# 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 Equit

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```					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)) =                                0.80
Unlevered Beta of Non-cash assets = 0.80/(1-.15) =                                        0.94

Levered Beta for Non-cash assets = 0.94 (1+0.6(.5)) =                                 1.222
Cost of Equity for Non-cash Assets = 6% + 1.22(5.5%) =                              12.71%
Cost of Capital for Non-cash Assets = 12.71%(.667)+.07*.6*(.333)=                    9.88%

Estimated FCFF next year from non-cash assets = (450-50)(1-.4)(1.05)-90 =                        \$     162
Estimated Value of Non-cash Assets = 162/(.0988-.05) =                                           \$   3,320
Cash Balance                                                                                            500
Estimated Value of the Firm =                                                                    \$   3,820
- Value of Debt Outstanding =                                                                           800
Value of Equity                                                                                  \$   3,020

Fall 1996
Problem 1
After-tax Operating Margin =                        0.18
WACC = 13.55% (.6) + 6% (.4) =                                     0.11
Value/Sales Ratio = .18 (1.05) / (.1053-.05) =                              3.42

Value/Sales Ratio of Generic Brand = 3.42 * 0.5 =                           1.71
Value of Brand Name = 342 - 171 = 171 million

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) =                          1.75
Expected PE/g ratio for AutoPred = 2.75 - 0.50 (1) =                           2.25
Actual PE/g ratio for GenieSoft = 50/40 =                                      1.25
Actual PE/g ratio for AutoPred = 20/10 =                                       2.00
Both GenieSoft and AutoPred are undervalued relative to the market.

Problem 2
EBITDA                       \$       550
Depreciation                 \$       150
EBIT                         \$       400
EBIT (1-t)                   \$       240
Next Year
EBITDA                       \$       578
EBIT                         \$       420
EBIT (1-t)                   \$       252
- Reinvestment               \$        84
FCFF                         \$       168

Firm Value                   \$     4,200

Value/FCFF                          25.00
Value/EBIT                          10.00
Value/EBITDA                         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) =                        1.81
Predicted V/S Ratio for Generic Company = 0.45 + 8.5 (.05) =                    0.875
Difference in V/S Ratios =                                                      0.935
Value of Estee Lauder Brand Name = 0.935 (500) =                      \$       467.50

Problem 3
Value of Straight Debt portion of Convertible = 12.5 (PVA, 10%, 10 years) =             \$   173.19
Value of Conversion Option = 275 - 173.2                                                \$   101.81

Value of the Firm =                      \$ 1,000.00
Value of Straight Debt =                 \$   273.19
Value of Equity =                        \$   726.81
Value of Conversion Option =             \$   101.81
Value of Warrants =                      \$   100.00
Value of Equity in Stock                 \$   525.00
Value per Share =                        \$    26.25

Fall 1998
Problem 1
Value of Equity in Common Stock = 50 * \$ 20 =                         \$ 1,000.00
Value of Equity in Management Options = 10 * \$ 15 =                   \$   150.00
Value of Conversion Option = 140 - 100 =                              \$    40.00
Value of Equity =                                                     \$ 1,190.00
Value of Equity =                            \$ 1,190.00
Value of Debt =                              \$   150.00
Value of Firm =                              \$ 1,340.00
- Value of Cash =                            \$   250.00
Value of non-cash assets =                   \$ 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 (1-tax 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 non-cash assets = \$ 200 million (1-.4) ( 1 - 4/10) =                                    72 ! Reinvestment rate = g/ ROC = 4/10
Unlevered Beta for non-cash assets = 1.20/.9 =                                         1.33333333 ! Reflects the fact that the average firm has 10% debt
Levered Beta for non-cash assets = 1.33 (1 + 0.6(15/85)) =                             1.47082353
Cost of Equity for non-cash assets = 6% + 1.47 (5.5%) =                                    14.09%
Cost of capital for non-cash assets = 14.09% (.85) + 10% (1-.4) (.15) =                                  12.88%
Value of non-cash assets = 72 (1.04)/(.1288 - .04) =                                  \$    843.24
Value of cash =                                                                                250
Value of firm =                                                                       \$ 1,093.24

