George Reeby proposes to sell 90,000 shares, or about 22%, of his company. How much are those shares worth? We have to value the company using Georges forecasts.

The forecasts presented in Tables 4.10 and 4.11 do not show free cash flow and financing requirements. These are calculated in Table 1. Note that free cash flow for 2005 is -$2.3 million. But dividends are $2.0, so the company will need 2.3 + 2.0 = $4.3 million in outside equity financing.

Table 2 shows that the book value of equity is forecasted to grow from $40.71 million in 2004 to $63.31 million at the end of 2010. Table 3 works out earnings, dividends and free cash flow for 2011. By that time Reeby Sports should be earning 12% on equity, paying out 40% of earnings, and growing steadily at 7.2% per year. Note that gross investment equals depreciation plus 60% of earnings. s

Its easiest to value the company by assuming that its current shareholders contribute all of the $4.3 million required in 2002 and receive all of the free cash flow afterwards. Note from Table 1 that the present value of free cash flow from 2004 to 2010 is $8 million.

Of course there are several ways to calculate PVH, the horizon value in 2010. The constant-growth DCF formula gives

implying a company value in 2003 of:

2002, R. A. Brealey and S. C. Myers

Next suppose that Reeby Sports will lose its competitive edge by 2010 and will have no PVGO looking forward from that date. In that case we just capitalize 2011 earnings at 10%:

George also has a comparable, Molly Sports. The case gives three ratios for Molly:

Ratio2010 ValuationPV in 2003

Market-to-book = 1.51.5 x 63.31 = 94.97$56.73 million

Price-earnings = 1212 x 7.60 = 91.20$54.80 million

Dividend yield = .03

$60.00 million

These calculations imply higher current valuations for Reeby Sports ” higher than the DCF calculations presented earlier. Perhaps George should revisit the forecasts in Tables 4.10 and 4.11.

Note that all the valuations presented so far are Reeby Sports as a whole. To get per-share value, just divide by 200,000.

These valuations also assume that George (or the new shareholders that buy the share issue in 2003) put up all the additional equity financing in 2005. That is not Georges plan. Lets work out the present value of Reeby Sports to current (year 2003) shareholders. Well use the constant-growth formula for PVH.

First calculate PV at the end of 2005 after that years investment and financing.

= $77.2 million.

To raise $4.3 million, new shares will have to comprise 4.3/77.2 = .0557, or

5.57% of the company, leaving 94.43% for the old shareholders. The number of new shares will be 70,141, because

The value to old shareholders in 2003 is:

PV = = $63.71 million,

just as in our earlier calculation. Again, all PVs and cash flows can be converted to per-share units by dividing by 200,000.

Table 1: Reeby Sports ” Investment, Financing Requirements and Free Cash Flow (Figures in $ millions)

2004200520062007200820092010

After-tax profits

5.25

5.70

3.00

3.40

4.35

6.00

7.60

Dividends2.002.002.502.502.502.503.00

Retained profits3.253.70.50.901.853.504.60

+ Depreciation2.403.103.123.173.263.443.68

= Retained cash flow5.656.803.624.075.116.948.28

Investment5.6511.103.624.075.116.948.28

= Financing required0- 4.3000000

Free cash flow2.00- 2.302.502.502.502.503.00

(= Dividends financing required)

PV of free cash flow at 10% = 8.01, about $8 million

Table 2: Investment and book value

(Figures in $millions)

2004200520062007200820092010

Equity book value,

start of year

40.71

43.96

51.96

52.46

53.36

55.21

58.71

+ Investment5.6511.103.624.075.116.948.28

Depreciation2.403.103.123.173.263.443.68

= Equity book value,

end of year43.9651.9652.4653.3655.2158.7163.31

Table 3: Earnings, Investment and Dividends for 2011

(Figures in $millions)

After-tax profits7.6012 % on start-of-year book equity

Dividends3.0440 % payout

Retained profits4.567.2 % growth

+ Depreciation3.95

= Retained cash flow8.51

Investment8.51= depreciation + 60% of profits

= Financing required0

Free cash flow3.04

(= Dividends financing required)

The forecasts presented in Tables 4.10 and 4.11 do not show free cash flow and financing requirements. These are calculated in Table 1. Note that free cash flow for 2005 is -$2.3 million. But dividends are $2.0, so the company will need 2.3 + 2.0 = $4.3 million in outside equity financing.

