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Unformatted text preview: Spring 1996
Problem 1 Price/BV for AlumCare =
4
P/BV ratio for HealthSoft = 2
If AlumCare's Price is thrice that of HealthSoft,
Let MV of Equity for AlumCare = $100.00 Then MV of Equity for HealthSoft = $33.33 BV of Equity for AlumCare = $25.00 BV of Equity for HealthSoft = $16.67 P/BV of Equity after merger = (100+33.33)/(25+16.67) = 3.20 Problem 2 Expected Growth = Net Margin * Sales/BV of Equity * Retention Ratio
.06 = Net Margin * 3* .40
Net Margin =
0.05
Price/Sales Ratio = .05 * (1.06)* .6/(.12 .06) = 0.53 Problem 3
Unlevered Beta (using last 5 years) = 0.9/(1+(1.4)(.2)) =
Unlevered Beta of Noncash assets = 0.80/(1.15) = 0.80
0.94 Levered Beta for Noncash assets = 0.94 (1+0.6(.5)) =
Cost of Equity for Noncash Assets = 6% + 1.22(5.5%) =
Cost of Capital for Noncash Assets = 12.71%(.667)+.07*.6*(.333)= 1.222
12.71%
9.88% Estimated FCFF next year from noncash assets = (45050)(1.4)(1.05)90 =
Estimated Value of Noncash Assets = 162/(.0988.05) =
Cash Balance
Estimated Value of the Firm = Value of Debt Outstanding =
Value of Equity $162 $3,320 500 $3,820 800 $3,020 Fall 1996 Problem 1
Aftertax Operating Margin =
0.18
WACC = 13.55% (.6) + 6% (.4) =
Value/Sales Ratio = .18 (1.05) / (.1053.05) = 0.11 3.42 Value/Sales Ratio of Generic Brand = 3.42 * 0.5 =
Value of Brand Name = 342 171 = 171 million 1.71 Part II
a. True; if firms have different risk levels, they will have different PE/g ratios. (Some of you also pointed out that the growth periods have to be the same. That is true too.
b. Firm B will have the higher Value/EBITDA multiple. Everything else about the two firms is identical.
c. Price/BV ratio will drop by more than half.
d. P/BV = 2.5 Value of Equity will drop by 30% after special dividend. Value of Book Value will drop by same dollar amount. Net Effect = (2.5 * .7) / (1 .75) = 7 Spring 1997
Problem 1 Expected PE/g ratio for GenieSoft = 2.75 0.50 (2) =
Expected PE/g ratio for AutoPred = 2.75 0.50 (1) =
Actual PE/g ratio for GenieSoft = 50/40 =
Actual PE/g ratio for AutoPred = 20/10 =
Both GenieSoft and AutoPred are undervalued relative to the market. Problem 2 EBITDA
Depreciation
EBIT
EBIT (1t) EBITDA
EBIT
EBIT (1t) Reinvestment
FCFF 1.75
2.25
1.25
2.00 $550 $150 $400 $240 Next Year $578 $420 $252 $84 $168 Firm Value $4,200 Value/FCFF
Value/EBIT
Value/EBITDA 25.00
10.00
7.27 Problem 3 I would use a higher Value/EBITDA multiple because the comparable firms have a lower return on capital. Spring 1998 Problem 1
Current PBV = (ROE g) / (COE g) 1.5 = (ROE 5%)/(12%5%): Solving for ROE = 15.5%
If you add 3% to ROE, ( I also gave full credit if you used 15.5% (1.03))
PBV = (.185.05)/(.12.05) = 1.93
1.9286
This assumes that the growth stays the same, but payout ratio goes up
If you had assumed that the payout ratio would remain the same, but growth would change:
Current Payout Ratio = 5/15.5 =
32.26%
New Growth Rate = 0.32 * 18.5% =
5.92%
New PBV = (.185.0592)/(.12.0592) =
2.07
Problem 2
Predicted V/S Ratio for Estee Lauder = 0.45 + 8.5 (.16) =
Predicted V/S Ratio for Generic Company = 0.45 + 8.5 (.05) =
Difference in V/S Ratios =
Value of Estee Lauder Brand Name = 0.935 (500) = 1.81
0.875
0.935 $467.50 Problem 3
Value of Straight Debt portion of Convertible = 12.5 (PVA, 10%, 10 years) =
Value of Conversion Option = 275 173.2
Value of the Firm =
Value of Straight Debt =
Value of Equity =
Value of Conversion Option =
Value of Warrants =