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% =                         10.95%
g = 5%
PE = 10.59
Payout ratio = 10.59(.1095 - .05)/(1.05) =                                     0.60
g = (1-Payout ratio) (ROE)
.05 = (1 - .6) ROE
ROE = 12.5%
Problem 3
Firm Value = 5000 + 1500 + 1000 =                                 7500
Firm Value net of cash = 7500 - 1750 =                            5750
Taxable Income = 250/(1-.4) =                              416.666667 ! Net income includes interest income
Taxable Income before interest income =                    291.666667
EBIT = 291.67 + 100 + 80 =                                      471.67
EBITDA                                                          721.67
Non-cash Value/EBITDA = 5750/722 =                                 7.96 ! If numerator is non-cash, denominator cannot include interest income
Alternatively,
Firm Value = 5000 + 1500 + 1000 =                                 7500
EBITDA + Interest Income =                                      846.67
Value/EBITDA = 7500/847 =                                  8.85478158

Spring 2000
Problem 1
EBIT at Reliable without auto parts subsidiary = 500 - 200 =                                   300
EBIT at Chemical products subsidiary =                                                         250
EBIT at Auto Parts Subsidiary =                                                                200

Tax rate =                      40%
Reinvestment Rate = (Growth/ROC) = 6%/12% =                                                   50%
Cost of Capital =                                                                             10%

Value of Reliable (stand-alone) = 300 (1-.4) (1-.5)(1.06)/(.10-.06) =                      \$2,385 ! Alternatively, we could have valued Reliable on a
Value of Chemical subsidiary = 250 (1-.4)(1-.5)(1.06)/(.10-.06) =                          \$1,988 consolidated basis and subtracted the 50% ofthe auto
Value of Auto Parts subsidiary = 200 (1-.4)(1-.5)(1.06)/(.10-.06) =                        \$1,590 parts subsidiary.

Value of Reliable (with subsidiaries) = 2385 + 0.1 (1988) + 0.5 (1590) =                                  \$3,379
Value per share =                                                                                         \$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 + 1000-500)/(250+100) =                         5.71
Spring 2002
Problem 1
a.
Revenues                    1050
EBIT                         210
EBIT (1-t)                   168
+ Depreciation              105
- Cap Ex                    160
- Chg in WC                  13 Only the change in working capital matters
FCFF                         100
Reinvestment                  68 ! I was pretty flexible on how this was computed….
b.
Reinvestment Rate      40.48%
Expected growth rate       5%
Return on Capital =    12.35%
c.
Reinvestment rate            0.5 ! As ROC changes, the reinvestment rate will change. You
Value =                     1680 cannot use cashflows from part a.

Problem 2
MV of Equity =              2000
+ Equity Options            100
Value of Equity             2100
+ Debt                     1000
- Cash                      500
Value of operating assets   2600

