Chapter 9 Solutions

Chapter 9 Solutions - 9- 1 DeltaCad Inc. Dividend (D1)...

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Unformatted text preview: 9- 1 DeltaCad Inc. Dividend (D1) Price (P1) Dividend Yield Percent Appreciation Total Return Probability State of the Economy 1/3 Boom $1.40 $51.00 3.5% 27.5% 31.0% 1/3 Average $0.75 $43.00 1.9% 7.5% 9.4% 1/3 Bust $0.00 $33.00 0.0% - 17.5% - 17.5% Current Price = $40.00 Expected Return = 7.6% Std. dev. of Expected Return = 19.8% 9- 2 Stave Four Enterprises Dividend (D1) Price (P1) Dividend Yield Percent Appreciation Total Return Probability State of the Economy 10% Boom $2.00 $35.00 7.4% 29.6% 37.0% 30% Good $1.25 $31.50 4.6% 16.7% 21.3% 40% Likely $1.00 $29.00 3.7% 7.4% 11.1% 20% Poor $0.25 $22.25 0.9% - 17.6% - 16.7% Current Price = $27.00 Expected Return = 11.2% Std. dev. of Expected Return = 15.9% Stave Four has a higher expected return and a lower standard deviaRon than DeltaCad, which would appear to make it a beVer investment. However, if the stocks were going to part of a diversified porYolio, we would also want to know the relaRve level of market risk as proxied by beta. 9- 3 Return Return SML 12 11 8 5 0 20 30 Std Dev 0 0.5 1.0 1.17 Beta a. The risk- free asset plots at a return of 5% and risk of 0 in both figures. The market por=olio plots at a return of 11% with standard deviaAon of 20% and beta of 1.0. b. The asset with 12% expected return and 30% total risk has beta risk of 1.167 based on a risk premium 1.167 Ames that of the market. Its correlaAon with the market is 0.78, computed using EquaAon 9.4. c. The asset with 8% expected return but 30% standard deviaAon must have lower market risk. The 8% return implies beta risk of 0.5 and a correlaAon with the market of 0.33. 9- 4 3 (a) Cost $ 30.00 Probability Payoff 50% $ 55.00 83% 50% $ 20.00 - 33% Expected Payoff = Std. Deviation = 3 (b) Cost = Expected Return = Std. Deviation = 3 (e) Risk- adjusted rate = 3 (c) risk free 3.0% MRP 6.5% $ 30.00 25.0% 58.3% #DIV/0! 18.0% 0.4 $ 33.954 3 (d) NPV (@ $30)= $ 37.50 $ 17.50 σmarket ρmarket, wager PVWager $ 3.954 3 (e) Risk- adjusted rate = 10.4% 9- 5 Comparable Transaction Apartment A Apartment B Apartment C Apartment D Average price/s.f. = Square feet = Estimated price = Average Selling/Assessed = Assessed Value Estimated price = Square Feet 900 675 1,100 845 $778 720 $560,088 0.96 $575,000 $550,420 Bedrooms 2 1 2 1 Baths 1 2 2 1 Assessed Selling Value Price $750,000 $695,000 $576,000 $565,000 887,500 865,000 $639,000 $605,000 Price/sf $772 $837 $786 $716 $778 Price/Bed $347,500 $565,000 $432,500 $605,000 $487,500 Price/bath $695,000 $282,500 $432,500 $605,000 $503,750 Selling/ Assessed 0.93 0.98 0.97 0.95 0.96 The discrete values for the number of bedrooms and bathrooms do not really provide good esOmates. The esOmates based on price/s.f. and selling vs. assessed values seem to be reasonably close. For this analysis to have value, it is assumed all of the comparable transacOons are in the same area as the property being considered for purchase (or in comparable neighborhoods). 9- 6 CF to all investors = $74 Discount Rate Unlevered cost of equity CF to creditors = $63 Cost of debt CF to stockholders = $11 Cost of equity Unlevered free CF = $70 WACC Cash Flow to All Investors (both stockholders and creditors) Cash Flow to All Investors = EBIT – Actual Taxes + D&A – Δ NWC – Δ Fixed Assets Cash Flow to Creditors Debt Cash to Creditors = Expected INT + Expected Δ Debt Cash Flow to Stockholders (residual, in light of expected cash flows to creditors) Cash Flow to Stockholders = EBIT – Actual Taxes + D&A – Δ NWC – Δ Fixed Assets – Expected INT – Expected Δ Debt Unlevered Free Cash Flow (f with no debt) Unlevered Free Cash Flow = EBIT – Theoretical Taxes without Debt + D&A – Δ NWC – Δ Fixed Assets PCR Financial Data Income Statement (000s) Revenue CGS Gross Profit Selling & Marketing G & A Product Development Operating Expenses Operating Income (EBIT) Interest Expense EBT Taxes Net Income Tax Rate = Statement of Cash Flows Operating Activities Net Income Depreciation Expense Changes in current items: Accounts Receivable Inventory Accounts Payable Operating Cash Flows Investing Activities Change in PPE Total Investment activities Financing Activities Bank Line of Credit LT debt Common Stock Total Financing Cash Flows Change in Cash for the period Beginning Cash Balance Ending Cash Balance 2010 (act.) $2,200 ($1,350) $850 ($550) ($125) ($75) ($750) $100 ($10) $90 ($27) $63 2011 (fcst.) $2,464 ($1,512) $952 ($590) ($155) ($90) ($835) $117 ($13) $104 ($31) $73 30% 30% 2005 $73 $15 ($20) ($15) $40 $93 ($40) ($40) ($15) ($35) $0 ($50) $3 $22 $25 Balance Sheet (000s) Cash Accounts Receivable Inventory Total Current Assets PP&E, Gross Less: Accumulated Depreciation Net PPE Total Assets Accounts Payable Line of Credit Total Current Liabilities Long Term Debt Total Liabilities Common Stock Retained Earnings Total Stockholders' equity Total Liabilities & Equity 2010 (act.) $22 $208 $316 $546 $250 ($50) $200 $746 $275 $70 $345 $135 $480 $200 $66 $266 $746 2011 (fcst.) $25 $228 $331 $584 $290 ($65) $225 $809 $315 $55 $370 $100 $470 $200 $139 $339 $809 9- 7 Problem 9-7 Valuation of a Success Scenario at Various Hurdle Rates by the Venture Capital Method Cash Flows Hurdle Rate Total Success Scenario 1 2 $0 3 $200,000 $2,000,000 Percent Required for $1,000,000 4 $8,000,000 Valued at 50 Percent Present Value 50% $2,261,728 $0 $88,889 $592,593 $1,580,247 44.21% Valued at 100 Percent Present Value 100% $800,000 $0 $50,000 $250,000 $500,000 125.00% $1,000,000 $0 $56,650 $301,500 $641,849 100.00% Implied Single Rate for Breakeven Present Value 87.89% 9- 8 Problem 9-8 Valuation of Expected Cash Flows by the Risk Adjusted Discount Rate Method Project Information Cash Flows 1 2 3 4 $0 $200 80% $2,000 60% $8,000 40% $0 Success Scenario Probability of Success $160 $1,200 $3,200 $0 $109 $673 $1,480 Expected Cash Flow Discount Rate 21.26% Market Value Estimate Present Value $2,262 Percent Required for $1,000,000 44.21% 9- 9 Problem 9-9 Year Problem 9-7 1 Valued at 50 Percent Present Value $2,261,728 2 3 4 Percent Required for $1,000,000 $0 $88,889 $592,593 $1,580,247 44.21% Market Value Estimate Present Value $2,261,728 $0 $108,810 $672,979 $1,479,939 44.21% Difference $0 ($19,921) ($80,387) Problem 9-8 $0 $100,308 9- 10 Problem 9-10 Valuation by the CEQ Method Based on Discrete Scenario Cash Flow Forecast Project Information Cash Flows 1 2 3 4 $0 $200 80% $2,000 60% $8,000 40% Expected Cash Flow $0 $160 $1,200 $3,200 Standard Deviation $0 $80 $980 $3,919 4.50% 11.00% 6.50% 20.00% 0.3 9.20% 23.21% 14.01% 28.00% 0.3 14.12% 36.76% 22.65% 35.00% 0.3 19.25% 51.81% 32.56% 40.00% 0.3 $0 $136 $885 $1,881 Success Scenario Probability of Success Market Information Risk- free Rate Market Rate Market Risk Premium Market Standard Deviation Correlation Market Value Estimate Present Value $2,901 Ownership required 34.47% 9- 11 Problem 9-11 Project Information Cash Flows 1 2 3 4 $0 $200 80% $2,000 60% $8,000 40% Expected Cash Flow $0 $160 $1,200 $3,200 Standard Deviation $0 $80 $980 $3,919 4.50% 11.00% 6.50% 20.00% 0.3 9.20% 23.21% 14.01% 28.00% 0.3 14.12% 36.76% 22.65% 35.00% 0.3 19.25% 51.81% 32.56% 40.00% 0.3 $0 $136 $885 $1,881 18.06% 35.61% 70.13% 8.66% 10.69% 14.21% 59.03% 4.96% 110.72% 11.63% 208.36% 25.00% 0.63 0.95 1.56 Success Scenario Failure Scenario Market Information Risk- free Rate Market Rate Market Risk Premium Market Standard Deviation Correlation Market Value Estimate Present Value $2,901 Risk Adjusted Discount Rate Estimate Required return (cumulative) Required return (annual) Implied Beta Std. Dev. of Returns Covariance with Market Beta Weighted Average Beta 1.33 9- 12 Problem 9-12 Project Information Cash Flows 1 2 3 4 $0 $200 80% $2,000 60% $8,000 40% Expected Cash Flow $0 $160 $1,200 $3,200 Standard Deviation $0 $80 $980 $3,919 4.50% 11.00% 6.50% 20.00% 0.3 9.20% 