Chapter 10 Solutions - 10-1 Problem 10- 1 2010 Cash ...

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Unformatted text preview: 10-1 Problem 10- 1 2010 Cash Flow = Growth rate = Discount rate = $1.45 million 3.0% 9.0% a. CBR Value = $24.9 million (Eq. 10.2) b. Cash flow multiplier = 17.2 (Eq. 10.3) 10-2 Problem 10-2 Year 1 2 3 4 5 6 7 Revenue Growth (year-to-year) $0 $850 $2,300 171% $6,100 165% $10,700 75% $13,100 22% $13,800 5% EBIT Growth (year-to-year) ($2,000) ($788) 61% ($1,925) -144% ($975) 49% ($325) 67% $275 185% $450 64% Assets Growth (year-to-year) $3,000 $1,000 -67% $4,500 350% $3,525 -22% $6,200 76% $6,475 4% $8,925 38% Total value in this case depends only on con2nuing value, as there are no posi2ve interim cash flows for investors. The asset levels indicate that addi2onal investments will be made in subsequent years, e.g., the increase in year 3 when EBIT is nega2ve indicates a new investment in assets. Because asset levels are con2nuing to change due to new investments and the growth rate of assets is vola2le, valua2on based on assets is unlikely to produce a reliable es2mate. EBIT has a similar problem. Only the last two years are posi2ve and the year- to- year growth rate of earnings in those years is very high. This suggests that it is unlikely that reliable comparables based on EBIT could be found. In contrast to Assets and EBIT, Sales growth is well behaved. By the last year of the forecast, the rate of sales growth has stabilized at something close to the infla2on rate. If profitablity is s2ll erra2c, a sales mul2ple might yield the best con2nuing value es2mate. With more informa2on, we might try to determine a normal profit level for the stabilized level of sales. $16,000 Revenue EBIT Assets $14,000 $12,000 $10,000 $8,000 $6,000 $4,000 $2,000 $0 1 2 3 4 -$2,000 -$4,000 Year 5 6 7 10-3 Problem 10-3 Dividends 3-Year Sales CAGR Assets Market Value ($2) $0 85% $85 $65 $2 $0 25% $155 $60 $130 $10 $0 3% $110 15 $45 $70 $4 $1 15% $80 17 $195 $280 $30 $16 6% $210 Market Value Multiples Firm A Firm B Firm C Firm D Firm E MV/BV Assets 2.1 1.3 1.8 1.8 1.1 MV/Sales 3.4 2.4 0.8 1.1 0.8 MV/EBIT -42.5 77.5 11.0 20.0 7.0 Div/MV N/A N/A N/A 1.3% 7.6% Value Based on Multiples Firm A Firm B Firm C Firm D Firm E Assets $74.4 $45.2 $64.2 $62.2 $37.7 Sales $176.8 $124.0 $44.0 $59.4 $39.0 EBIT ($85.0) $155.0 $22.0 $40.0 $14.0 Dividends N/A N/A N/A $0.0 $0.0 Age in Years Assets: Book Value Sales EBIT Firm A 4 $40 $25 Firm B 6 $120 Firm C 9 Firm D Firm E Comparable Firms Firm A: Similar age and asset size, lower sales, nega2ve profit, but much more rapid growth - assets mul2ple okay - sales mul2ple is likely to be too high. Firm B: Similar age, sales , EBIT, and growth rate, higher assets - sales mul2ple seem most useful - assets mul2ple is too low. Firm C: Older, larger, more profitable, slower growth - assets mul2ple seems most representa2ve. Firm D: Older but similar asset size, sales, EBIT, growth - valua2ons a bit on low side due to somewhat lower growth. Firm E: Large and slow growing, like Firm C - tends to undervalue. Assets mul2ples seem more reliable than sales or EBIT due to more consistency - dividend mul2ple is not useful. Possibly base the es6mate on the four shaded mul6ples - the median would be about $70 million. 10-4 Problem 10-4 Valuation of a Success Scenario at Various by the Venture Capital Method Cash Flows (000s) Success Scenario Discount Rates Percent required for $6,000,000 Total 1 $0 2 $0 3 $0 4 $0 5 $270,000 Valued at 50 Percent Present Value $35,556 $0 $0 $0 $0 $35,556 16.88% Valued at 100 Percent Present Value $25,749 $0 $0 $0 $0 $25,749 23.30% 3 $8,000 4 $35,000 5 $54,000 Because this would be start-up financing, we tried a range of 50-100 percent as hurdle rates. Year Revenue Development expenses Marketing expenses Content expenses Delivery expenses Net income 1 $0 2 $1,500 $1,200 $800 $600 $1,500 $2,500 $400 $2,000 $3,000 $7,000 $12,000 $0 $150 $800 $3,500 $9,000 $500 $1,800 $3,000 $5,000 $8,000 ($2,100) ($3,250) $600 $18,000 $22,500 10-5 Problem 10-5 Equity Beta Share Price Shares Outstanding Firm A 1.85 $12.00 2,650,000 $4,350,000 Firm B 1.60 $8.50 4,750,000 $2,800,000 Firm C 1.42 $20.50 3,280,000 $1,700,000 Comparable Firm Market Value of Comparable Firm Equity Firm A $31,800,000 Firm B $40,375,000 Firm C $67,240,000 Total Average Asset Beta Weighted Average Asset Beta Required Return Risk- free rate Market risk premium 4.00% 7.50% Asset Beta Cost of capital 1.50 15.27% Asset Value $36,150,000 $43,175,000 $68,940,000 $148,265,000 Book Value of Debt Equity/Value