Problem 3
a.
PE Ratio for the firm =      32
Expected growth rate = 17.30
b.
PE Ratio =                42.45 ! 12.13 + 1.56 (24) - 3.56 (2)
PEG ratio =             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 =                                     33.33% ! Don't forget this
Terminal value = 250 (1-.333)/(.09 - .04) =                             \$3,333.33               ! This income is already in year 6. You don't need (1+g)
b. If no excess returns, return on capital = 9%
Reinvestment rate in stable growth = 4/9 =                                              44.44%                 ! There are other ways you could solve this problem
Terminal value = 250 (1-.4444)/(.09-.04) =                              \$2,777.78                              a. You could make the cost of capital 12%
Value due to excess returns =                                             \$555.56 ! 3333-2778                  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              2            3             4 Terminal year
Revenues                            650            845       1098.5       1428.05   1470.8915
Op Margin                          -5%             0%           5%           10%          10%
EBIT                              -32.5              0       54.925       142.805   147.08915
Taxes                                 0              0            0        29.122    58.83566 ! Remember to adjust your tax rate to 40% in year 5; NOLs are gone….
EBIT(1-t)                         -32.5              0       54.925       113.683    88.25349
- Reinvestment                  \$600.00        \$780.00    \$1,014.00     \$1,318.20   26.476047 ! Reinvestment in stable growth = g/ROC =3%/10% = 30%
FCFF                           -\$632.50       -\$780.00     -\$959.08    -\$1,204.52   61.777443
Terminal value                                                            \$686.42               ! Use the new cost of capital to compute the terminal value
PV                             -\$550.00      -\$589.79      -\$630.61      -\$296.23               ! Use a 15% discount rate to discount the cashflows and the terminal value
Value of equity=             -\$2,066.63 ! Discount back the cashflows at 15%….
Value per share =              -\$136.11 ! (-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 =                          2000
+ Debt                                            1200
- Cash                                             300
- 5% of Equity of Abigail =                        250 ! Subtract out the 5% of market value of equity in Abigail
- 60% of Nuveen equity =                           792 ! Minority interest = 240; Book value of equity = 600; Market value of equity = 2.2*600 = 1320
- 100% of Nuveen debt =                            300 ! Debt is consolidated; Hence you need to subtract out 100% of Nuveen's debt
Enterprise value after adj =                      1558

EBITDA for Hollywood Holdings =                    800
- 100% of EBITDA of Nuveen =                       400 ! The EBITDA of Abigail does not show up in the parent company but 100% of Nuveen's EBITDA does
EBITDA of parent company =                         400

EV/EBITDA =                                      3.895

If I had not screwed up on the sales to capital ratio (if I had used 2.5, as I meant to, instead o 0.25 as it showed up on the quiz, this is what the s
Modified Problem 1
1              2             3            4 Terminal year
Revenues                            650            845        1098.5      1428.05   1470.8915
Op Margin                          -5%             0%            5%          10%          10%
EBIT                              -32.5              0        54.925      142.805   147.08915
Taxes                                 0              0             0       29.122    58.83566 ! Remember to adjust your tax rate to 40% in year 5; NOLs are gone….
EBIT(1-t)                         -32.5              0        54.925      113.683    88.25349
- Reinvestment                   \$60.00         \$78.00       \$101.40      \$131.82   26.476047 ! Reinvestment in stable growth = g/ROC =3%/10% = 30%
FCFF                            -\$92.50        -\$78.00       -\$46.48      -\$18.14   61.777443
Terminal value                                                            \$686.42               ! Use the new cost of capital to compute the terminal value
PV                              -\$80.43       -\$58.98       -\$30.56       \$382.09               ! Use a 15% discount rate to discount the cashflows and the terminal value
Value of equity=                \$212.12 ! Discount back the cashflows at 15%….

Value per share =                \$15.81 ! (212.12+25)/(10+5)            Add the exercise proceeds to the numerator and divide by fully diluted number of shares

Fall 2003
Problem 1
Most Recent               1              2
Revenues                         \$100.00       \$120.00        \$124.80
EBIT (1-t)                         \$5.00        \$12.00         \$12.48                  You have to estimate the cashflows for next year first and then compute the
- Net Cap ex                                     \$6.00          \$4.16                  terminal value based upon estimated cashflow in year 2.
FCFF                                             \$6.00          \$8.32
Terminal value                                 \$138.67
Value today                      \$131.52

Problem 2
Value of operating assets =        1000
+ Cash & Mkt securities              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 do
+ Minority passive holdings          200                The income from minority passive investments is also not shown in operating income. (it shows up below the operating income lin
- Minority interests                 240                The minority interests represent 40% of the Ajax Leasing that you do not own. Since you counted a 100% in your operating incom
- Debt                               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 Aja
Value of Equity                      710
- Value of options                    60                Subtract out the value of the equity options to get to value of common stock.
Value of equity in stock             650
Value per share =                   32.5 ! Divide by actual number of shares outstanding

Problem 3
a. PE ratio for Vortex =              12
PEG ratio for Vortex =              1.2
PEG ratio for sector =              1.25
Vortex undervaluation =           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 = 0.16666667 ! Payout ratio = 1 - g/ROE                   This is the key step. You have to compute the payout ratio first before you can use the equation. I w
Payout ratio - perpetuity =        75.00%                                              your algebra.