Value of Equity in Stock
Value per Share = $173.19 $101.81 $1,000.00 $273.19 $726.81 $101.81 $100.00 $525.00 $26.25 Fall 1998 Problem 1
Value of Equity in Common Stock = 50 * $ 20 =
Value of Equity in Management Options = 10 * $ 15 = Value of Conversion Option = 140 100 =
Value of Equity =
Value of Equity =
Value of Debt =
Value of Firm = Value of Cash =
Value of noncash assets = $1,000.00 $150.00 $40.00 $1,190.00 $1,190.00 $150.00 $1,340.00 $250.00 $1,090.00 Problem 2
a. Firms with high risk and/or low quality projects (ROE) will have low PEG ratios
I would therefore Delphi Systems for my undervalued stock. It has a low PEG ratio, low risk and a high ROE
b. Firms with low risk and high quality projects will have high PEG ratios
I would therefore pick Connectix as my overvalued stock, since it has a high PEG ratio, high risk and a low ROE.
Problem 3
a. Value/FCFF = (1+g)/(WACC g) = 1.05/(.10.05) =
21 ! Answer is 20 if you look at Value/FCFF1
(If you assume that the multiple is Value/Current FCFF, this will become (1+g)/(WACC g) which would yield 21.
b. If the ROC is 12.5%, the reinvestment rate = g/ROC = .05/.125 = 0.40 FCFF = EBIT (1tax rate) ( 1 Reinvestment Rate) = EBIT (1.4)(1.3)
Value /EBIT = 21 (1.4) (1.3) = 8.82
! Answer is 8.40 if you look at Value/EBIT1 Spring 1999 Problem 1
FCFF on noncash assets = $ 200 million (1.4) ( 1 4/10) =
Unlevered Beta for noncash assets = 1.20/.9 =
Levered Beta for noncash assets = 1.33 (1 + 0.6(15/85)) =
Cost of Equity for noncash assets = 6% + 1.47 (5.5%) =
Cost of capital for noncash assets = 14.09% (.85) + 10% (1.4) (.15) =
Value of noncash assets = 72 (1.04)/(.1288 .04) =
Value of cash =
Value of firm =
Problem 2
PE = Payout ratio (1+g)/(r g) Payout ratio = PE (r g)/(1+g)
r = Cost of Equity = 6% + 0.9*5.5% =
g = 5%
PE = 10.59
Payout ratio = 10.59(.1095 .05)/(1.05) =
g = (1Payout ratio) (ROE)
.05 = (1 .6) ROE
ROE = 12.5% 72 ! Reinvestment rate = g/ ROC = 4/10
1.33333333 ! Reflects the fact that the average firm has 10% debt
1.47082353
14.09%
12.88% $843.24 250 $1,093.24 10.95%
0.60 Problem 3
Firm Value = 5000 + 1500 + 1000 =
Firm Value net of cash = 7500 1750 =
Taxable Income = 250/(1.4) =
Taxable Income before interest income = EBIT = 291.67 + 100 + 80 =
EBITDA Noncash Value/EBITDA = 5750/722 =
Alternatively,
Firm Value = 5000 + 1500 + 1000 =
EBITDA + Interest Income = Value/EBITDA = 7500/847 = 7500
5750
416.666667 ! Net income includes interest income
291.666667
471.67
721.67
7.96 ! If numerator is noncash, denominator cannot include interest income
7500
846.67
8.85478158 Spring 2000 Problem 1
EBIT at Reliable without auto parts subsidiary = 500 200 =
EBIT at Chemical products subsidiary =
EBIT at Auto Parts Subsidiary = 300
250
200 Tax rate =
40%
Reinvestment Rate = (Growth/ROC) = 6%/12% =
Cost of Capital = 50%
10% Value of Reliable (standalone) = 300 (1.4) (1.5)(1.06)/(.10.06) =
Value of Chemical subsidiary = 250 (1.4)(1.5)(1.06)/(.10.06) =
Value of Auto Parts subsidiary = 200 (1.4)(1.5)(1.06)/(.10.06) = $2,385 ! Alternatively, we could have valued Reliable on a $1,988 consolidated basis and subtracted the 50% ofthe auto $1,590 parts subsidiary. Value of Reliable (with subsidiaries) = 2385 + 0.1 (1988) + 0.5 (1590) =
Value per share = $3,379 $33.79 Problem 2
a. will become more sensitive to changes in expected growth rates. (The value of growth is a present value effect)
b. Firm A will have the higher PEG ratio, because it has the lower expected growth rate.