23.21% 14.01% 28.00% 0.3 14.12% 36.76% 22.65% 35.00% 0.3 19.25% 51.81% 32.56% 40.00% 0.3 $2,901 $0 $136 $885 $1,881 Equivalent Single Discount Rate and Beta Discount Rate 13.20% Implied Present Value $2,901 PV Differences $0 Implied Beta 1.34 $0 $125 $827 $1,949 $11 $58 Success Scenario Failure Scenario Market Information Risk- free Rate Market Rate Market Risk Premium Market Standard Deviation Correlation Market Value Estimate Present Value $0 ($68) 9- 13 Problem 9-13 Income Statement Success Failure Expected Sales Revenue Cost of Goods Sold Gross Profit Operating Expenses Operating Profit Interest Expense Net Taxable Income Income Tax Net Income $ 10,000 $ 4,000 $ 6,000 $ 4,500 $ 1,500 $ 700 $ 800 $ 280 $ 520 $ 6,000 $ 3,000 $ 3,000 $ 2,500 $ 500 $ 500 $ - $ - $ - $ 8,400 $ 3,600 $ 4,800 $ 3,700 $ 1,100 $ 620 $ 480 $ 168 $ 312 Additional Assumptions Depreciation Expense Debt Outstanding Interest Rate New Capital Expenditures Investment in Working Capital Tax Rate Probability of Scenario Debt Repayment Debt Issued Resulting Cash Flow Measures Operating Cash Flow Total Capital Cash Flow Debt Cash Flow Equity Cash Flow Contractual Cash Flow to Creditors Theoretical Taxes as Unlevered Unlevered Free Cash Flow EBITDA Success Failure Expected $ 2,200 $ 5,000 14% $ 1,500 $ 250 35% 60% $ - $ 1,000 $ 2,200 $ 5,000 14% $ - $ - 35% 40% $ 2,200 $ - $ 2,200 $ 5,000 14% $ 900 $ 150 35% Success $ 1,950 $ 1,670 $ (300) $ 2,250 $ (300) $ 525 $ 1,425 $ 3,700 Failure $ 2,700 $ 2,700 $ 2,700 $ - $ (300) $ 175 $ 2,525 $ 2,700 $ 880 $ 600 Expected $ 2,250 $ 2,082 $ 900 $ 1,350 $ (300) $ 385 $ 1,865 $ 3,300 9- 14 Problem 9-14 Income Statement Expected Equity Cash Flows $ Sales Revenue Cost of Goods Sold Gross Profit Operating Expenses Operating Profit Interest Expense Net Taxable Income Income Tax Net Income $ 85,000 $ 32,000 $ 53,000 $ 32,000 $ 21,000 $ 7,500 $ 13,500 $ 4,725 $ 8,775 Cost of Equity Value of Equity 12.500% $ 70,200 Debt Cash Flows $ Cost of Debt Value of Debt 6.500% $ 115,385 Total Value Cost of Assets Asset Beta $ 185,585 8.770% 0.628 Total Capital Cash Flow $ Value of Cash Flows WACC Hypothetical Tax - All Equity $ 185,585 7.355% $ 7,350 Hypothetical Cash Flow - All Equity $ Value of Hypothetical Cash Flows $ 185,585 Additional Assumptions Risk- free rate Market risk premium Equity beta Debt beta Tax rate 5% 6% 1.25 0.25 35% 8,775 7,500 16,275 13,650 9- 15 Problem 9-15 Holding Period Returns Analysis a,b,c Investments Success Value Failure Value a b c $ 2.500 $ 2.000 $ 2.235 $ 15.000 $ 15.000 $ 15.000 $ - $ - $ - Success Holding Period Return Failure Holding Period Return 500.0% - 100.0% 650.0% - 100.0% 571.2% - 100.0% Probablity of Success Probability of Failure 25.0% 75.0% 25.0% 75.0% 25.0% 75.0% Expected Holding Period Return 50.0% 87.5% 67.8% Variance of Holding Period Returns 675.0% 1054.7% 844.8% Standard Deviation of Holding Period Returns RADR Model 259.8% 324.8% 290.6% Expected Harvest Cash Flow $ 3.75 Variance of Harvest Cash Flows $ 42.19 Standard Deviation of Harvest Cash Flows c $ 6.50 Risk- free Rate Market Risk Premium Standard Deviation of Market Returns Correlation of Venture with Market Present Value 18% 30% 35% 0.20 $ CAPM Rate Required Rate Difference d CEQ Model Present Value 2.235 67.8% 67.8% 0.0% $ 2.234 9- x Problem 9-x Return Return CML SML 12 11 8 5 0 20 30 Std Dev 0 0.5 1.0 1.17 The risk- free asset plots at a return of 5% and risk of 0 in both figures. The market portfolio plots at a return of 11% with standard deviation of 20% and beta of 1.0. The asset with 12% expected return and 30% total risk has beta risk of 1.167 based on a risk premium 1.167 times that of the market. Its correlation woth the market is 0.78, computed using Equation 9.7. The asset with 8% expected return but 30% standard deviation must have lower market risk. The 8% return implies beta risk of 0.5 and a correltion with the market of 0.33. Beta ...
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