so payout = 50%; g = (0.50)(0.096) = 4.8%. Residual income = 2.40 - 2.50 = -0.10. V = 25.00 - 0.10/(0.10 - 0.048) = 25.00 - 1.92 = EUR 23.08; P/B = 0.92.
Driver of the difference. Not just the EUR 0.60 of earnings: the gain also inflated ROE and therefore the assumed growth rate. Stripping it cuts ROE below the 10% cost of equity, flipping the sign of residual income. Once ROE is below r, growth destroys value, so the model discounts book value - the exact opposite of the unadjusted result.
2. Does Corvane satisfy the clean surplus relation? Quantify the effect of the OCI item and of the share issuance.
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Clean surplus requires ending book value = beginning book value + comprehensive income - dividends. Reported ending book value would be 25.00 + 3.00 - 1.20 = 26.80. Including the EUR 0.50 OCI loss gives 25.00 + 3.00 - 0.50 - 1.20 = 26.30. The relation is therefore broken by EUR 0.50 per share, and the model should use the lower starting book value for the next period and treat the currency loss as a recurring drag if the exposure persists.
The 2% mid-year issuance at market price does not create value per share in theory - shares were sold at fair value, so new capital earns the cost of equity. In practice it changes book value per share, the payout ratio denominator and the growth calculation if Brix mixes aggregate and per-share figures. He should forecast per-share numbers consistently and confirm the issuance was not priced at a discount, which would transfer value from existing holders.
3. Which assumption is most fragile, and how should Brix handle a negative residual income that is assumed to grow?
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The most fragile input is the pair (payout ratio, g). Holding dividends at EUR 1.20 while earnings drop to 2.40 raises the payout to 50%, and the resulting g of 4.8% is a plug from a single year's data. The value in part (b), 25.00 - 1.92, is highly sensitive to the denominator, r - g = 5.2%: a 1-point error in r moves value about 2 euros per share.
With negative residual income, higher growth makes the valuation lower, not higher. That is economically coherent - growth at ROE below r is value-destroying - but it means the model must not be read mechanically. A perpetuity of negative RI forever implies the firm is sold off at book value. A better treatment is to forecast RI explicitly for a long horizon while the warehouse-sale proceeds are redeployed and margins normalize, then fade to a terminal value; and to cross-check with a relative valuation. Present the range (b) to (a) with the assumptions stated.