c. Low tax rate, high return on capital, low reinvestment rate: Best possible combination
d. The price to book value ratio will drop. The simplest way to do this is to use the following equation:
PBV = (ROE growth rate)/(Cost of equity growth rate)
Inciientally, this is true only if the price to book value ratio is greater than 1, which it is in this case.
e. Enterprise Value = (Market Value of Equity + Market Value of Debt Cash and Marketable Securities)/(EBIT + DA)
= (150 *10 + 1000500)/(250+100) =
5.71 Spring 2002 Problem 1
a.
Revenues
EBIT
EBIT (1t) + Depreciation Cap Ex Chg in WC
FCFF
Reinvestment
b.
Reinvestment Rate
Expected growth rate
Return on Capital =
c.
Reinvestment rate
Value = 1050
210
168
105
160
13 Only the change in working capital matters
100
68 ! I was pretty flexible on how this was computed….
40.48%
5%
12.35%
0.5 ! As ROC changes, the reinvestment rate will change. You
1680 cannot use cashflows from part a. Problem 2
MV of Equity = + Equity Options
Value of Equity + Debt Cash
Value of operating assets 2000
100
2100
1000
500
2600 Problem 3
a.
PE Ratio for the firm =
Expected growth rate =
b.
PE Ratio =
PEG ratio = 32
17.30
42.45 ! 12.13 + 1.56 (24) 3.56 (2)
1.76875 ! 42.45/24 Fall 2002
Problem 1 Return on capital on existing assets =
10%
Reinvestment rate =
0.7
a. Expected growth over next 5 years = ROC on new investments * Reinvestment rate + Growth from improved efficiency = (15%)(.70) +(1+ (.15.10)/.10)^(1/5)1
18.95%
b. Portion due to improved efficiency
New Investment growth = 15% *.7 =
10.50%
Growth due to improved efficiency = .1895.105 =
8.45% Problem 2 a. Reinvestment rate in perpetuity = g/ rOC = 4/12 =
Terminal value = 250 (1.333)/(.09 .04) =
b. If no excess returns, return on capital = 9%
Reinvestment rate in stable growth = 4/9 =
Terminal value = 250 (1.4444)/(.09.04) =
Value due to excess returns = 33.33% ! Don't forget this
! This income is already in year 6. You don't need (1+g) $3,333.33 44.44%
$2,777.78
$555.56 ! 33332778 ! There are other ways you could solve this problem
a. You could make the cost of capital 12%
b. You could estimate the present value of the excess returns. Problem 3 Current PE ratio =
8
Payout ratio =
60%
PE = Payout ratio/ (Cost of equity g)
8 = .60/(Cost of equity g)
! You don't need a (1+g) since you have expected income next year
Cost of equity g =
7.50%
If the riskfree rate rises by 1% and expected growth is unchanged, r g = 8.5%
PE = .60/(.085) =
7.06 Spring 2003
Problem 1 1
650
5%
32.5
0
32.5
$60.00
$92.50 4 Terminal year
1428.05 1470.8915
10%
10%
142.805 147.08915
29.122
58.83566 ! Remember to adjust your tax rate to 40% in year 5; NOLs are gone….
