What is the company worth per share? We will value the company using George’s forecasts.

The spreadsheet accompanying this solution (sheet 4) sets out a forecast in the same general format as Table 4.4. Historical results from 1999 to 2004 are also shown. Earnings per share (EPS) equals return on equity (ROE) times starting book value per share (BVPS). EPS is divided between dividends and retained earnings, depending on the dividend payout ratio. BVPS grows as retained earnings are reinvested.

The keys to the company’s future value and growth are profitability (ROE) and the reinvestment of retained earnings. Retained earnings are determined by dividend payout. The spreadsheet sets ROE at 15% for the five years from 2006 to 2010. If Reeby Sports will lose its competitive edge by 2011, then it cannot continue earning more than its 10% cost of capital. Therefore ROE is reduced to 10% starting in 2011.

The payout ratio is set at .30 from 2006 onwards. Notice that the long-term growth rate, which settles in between 2011 and 2012, is ROE × ( 1 – dividend payout ratio ) = .10 × (1 – .30) = .07.

The spreadsheet allows you can vary ROE and the dividend payout ratio separately for 2006-2010 and for 2011-2012. But let’s start with the initial input values. To calculate share value, we have to estimate a horizon value at 2010 and add its PV to the PV of dividends from 2005 to 2010. Using the constant-growth DCF formula,

The PV of dividends from 2005 to 2010 is $3.43 in 2004, so share value in 2004 is:

The spreadsheet also calculates the PV of dividends through 2012 and the horizon value at 2012. Notice that the PV in 2004 remains at $16.82. This makes sense, since the value of a firm should not depend on the investment horizon chosen for valuation.

We have reduced ROE to the 10% cost of capital after 2010, assuming that the company will have exhausted valuable growth opportunities by that date. With PVGO = 0, PV = EPS/r. So we could discard the constant-growth DCF formula and just divide EPS in 2011 by the cost of capital:

This PV is identical to the PV from the constant-growth DCF formula. It doesn’t matter how fast a company grows after the horizon date H if it only earns its cost of capital.

How much of the company’s 2004 value is due to PVGO? You can check by setting ROE = .10 for 2006-2010 as well as 2011-2012. You should get PV = $13.82. Thus PVGO = 16.82 – 13.82 = $3.00 per share for investments made in 2005 and in later years.

George has also identified a “comparable,” the competitor. We could use its P/E ratio of 13.1 to calculate horizon value in 2010 and PV in 2004:

We could also use the comparable’s P/E ratio to calculate the company’s 2004 value directly from 2005 EPS:

PV = 13.1 × 2.03 = $26.59

Both values based on the comparable’s P/E are higher than our DCF calculations. Is the comparable significantly more profitable than the company, or does our spreadsheet understate the company’s prospects?

What if compamy could continue to earn ROE = .15 for two extra years, until 2012? You can check by changing ROE for 2011 and 2012 from .10 to .15. You should get NPV of $18.04 in 2004, somewhat higher than our original DCF calculations, but not enough for the company to match the comparable’s P/E. You may wish to experiment to find inputs that generate P/E = 13 for the company in 2004. Do you think these inputs are reasonable?