Ratio Asset Beta 87.97% 1.63 93.51% 1.50 97.53% 1.38 1.50 1.48 5- year Treaury rate Historical S&P 500 return minus the historical 5- year Treasury rate From above 10-6 Problem 10-6 Valuation Template 1 RADR Valuation Based on Discrete Scenario Cash Flow Forecast Project Information Cash Flows Success Scenario Expected Scenario Failure Scenario Probability 0.25 0.5 0.25 1 $0 $0 $0 Market Information Risk- free Rate Market Rate Market Risk Premium Comparable firm beta Estimated Cost of Capital 3 $0 $0 $0 4 $0 $0 $0 5 $270,000 $130,000 $1,500 $0 Expected Cash Flow 2 $0 $0 $0 $0 $0 $0 $132,875 4.00% 11.50% 7.50% 1.50 15.27% Market Value Estimate Present Value $67,169 Investment Percent of Equity Required $6,000 8.93% 8.16% 24.32% 16.16% 1.50 32.45% 12.49% 38.62% 26.13% 1.50 51.76% 16.99% 54.56% 37.57% 1.50 73.46% 21.67% 72.34% 50.67% 1.50 97.82% $0 $0 $0 $0 $67,169 10-7 Problem 10-7 Valuation Template 2 CEQ Valuation Based on Discrete Scenario Cash Flow Forecast Project Information Cash Flows Success Scenario Expected Scenario Failure Scenario Probability 0.25 0.5 0.25 1 $0 $0 $0 2 $0 $0 $0 3 $0 $0 $0 4 $0 $0 $0 5 $270,000 $130,000 $1,500 Expected Cash Flow $0 $0 $0 $0 $132,875 Standard Deviation $0 $0 $0 $0 $94,973 4.00% 11.50% 7.50% 8.16% 24.32% 16.16% 12.49% 38.62% 26.13% 16.99% 54.56% 37.57% 21.67% 72.34% 50.67% 14.50% 0.15 20.51% 0.15 25.11% 0.15 29.00% 0.15 32.42% 0.15 Market Information Risk- free Rate Market Rate Market Risk Premium Market Variance Market Standard Deviation Correlation Market Value Estimate Present Value Equity investment Equity share required by CAPM $90,913 $6,000 6.60% $0 $0 $0 $0 $90,913 10-8 Problem 10- 8 Year Explicit Value Period Projected Free Cash Flow Probability of Survival Expected Free Cash Flow Annual Discount Rate Cumulative Discount Rate Present Value Total Explicit PV Continuing Value Period Cost of Capital Growth Rate Multiplier Trailing Expected Free Cash Flow Continuing Value PV of Continuing Value Ownership Required Explicit Value Continuing Value Total Value Investment Minimum Ownership 1 2 3 4 5 6 ($1,000,000) 70% ($700,000) 4.0% 4.0% ($673,077) ($240,226) $0 70% $0 11.0% 23.2% $0 $0 70% $0 11.0% 36.8% $0 $200,000 50% $100,000 11.0% 51.8% $65,873 $600,000 40% $240,000 11.0% 68.5% $142,428 $1,400,000 30% $420,000 11.0% 87.0% $224,549 11% 6% 21.2 $420,000 $8,904,000 $4,760,442 ($240,226) $4,760,442 $4,520,216 $750,000 16.6% (from Equation 10.3) 10-9 Problem 10-9 Year Percent Return 1994 1995 1996 1997 1998 1999 2000 2001 11.1% 47.4% 33.5% 28.0% 17.8% 165.3% 37.6% - 32.4% a. Arithmetic Average Return 38.54% b. Compound Return 713.49% 29.96% Geometric Average Return c. The long- term expected return can be found by compounding the arithmetic average return. d. Simulation Model Year Return Fund Value Cumulative Return Compound Annual Return 1 #NAME? #NAME? 2 #NAME? #NAME? #NAME? #NAME? 3 #NAME? #NAME? #NAME? #NAME? 4 5 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? Standard Deviation Skewness 6 #NAME? #NAME? #NAME? #NAME? 7 8 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? Minimum 25% 50% 75% Sample Simulation Result (based on 10,000 iterations of the model) Output 1 Cumulative Return 2 Average Median Maximum 1285.4% 698.5% 1856.2% 458.6% -72.8% 299.6% 698.5% 1507.3% 38020.8% Compound Annual Return 36.3% 34.6% 20.1% 53.8% -17.0% 21.9% 34.6% 48.7% 133.7% Compound Arithmetic Average 38.90% 10-10 Problem 10-10 Projected Cash Flow per Acre at Harvest Compound Annual Return on Investment Scenario Boom 40% 25% $96,000 12% Normal Growth 30% 10% $67,000 10% Bust a. Probability Return on Market Portfolio 30% -8% $32,000 6% Expected return on market portfolio Step 2: Variance of returns on market portfolio 1.87% Step 3: Expected return on project 9.60% Step 4: Covariance between project and market 0.0034 Step 5: b. Step 1: Beta 0.181 Steps 1 through 3 are the same as in part a. Step 3: Expected cash flow Step 4: Covariance of cash flows with market returns Step 5: c. 10.60% Cash flow beta $68,100 $3,623 $193,931 Risk-free rate 5.50% Market risk premium 6.00% Estimated cost of capital by RADR method 6.59% Estimated present value per acre by RADR method Estimated net present value $19,015 $9,015 CEQ cash flow $56,464 d. Present value by CEQ method $19,352 e. CEQ implied required rate 6.493% ...
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This note was uploaded on 02/19/2012 for the course FIN 124 taught by Professor Jackson during the Spring '05 term at University of Texas at Dallas, Richardson.

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