113.683
88.25349
$131.82 26.476047 ! Reinvestment in stable growth = g/ROC =3%/10% = 30%
$18.14 61.777443
$686.42
! Use the new cost of capital to compute the terminal value
$80.43
$58.98
$30.56
$382.09
! Use a 15% discount rate to discount the cashflows and the terminal value
$212.12 ! Discount back the cashflows at 15%…. Revenues
Op Margin
EBIT
Taxes
EBIT(1t) Reinvestment
FCFF
Terminal value
PV
Value of equity= 2
845
0%
0
0
0
$78.00
$78.00 3
1098.5
5%
54.925
0
54.925
$101.40
$46.48 Value per share = $15.81 ! (2066.63+25)/(10+5)
Add the exercise proceeds to the numerator and divide by fully diluted number of shares
Since the value of equity cannot be less than zero, the stock is worth nothing… Problem 2 a. EV/EBITDA for parent company alone
Market value of equity = + Debt Cash
Enterprise value before adj= 5% of Equity of Abigail = 60% of Nuveen equity = 100% of Nuveen debt =
Enterprise value after adj = 2000
1200
300
2900
250 ! Subtract out the 5% of market value of equity in Abigail
792 ! Minority interest = 240; Book value of equity = 600; Market value of equity = 2.2*600 = 1320
300 ! Debt is consolidated; Hence you need to subtract out 100% of Nuveen's debt
1558 EBITDA for Hollywood Holdings = 100% of EBITDA of Nuveen =
EBITDA of parent company = 800
400 ! The EBITDA of Abigail does not show up in the parent company but 100% of Nuveen's EBITDA does
400 EV/EBITDA = 3.895 Fall 2003
Problem 1 Revenues
EBIT (1t) Net Cap ex
FCFF
Terminal value
Value today Most Recent
$100.00
$5.00 1
$120.00
$12.00
$6.00
$6.00
$138.67 $131.52 Problem 2 Value of operating assets = + Cash & Mkt securities + Minority passive holdings Minority interests Debt
Value of Equity Value of options
Value of equity in stock
Value per share = 2
$124.80
$12.48
$4.16
$8.32 You have to estimate the cashflows for next year first and then compute the
terminal value based upon estimated cashflow in year 2. 1000
150
The operating income does not include income from cash holdings. So, you have to add it on. The interest rate is a decoy and does not play a role in the valuation.
200
The income from minority passive investments is also not shown in operating income. (it shows up below the operating income line). Add estimated market value = 80 *2.5
240
The minority interests represent 40% of the Ajax Leasing that you do not own. Since you counted a 100% in your operating income, you have to subtract estimated market value: 120* 2
400
Debt has to be netted out. Since you are doing a consolidted valuation, it does not matter even if some of this debt belongs to Ajax Leasing
710
60
Subtract out the value of the equity options to get to value of common stock.
650
32.5 ! Divide by actual number of shares outstanding Problem 3 a. PE ratio for Vortex = PEG ratio for Vortex = PEG ratio for sector = Vortex undervaluation = 12
1.2
1.25
4.17% ! (.05/1.20) b. Vortex may be riskier than the sector. (None of the other explanations are consistent with a lower PEG ratio)
c. ROE =
12%
Payout ratio first 5 years =.16666667 ! Payout ratio = 1 g/ROE 0
Payout ratio perpetuity =
75.00%
Fundamental PE =
14.3330844
Fundamental PEG ratio = 1.43330844 This is the key step. You have to compute the payout ratio first before you can use the equation. I was very, very easygoing about
your algebra. ! I used the 2stage model for the PE ratio. You cannot use the stable growth model, since you have high growth.
