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 97 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 98 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 99 Year
Problem 97 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 98 $0 $100,308 9 10 Problem 910 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 911
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 912
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 913
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 914 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 915
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 9x 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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 Spring '05
 jackson
 Finance, Corporate Finance, Financial Markets, Net Present Value, Internal rate of return, Mathematical finance

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