If all underlying assumptions are consistent, all equity valuation approaches including the dividend discount model (DDM), the residual income model at equity level (RIVM), the abnormal earnings growth model (AEG), and the P/E multiple should, in theory, generate the same value of equity shares. You want to verify the above statement yourself by collecting the following information for Grange PLC.

The firm has a beta of 1.2, the risk free rate is 3% and the market risk premium is 3.5%. You may assume that the cost of equity is given by the capital asset pricing model (CAPM).

Current book value is 10 per share.

The forecast earnings per share (EPS) for the next three years are:

Year 1, 0.8; Year 2, 0.832; Year 3, 0.865

The company has a constant dividend payout ratio of 50% for the next three years.

For year 4 and beyond, the forecast growth in book value and earnings will be 4% per year

(a) Calculate the return on equity (ROE) and residual income (RI) for years 1-4, as well as the abnormal earnings growth (AEG) for years 2-4 in 4 decimal places.

(b) Calculate the value of Grange PLC using the DDM, Residual Income Value and AEG models at the beginning of Year 1, Year 2 and Year 3.

(c) Calculate the value of Grange PLC using the forward P/E at the beginning of Year 2 and Year 3. Explain the conditions under which the P/E multiple can generate consistent results.

(d) Discuss any possible reasons why the DDM and RIVM models may not reconcile in practical valuation.