! Divide by the 10% growth rate. Spring 2004
Problem 1 Total equity value estimated by analyst = + Value of minority interest =
Total firm value estimated by analyst = 140
20
160 Analyst asssumed stable growth rate of 3%, cost of capital of 10% and return on capital of 10%
Reinvestment rate assumed by analyst =
0.3 ! G/ROC
Firm value = 160 = FCFF / (.10 .03) FCFF =
11.2
Aftertax operating income =
16 ! FCFF/ (1 Reinvestment Rate)
Aftertax operating income at Nova =
Reinvestment rate for Nova =
Value of Nova =
Value of 50% stake in Nova = 4 ! 25% of firm's consolidated operating income
0.25 ! Growth rate/ Nova's return on capital
60 ! After tax operating income (1 Reinvestment Rate)/ (Cost of capital g)
30 Springfleld's operating income =
Springfield's value = + Value of 50% stake in Nova =
Correct value of equity in Springfield =
Corect value of equity per share = 12 ! 75% of firm's consolidated operating income
120 ! Use Springfield's cost of capital and reinvestment rate: 12 (1.3)/(.10.03)
30 ! Half of 60 from above
150
15 Problem 2
a. There were two inconsistent multiples and you got full credit for picking either. The first was enterprise value/ net income from continuing operations. The word operations here is misleading; what matters is that net income is to equity investors The second was market value of equity/ cable subscribers ! Subscribers generate revenue for the firm and not just for equity investors
b. Low EV/EBITDA, Low Tax Rate, High ROC
c. Bank A will be able to pay out more of its earnings as dividends since it has a higher ROE. It should have the higher PE.
d. Stocks with very low growth rates will tend to have very high PEG ratios Problem 3 ROE =
Cost of equity =
Price to Book Ratio = 20%
12%
2 You could also value this company as a dividend discount model
Value of equity = 100 ! Value of stock = 10 *(1.04/.2)/(.12.04)
Price to book ratio =
2 ! 100/50 Spring 2005 Problem 1
Current Reinvestment Rate = 50.00% ! (250 100 + 50)/400
Current return on capital
8.00% ! 400/5000
Expected growth rate =
30%
(ROC 8%)/8% + ROC * .50 = 30%
Solve for ROC, ROC = 10% Problem 2 1
2
3
Net Income
150
165
181.5
FCFE
50
55
60.5
Expected Growth rate in net income =
10.00%
Equity Reinvestment Rate = 66.67% ! 1 FCFE/ Net Income
Return on equity = g/ Reinvestment rate =
15.00%
Growth rate in stable growth = 3%
Equity reinvestment rate in stable growth =
20.00% ! G/ ROE
FCFE in year 4 = 149.556 ! 181.5 (1.03) (1.20)
Terminal value of equity =
2991.12 Problem 3 Market value of equity =
500 ! Since you are given the market value of common + Equity options
100 equity, you have to reverse the process (and the signs) Cash
150 to get to value of operating assets. + Debt
300
Market's assessment of value of operating assets =
750 Problem 4 Value of equity in VRW =
880 ! Value of operating assets + Cash Debt
Value of equity in Centaur Steel = 620
Value of 60% stake =
372
Total value of equity in VRW = 1252 Fall 2007
Problem 1 1
$1,000
5.00%
$50.00
0%
1
$50.00
$50.00
0
$50.00 EBIT
EBIT (1t)
Reinvestment
FCFF
Terminal value
PV
Nol
Value of firm = + Cash Debt
Value of equity
Value per share = 2
$1,030
1.00%
$10.30
0%
2
$10.30
$10.30
0
$10.30 $44.64
$50.00 Revenues
Operating Margin
EBIT
Tax rate $8.21
$39.70
$230.86
$25.00
$100.00
$155.86
$15.59 Reinvestment Rate = g/ ROC = 3/10 = 3
$1,061
5.00%
$53.05
40%
3
$53.05
$47.71
0
$47.71
$327.82
$267.29
$0.00 Grading scale Part a
