# Firm Value 03/11/2008 Ch. 12. 2 What is a firm worth? Firm Value is the future cash flow to each of the claimants Shareholders Debt holders Government.

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Firm Value 03/11/2008 Ch. 12

2 What is a firm worth? Firm Value is the future cash flow to each of the claimants Shareholders Debt holders Government When we talk of value of an asset…it is the price two independent agents are willing to exchange the asset at an arm’s length Neither are forced to complete the transaction The price reflects the value to the two parties For a real asset it is the characteristics of the asset For a financial asset it is simply the cash flows or the rights to the cash flows

3 Firm Valuation Determining the cash flow to the owner… Four Methods Efficient Market Approach, take trading price of the share x number of outstanding shares Discounted Cash Flow Approach I  CF to Equity discounted at cost of equity Discounted Cash Flow Approach II  CF to Firm discounted by WACC Relative Value  Use financial ratios to determine value In Theory all four methods should give same value

4 Firm Value in an Efficient Market From the perspective of the owner Value of the firm is the price of the shares times the outstanding shares Example, 3M Current price per share is \$76.51 (as of close of business 3-7-2008) Shares outstanding 707,660,000 (as of close of business 3-7-2008) Value = \$54,138,935,060 Is the market right?

5 Firm Value DCF Approach l Discount all future cash flows to equity holders Method A – Dividends are all future cash flow Method B – Find Free Cash Flow to Equity (FCFE) Assumption of models… Growth rate is needed Growth rate may be different over time High Growth Period Stable Growth Period

6 Quick Review of Dividend Model Gordon’s Dividend Growth Model No-growth, infinite horizon No-growth, finite horizon Constant growth, infinite horizon Constant growth, finite horizon

7 Different Growth Periods High Growth Period Start-up or time when firm is still expanding Transition Growth Period Moving to Stable or Constant Growth Stable or Steady or Constant Growth Period Mature Business – will continue at this rate forever Means that the firm is growing at the risk-free rate Find the PV of the dividends (of FCFE or FCFF) for each of these periods Assumption today…transition is immediate High Growth Period + Stable Growth Period = Value

8 3M and Discounting Dividends Dividend (annual for 2007…\$0.48 x 4 = \$1.92) Dividend growth rate past ten years 1996 \$1.06 2007 \$1.92 Growth rate 6.12% Required Return on Equity Beta 0.82 Risk-free rate 3% Expected return on the market 12% R = 3% + 0.82 (9%) = 10.38% If 3M at steady growth… Price = \$1.92 x (1.0612) / (0.1038 – 0.0612) = \$47.83 Market has overpriced 3M unless…

9 Fixing the Dividend Model 3M is still in its growth period and will move to stable in 20 years… Need to have estimate for years 1 to 20 at the current rates Need to estimate 21 to infinity with infinite model but need to change… Growth rate to 3% (risk-free rate) Beta to 1.0 P = \$47.83 x (0.5448) + \$36.70 / (1.1038) 20 P = \$31.15

10 Finding Numbers that Work If we believe the market is efficient… Then our estimates of beta may be off Growth rate may be off Risk-free rate may be off Expected return on the market may be off Finding values that work for \$76.50 At a steady growth and infinite horizon If beta is 0.64256 all else held constant… Price = \$1.92 x (1.0612) / (0.0878 – 0.612) = \$76.50 Which variable needs adjusting?

11 DCF Approach l Same concept except now we find the FCFE and plug into the dividend model with a growth rate and required return on equity FCFE = Net Income + Depreciation – Capital Expenditures - Δ Working Capital – Principal Repayments on Debt + New Debt Issued We also need growth in FCFE Required return on equity (from SML)

12 After-Tax Cash Flow of Dividends FCFE 2005 -- \$2,480,000 2006 -- \$4,793,000 2007 -- \$5,053,000 Growth rates 2006 – 93% 2007 – 5% Cost of Equity…10.38% or 12.0% or 15.2% \$5,053 x (1.054) / (.152 -.054) = \$54,345 Implies a beta of 1.3555

13 DCF Approach ll Free Cash Flow to Firm and then divide by WACC FCFF = EBIT x (1 - t) (1 – Reinvestment Rate) Where Reinvestment rate: (Capital Expenditures – Depreciation + Δ Working Cap.) EBIT ( 1 – tax rate) Again we can look a 3M and estimate this number FCFF = \$4,029 (million) Estimate of growth rate of FCFF 6.19% WACC estimate…11.37% Firm Value = \$4,029 x (1.0619) / (0.1137 – 0.0619) Firm Value = \$82,594 Equity Value = \$82,594 – \$7,585 = \$75,009

14 Adjustments to DCF ll Fix WACC to find equity value of \$54,139 IF we choose a WACC of 13.12% \$4,029 x (1.0619) / (0.1312 – 0.0619) = 61,737 Equity Value = \$61,737 - \$7,585 = \$54,152 What beta does this imply? If book D/E is \$7,585 / \$11,747 = 0.6457 Keep cost of debt at 8% and tax rate at 32% Cost of Equity must be 17.82% Beta must be 1.647

15 Method Four – Relative Value Standardize the assets Relative to earnings Relative to book value or replacement value of the assets Relative to revenues Sensitivity Analysis also needed to adjust the numbers for differences across firms Find comparable firms… Similar risk, cash flow, and growth potential

16 Relative Value Continued Price to Earnings Ratio Here we assume that the market has properly priced the cash flow of a firm P/E is price per share divided by earnings per share Backward looking vs. Forward looking Price = \$76.51 and Earnings = \$6.03 Forward P/E = 12.69 Net Income is \$4,096 Equity Value = \$4,096 x 12.69 = \$51,635 If 3M P/E looks out of line with other large manufacturing firms…substitute the industry average

17 Relative Value Continued Price to Book-Value Return on Equity x Payout Ratio x (1+g) (Cost of equity – g) Return on Equity = 37.74% Payout Ratio = 34% Growth rate = 6% Cost of Equity = 10% (mature firm beta = 0.82) PBV = 3.3760 How does this compare?

18 Relative Value Price to Sales From the “book” regression… PS = 0.04 x g + 0.011 payout ratio + 0.549 beta + 0.234 net margin For 3M g = 6% Payout ratio is 34% Beta is 0.82 Net margin (profit margin) 16.74% PS = 0.04 (0.06) + 0.011 (0.34) + 0.549 (0.82) + 0.234 (0.1674) = 0.4933 or 49.33% PS for 3M is revenue / price = \$34.055 / \$76.51= 0.4451

19 What is the true value of a Company? What you can sell it for… If you believe efficient markets and the markets are liquid… Share price is the true value Some caveats Share price is for a small portion of ownership What if you wanted to sell the whole company in a short period of time? Takeover prices higher than current share price

20 Thursday 3-13 Review for exam Last minute questions on projects Other

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