Complex Valuation - Amazon 1.Most of the spreadsheet involves calculating the value of the equity (the stockholders value) using the Discounted Free Cashflow Method (DFCF). a. He finds the total value of the firm (Amazon). b. Then he subtracts the pieces of value that get paid to others, such as bondholders and managers (through their options). 2.Part of the spreadsheet involves calculating the value of the equity using the relative valuation method of Price-to-Sales. 3.Basic Steps for DFCF – Firm Value a. Estimate the discount rate or rates. b. Estimate the firm’s free cashflows from operating assets during a period of years of unusual circumstances including high unstable growth. c. Estimate the year when cash flows will have stable growth forever afterward – for Amazon – year 10. d. Apply the appropriate discount rates to the appropriate free cash flows. For Amazon, the first 9 years have high and sometimes changing discount rates that decline and then remain fixed. The fixed rate and constant growth cashflows after year 10 allow a “residual value” of cashflows to be valued using the constant growth model P = D/(K – g). This “residual value” is then discounted back over the 10 years using the cumulative discount rate.

4. Main Results a. The large negative cash flows in the early years don’t impact the value that much because they last for a limited number of years. But, much effort goes into calculating them. b. Much of the value comes from the stable growth after year 10. The inputs to this part rely partly on the first 10 years. Slight changes to the inputs, particularly growth, make for large changes in value. This illustrates why the market valuation of companies like Amazon can be way off and why the stock price can be volatile if peoples perceptions of these input changes frequently. Since many companies themselves have no idea what inputs such as growth will be even a year or two in the future, it is not surprising that stock investors make mistakes. c. Growth rate depends upon - firm size relative to market size - barriers to entry – sustainable advantage - margin - current growth

Topic: How to value young, high-growth firms when they have no earnings, no financial history or comparable firms. Basic Solution: Value the firm 10 years in the future assuming some rough convergence to comparable industry free cash flow to the firm (FCFF) using FCFF/(k-g). Calculating the Valuation Inputs for Firms With Financial Data 1. FCFF - is the cash available to the firm after taxes and reinvestment needs required to sustain growth. FCFF = EBIT(1-T) - (CE - D) - (  NCWC) Where EBIT = earnings before interest and taxes - also called operating income. T = marginal tax rate CE = Capital Expenditure D = depreciation  NCWC = Change in non-cash working capital NOTE: EBIT(1-T) is used instead of EBT(1-T) because the cost of capital (debt) used to discount FCFF is after-tax.

2. g = RR * ROC Where g = Expected Growth in EBIT RR = Reinvestment Rate = (CE - D +  NCWC) ROC = Return on Capital = EBIT(1-T)/capital invested 3. Cost of capital = k = k e [E/(D+E)] + k d [D/(D+E)] Where k e = cost of equity k d = after-tax cost of debt E = market value of equity D = market value of debt 4. Terminal Value n = FCFF n+1 / (k n - g n ) This value is discounted back n years at the appropriate k that covers the first n years, usually 10 years. Although first ten years FCFF is estimated and discounted, value comes largely from value after 10 years for the young firms of interest here. All inputs should be sustainable rates.

5. For the total firm value add the value of cash (C), marketable securities (MS) and other assets whose income is not consolidated in operating income (NOA). 6. Firm Value = C + MS + NOA + Note: We allow for different k in each of the first t years. 7. Equity Value = Firm Value - Debt Value 8. Equity Value Per Share = [Equity Value - Options Value]/ Shares Outstanding 9. Options value comes from management options, warrants and convertible debt or preferred.

Typical Methods to Handle Problems 1. Negative earnings - Use Normal Earnings A. Past average over cycle - adjust for increase in scale if growth will occur in future B. Estimate normal operating or net profit margins or use prior years’ average or industry average and apply to revenue (which is never negative) C. Estimate normal ROC or use industry average and apply to invested capital. D. Reduce leverage over time - if negative earnings due to financing costs. Assume debt ratio goes to optimum (at lowest k) or use industry average. -assume firm reduces future investment to pay down debt, issues equity to pay down debt or grows to scale that can support current debt. 2. Note: In all cases if earnings are expected to normalize after some lag, not immediately, then estimate future normal earnings and discount back to present. Typically, the farther away current figures are from normal figures, the longer it is assumed to take until convergence to normal figures. If large growth is expected, then convergence may be quicker. 3. To handle tax effects of net operating losses (NOL), get PV of NOL = NOL(T)/(1+r) n where n is the year into which the losses are carried.

4. When should normal earnings be used? - when losses are transient - or cyclical. - use profitability and current revenues or capital to estimate normal earnings when scale of firm is changing. - long-term operational/structural problems - require adjusting margins to sustainable levels - industry average of stable firms. If problems seem insurmountable - consider bankruptcy so no value (or perhaps option value).

Young Firms With No History or Apparent Comparable Firms 1. Get data from firms as similar as possible even if not directly comparable. - Similar businesses - Amazon - retailers/booksellers. - Richness of information - more data on retailers than booksellers. - Life cycle similarity - data from retailers shows us how margins and revenue change with age. This can be used to project similar changes for a young firm - this is unavailable if we select an industry with only young firms. 2. Expected Revenue Growth alternatives - use most recent 12 months growth for firm - growth for market the firm serves - sustainability depends on barriers to entry or competitive advantages 3. Sustainable Operating Margin - examine true competitors - Amazon - Specialty retailers - adjust firms own negative margins by removing research, development and advertising that are unusually high but must be expensed rather than capitalized by GAAP.

4. Reinvestment Needs - steady state - RR = g/ROC - all figures for steady state (see earlier) - assume RR growth = revenue growth - assume converges to RR = industry average RR A. Then get $reinvestment = RR*current $Capital B. Or use $reinvestment =  $Revenues/ (S/C) where S/C = Revenues/ Capital 5. Risk - estimate beta from financial characteristics - use industry average (internet firms) or assume convergence to industry average (specialty retail) in future. 6. Estimate k e with CAPM and beta 7. Estimate k d with rate for bond rating - use 0 tax rate for loss period, carry-forward period and then apply full tax rate. 8. Use convergence to industry average capital structure D/(E+D). 9. Use compound cost of different yearly capital costs in later years which converge to stable rate for terminal value.

Final Value 1. Firm Value = C + MS + NOA + 2. Equity Value = Firm Value - Debt Value 3. Equity Value Per Share = [Equity Value - Options Value]/ Shares Outstanding 4. Perhaps adjust equity value for probability of default. Adjusted Equity Value Per Share = (Equity Value Per Share) * (1-default probability) 5. The most important value drivers are - sustainable margins - revenue growth - important but less - convergence time, reinvestment needs

Other Considerations 1. To deal with the uncertainty in pricing young firms - consider investing in a portfolio of those you find undervalued rather than the most undervalued -you could be mistaken on the one- I.e. diversify. 2. Valuation shows what type of assumptions are required to justify market price - assumptions may seem reasonable or not. 3. Earnings growth obtained by cutting investment below that required to remain competitive and sustain future earnings may be misleading. 4. Comparables methods are popular because they are often easier to apply but actually implicitly rely on the same assumptions as the FCFF method. The FCFF method makes the assumptions easier to see and judge for reasonability. For young firms, many get comparable ratio out 5-10 years and discount price back. Main problem: if all firms in comparable group are under or over-valued then results are bogus.