a. Did not use year 4 numbers: 0.5
b. Did not compute reinvestment rate: 1
c. Wrong cost of capital: 0.5
4 d. Mechanical errors: 0.5
$54.64
$32.78
9.834543 ! Reinvestment rate = g/ ROC = 3/10 = 30%
$22.95
Terminal value cost of capital = 10%
! Dicount back all cashflows at 12%
Grading scale: Part b
a. Used wrong cost of capital: 0.5
b. Cash incorrectely treated: 0.5
c. Debt incorrectly treated: 0.5
d. Mechanical errors: 0.5 30.00% c. Price of bond =
600
Setting up the problem
600 = 1000 (1 probability of distress)/ 1.05^3
Probability of distress =
30.54%
Value of equity per share = a. Probability of default not computed: 1
b. Mechanical errors: 0.5
c. Value of equity per share not computed: 0.5
$10.83 ! 15.59*(1.3054) Problem 2
a. Value of Zookin's operating assets =
1250
All or nothing
b. Value of equity = 1250 + 250 + 250 =
1750
All of nothing
c. Treasury stock approach = (1750 + 10*5)/ (50+10) =
$30.00 Mechancal error: 0.5
d. Overstate the value per share. In the treasury stock appraoch, we value options at exercise value. They are worth more. Spring 2008 Problem 1
Return on capital =
Expected growth rate =
Cost of capital = 6.00%
3%
10% Reinvestment rate = ! Failed to estimate reinvestment; 1 point 50.00% FCFF next year =
$9.27 ! I gave full credit even if you missed the (1+g)
Value of operating assets = $132.43
! Minority interest miscalculated: 1 point + Cash
$25.00
! Other errors: 0.5 point Debt
$50.00 Minority interests
$40.00 ! Replace book value of minority interest with estimated market value
Value of equity =
$67.43
Prob lem 2 Net Income
 Reinvestment
= FCFE
Cost of equity 1
10
10
20
20% a. Terminal value
Return on equity =
Expected growth rate
=
Reinvestment rate =
Net income in year 4
=
Reinvestment in year
4=
FCFE in year 4 =
Terminal value of
e quity = 2
5
5
10
16% 3
10
5
5
12% 12% ! Reinvestmeent rate not computed: 1 pt 4%
33.33%
$10.40
$3.47
$6.93
$86.67 ! The reinvestment rate has to be reestimated with ROE = Cost of equtiy b. Value of equity
today 1
$20.00 Compounded cost of
e quity
Present value 2
$10.00 3
$5.00
$86.67 1.2
$16.67 FCFE Terminal value 1.392
$7.18 1.55904
$58.80 Value of equity today
= ! No compounded cost of equity: 1 point
! Use compounded cost of equity since r changes $34.95
$4.00 ! Exercise price * 2
12.00 ! Includes options but not expected future share issues
$3.25 Exercise proceeds = Number of shares =
Value per share = ! Double counted shares: 1 point
! Did not compute exercise value: 1 point Fall 2008
Problem 1 Year
Expected growth
EBIT (1t) + Depreciation Cap Ex Change in WC
FCFF Current
$300.00
$50.00
$175.00
$75.00
$100.00 a. Reinvestment rate =
66.67% Growth rate =
8.00% Return on capital =
12.00%
b. Reinvestment rate =
33.33%
FCFF in year 4 =
$262.02
Terminal value
$4,367.00
c. & d.
FCFF
Cost of capital
Cumulated WACC
Present value
Value of firm
$3,475.74 + Cash
400 Debt
1000 Minority interest
500
Value of equity
$2,375.74
Value of options
200
Value of equity in common stock
$2,175.74
Value per shaer
$27.20 1
8%
$324.00
$54.00
$189.00
$81.00
$108.00 2
8%
$349.92
$58.32
$204.12
$87.48
$116.64 3
8%
$377.91
$62.99
$220.45
$94.48
$125.97 ! (Net Cap Ex + Change in WC)/ EBIT (1t) ! g/ ROC
! 377.91 (1.04) (1.33)
! 262.02/(.10.04)
$108.00
12%
1.12
$96.43 ! 250 * 2 $116.64
11%
1.2432
$93.82 ! Cashflows grow 4% a year forever after year 5, but if the return on capital stays at 12%,
the reinvstment rate has to be reestimated.