Table 2 shows that the book value of equity is forecasted to grow from $40.71 million in 2004 to $63.31 million at the end of 2010. Table 3 works out earnings, dividends and free cash flow for 2011. By that time Reeby Sports should be earning 12% on equity, paying out 40% of earnings, and growing steadily at 7.2% per year. Note that gross investment equals depreciation plus 60% of earnings. s

Its easiest to value the company by assuming that its current shareholders contribute all of the $4.3 million required in 2002 and receive all of the free cash flow afterwards. Note from Table 1 that the present value of free cash flow from 2004 to 2010 is $8 million.

Of course there are several ways to calculate PVH, the horizon value in 2010. The constant-growth DCF formula gives

implying a company value in 2003 of:

2002, R. A. Brealey and S. C. Myers

Next suppose that Reeby Sports will lose its competitive edge by 2010 and will have no PVGO looking forward from that date. In that case we just capitalize 2011 earnings at 10%:

George also has a comparable, Molly Sports. The case gives three ratios for Molly:

Ratio2010 ValuationPV in 2003

Market-to-book = 1.51.5 x 63.31 = 94.97$56.73 million

Price-earnings = 1212 x 7.60 = 91.20$54.80 million

Dividend yield = .03

$60.00 million

These calculations imply higher current valuations for Reeby Sports ” higher than the DCF calculations presented earlier. Perhaps George should revisit the forecasts in Tables 4.10 and 4.11.

Note that all the valuations presented so far are Reeby Sports as a whole. To get per-share value, just divide by 200,000.

These valuations also assume that George (or the new shareholders that buy the share issue in 2003) put up all the additional equity financing in 2005. That is not Georges plan. Lets work out the present value of Reeby Sports to current (year 2003) shareholders. Well use the constant-growth formula for PVH.

First calculate PV at the end of 2005 after that years investment and financing.

= $77.2 million.

To raise $4.3 million, new shares will have to comprise 4.3/77.2 = .0557, or

5.57% of the company, leaving 94.43% for the old shareholders. The number of new shares will be 70,141, because

The value to old shareholders in 2003 is:

PV = = $63.71 million,

just as in our earlier calculation. Again, all PVs and cash flows can be converted to per-share units by dividing by 200,000.

Table 1: Reeby Sports ” Investment, Financing Requirements and Free Cash Flow (Figures in $ millions)

2004200520062007200820092010

After-tax profits

5.25

5.70

3.00

3.40

4.35

6.00

7.60

Dividends2.002.002.502.502.502.503.00

Retained profits3.253.70.50.901.853.504.60

+ Depreciation2.403.103.123.173.263.443.68

= Retained cash flow5.656.803.624.075.116.948.28

Investment5.6511.103.624.075.116.948.28

= Financing required0- 4.3000000

Free cash flow2.00- 2.302.502.502.502.503.00

(= Dividends financing required)

PV of free cash flow at 10% = 8.01, about $8 million

Table 2: Investment and book value

(Figures in $millions)

2004200520062007200820092010

Equity book value,

start of year

40.71

43.96

51.96

52.46

53.36

55.21

58.71

+ Investment5.6511.103.624.075.116.948.28

Depreciation2.403.103.123.173.263.443.68

= Equity book value,

end of year43.9651.9652.4653.3655.2158.7163.31

Table 3: Earnings, Investment and Dividends for 2011

(Figures in $millions)

After-tax profits7.6012 % on start-of-year book equity

Dividends3.0440 % payout

Retained profits4.567.2 % growth

+ Depreciation3.95

= Retained cash flow8.51

Investment8.51= depreciation + 60% of profits

= Financing required0

Free cash flow3.04

(= Dividends financing required)