! Used cash flow in year 3 to growt at 4%: 1 point
! Did not use 10% as discount rate: 0.5 point
$4,492.97
10%
! Discounted at yearspecific cost of capital: 0.5 point
1.36752 ! Discount at cumulated WACC
! Mistake on minority interest: 0.5 to 1 point
$3,285.49
! Other errors: 0.5 point I also gave full credit if you used the treasury stock approach.
Add exercise value of $ 400 million (20*20 to numerator) and divide by 100 million shares e. False. (The cash wll be discounted only if investstor expect the firm to waste the cash. This firm has a return on captial > Cost of captial. I would expect investors to trust the
management of this firm.
f.
EBIT (1t) of diversted stores =
Cost of capital =
Value of stores =
Divestiture proceeds =
Net effect on value =
Effect on value/share = $30.00
10%
$300.00
250
$50.00
$0.63 ! Used weird combinatiions of treasury stock and option approaches: 0.5 to 1 point ! ALL OR NOTHING ! With no growth, we can assume EBIT (1t) = FCFF ! Estimated a reinvstment even though growth was zero: 0.5 top 1 point
! Did not net out proceeds: 0.5 point ! Sold for less than these stores are worth
! Value per share will decrease Fall 2009
Problem 1 1
$100.00
$0.00
$100.00
$100.00
$200.00
1.1500
$173.91
$150.00 Capital invested 1.2880
$38.82
$50.00 3 Terminal year
$150.00
154.5 ! Ignored NOL: 1 point
$40.00
61.8 ! Failed to accumulate losses: 0.5 points
$110.00
92.7 ! Did not compute FCFF: 1 point
$50.00
23.175
$60.00
69.525
$993.21
1.4168
! Did not cumulate discount rates: 1 point
$743.38
$0.00 $572.50 EBIT
Taxes
EBIT (1t)
Reinvestment
FCFF
Terminal value
Cumulated Cost of capital
PV
NOL 2
$100.00
$0.00
$100.00
$150.00
$50.00 $722.50 $772.50 Return on capital in terminal year =
Reinvestment in terminal year = 12.00%
25.00% Value of operating assets = + Cash + Value of cross holding Expected lawsuit liability
Value of equity $530.64
$80.00
$100.00 40*2.5
$25.00 ! .25*100
$685.64 Value of equity = + Exercise proceeds
/ Number of diluted shares
Value per share today = $685.64
$60.00
110
$6.78 Fall 2010 Year 1
Revenues
$150
EBIT (1t)
$15 + Depreciation
$15 Cap EX
$5
FCFF
$5
Cost of capital
14%
a. PV of cash flows for first 3 years =
Cumulated Cost of capital
1.1400
Cash Flow
$5
Present Value
$4.39
Total
$10.57
b. Return on capital invested
EBIT (1t)
Capital invested: end of year
ROC
c. Terminal value
Return on capital =
Expected growth rate =
Reinvestment Rate =
Terminal Value $15
$180
8.33% Year 2
$160
$15
$20
$25
$10
12% ! Did not compute ROC in year 3: 1 point
! Errors on reinvestment rate: 1 point
! Errors on terminal value computation: 0.5 to 1 point ! Did not add cash: 1 point
! Did not compute minority holding value: 1 point
! Did not subtract out lawsuit liability: 1 point
! Any mistake: 1 point Year 3
$180
$25
$25
$40
$10
10% Grading notes 1.2768
$10
$7.83 1.4045 ! Discount at the cumulated cost of capital
! Did not cumulate: 1 point
$10 ! In year 3: 1.14*1.12*1.1
Math errors: 0.5 point each
$7.12 $15
$185
8.11% $25 ! Capital invested in year n+1 =
! All or nothing…. Sorry
$200 Capital invested in year n + (Cap ex Depreciation)
12.50% g/ROC will not work, since ROC is changing 12.50%
3%
20.0%
273.333333 ! 25*1.025* (10.2)/(.10.025) ! Did not compute reinvestment rate: 1 point
! Math errors: 0.5 point each c. PV of terminal value = 194.615326 ! Discount back at cumulated cost
! Used book value of debt: 0.5 point
Sum of FCFF next 3 years
$10.57
! Did not discount terminal value: 0.5 point
Value of opeating assets =
$205.18 + Cash 25 Debt
75 ! Cannot use book value ina DCF valuation
Value of equity =
$155.18
Value per share= $7.76 Problem 2 FCFE value of equity
FCFE =
120 ! Already next year's number
Cost of equity =
10%
Value of equity =
2000 120/(.10.04)
Market value of equity
1500 ! Share price * No of shares
Market value of equity =FCFE value (1 Prob of Natl) + 0 (Prob of Natl)
Probability of nationalization
25% Problem 3 Expected return =
Fund's expected return = 12.000% ! Riskfree rate + beta (Risk premium)
10% ! Did not compute FCFE value = 1 point
! Did not set up probability of nationalization: 1 point
! Other math errors: 0.5 point each ! All or nothing Value of $ 1 investment = 0.83333333 ! .10/.12
Discount on fund =
16.67% Problem 4 Value of operating assets = + Cash Debt MV of minority interests
Value of Equity = 1500
200
300
240
1160 ! Used book value of miniority interest: 1 point
! Addedminority interest: 1 point
! Added debt or netted out cash: 0.5 each Fall 2011 a. Expected EBIT (1t) =
Capital invested = 60
1000 Return on capital =
Cost of capital = 10% ! Did not compute reinvestment: 1 point
! Other errors: 0.5 point each 6% Expected growth rate =
2%
Expected Reinvestment rate = 33.33%
Value of operating assets = 500 b. To value cash,
Assuming that the cash does not get wasted
Probability of happening =
40%
! Did not value cash right under "not wasting" scenario: 0.5 point
Value of cash =
100
! Did not value cash right under "wasting" scenario: 0.5 to 1 point
Assuming that cash gets wasted on projects making 6% (cost of capital of 10%
! Did not apply probabilities: 0.5 point
Probablity of happening =
60%
Value of cash =
60
Expected value of cash =
76 Problem 2 Value of operating assets =
1200 Estimated value of minority interest ! 25% of Value of subsidiary = 40/(.10.02) = 500
125 + Cash 100 Debt 300
Value of equity 875 Value of equity options 100 ! Value of options =20 *5
Value of equity in common stock 775
Value per share =
7.75 ! Divide by 100 million shares Problem 3 Value of Drake Drugs operating assets =
1000
Expected growth rate =
2%
Cost of capital =
10%
Imputed FCFF next year =
80 ! 1000 = FCFF next year/ (Cost of capital g)
Imputed Reinvestment Rate= 10.0% ! Growth rate/ ROC ! Error on valuing minority interests: 0.5 to 1 point
! Added option value to value instead of subtracting: 0.5 point
! Adjusted number of shares for options: 0.5 point
! Other errors: 0.5 point each
You cannot use the treasury stock approach since you do not have the exercise price of the options.
All you have is the value per option. ! Did not reestimate the growth rate: 1 point (If you use 2% growth and a 20% reinvesment rate, you are being internally inconsistent)
! Left EBIT (1t) at preadjustment level: 0.5 to 1 point
! Other errors: 0.5 point each When you capitalize R&D, neither FCFF nor cost of capital should change
Some of you did try to back out the EBIT (1t) from the FCFF
FCFF =
80
PreR&D
Cost of capital =
10%
EBIT (1t) = 88.8888889 ! 80.9
The R&D does affect the reinvestment rate and ROC
Reinvestment 8.88888889
Reinvestment rate =
20.00%
FCFF
80
Return on capital =
12.50%
Post R&D adjustment
Expected growth rate =
2.50%
EBIT (1t) 88.89 + Current year's R&D R&D amortization
Reinvestmetn 8.89 + Current year's R&D R&D amortization
Corrected value of operating assets=
1066.66667
FCFF
80
Value increases by $66.67 million ...
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 Fall '11
 BANKO

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