Fundamental PE =              14.3330844                 ! I used the 2-stage model for the PE ratio. You cannot use the stable growth model, since you have high growth.
Fundamental PEG ratio =       1.43330844                 ! Divide by the 10% growth rate.

Spring 2004
Problem 1
Total equity value estimated by analyst =                                        140
+ Value of minority interest =                                                    20
Total firm value estimated by analyst =                                          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
After-tax operating income =          16 ! FCFF/ (1- Reinvestment Rate)

After-tax operating income at Nova =                                4 ! 25% of firm's consolidated operating income
Reinvestment rate for Nova =                                     0.25 ! Growth rate/ Nova's return on capital
Value of Nova =                                                    60 ! After tax operating income (1 - Reinvestment Rate)/ (Cost of capital - g)
Value of 50% stake in Nova =                                       30

Springfleld's operating income =                                   12 ! 75% of firm's consolidated operating income
Springfield's value =                                             120 ! Use Springfield's cost of capital and reinvestment rate: 12 (1-.3)/(.10-.03)
+ Value of 50% stake in Nova =                                     30 ! Half of 60 from above
Correct value of equity in Springfield =                          150
Corect value of equity per share =                                 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 =                                20%
Cost of equity =                     12%
Price to Book Ratio =                  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
10.00%
Expected Growth rate in net income =
Equity Reinvestment Rate =      66.67% ! 1- FCFE/ Net Income
15.00%
Return on equity = g/ Reinvestment rate =

Growth rate in stable growth =        3%
20.00% =
Equity reinvestment rate in stable growth ! 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
750
Market's assessment of value of operating assets =

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              2             3
Revenues                       \$1,000         \$1,030        \$1,061          Grading scale -Part a
Operating Margin              -5.00%          1.00%         5.00%           a. Did not use year 4 numbers: -0.5
EBIT                          -\$50.00         \$10.30        \$53.05          b. Did not compute reinvestment rate: -1
Tax rate                          0%             0%           40%           c. Wrong cost of capital: -0.5
1              2             3        4 d. Mechanical errors: -0.5
EBIT                          -\$50.00         \$10.30        \$53.05   \$54.64
EBIT (1-t)                    -\$50.00         \$10.30        \$47.71   \$32.78
Reinvestment                        0              0             0 9.834543 ! Reinvestment rate = g/ ROC = 3/10 = 30%
FCFF                          -\$50.00         \$10.30        \$47.71   \$22.95
Terminal value                                             \$327.82          Terminal value cost of capital = 10%
PV                            -\$44.64           \$8.21      \$267.29          ! Dicount back all cashflows at 12%
Nol                       \$50.00        \$39.70        \$0.00
Value of firm =                        \$230.86
+ Cash                                 \$25.00                     Grading scale: Part b
- Debt                                \$100.00                     a. Used wrong cost of capital: -0.5
Value of equity                        \$155.86                     b. Cash incorrectely treated: -0.5
Value per share =                       \$15.59                     c. Debt incorrectly treated: -0.5
d. Mechanical errors: -0.5
Reinvestment Rate = g/ ROC = 3/10 =                  30.00%

c. Price of bond =                      600
Setting up the problem                                           a. Probability of default not computed: -1
600 = 1000 (1- probability of distress)/ 1.05^3                  b. Mechanical errors: -0.5
Probability of distress =           30.54%                       c. Value of equity per share not computed: -0.5
Value of equity per share =                     \$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 =    6.00%                                                              ! Failed to estimate reinvestment; -1 point
Expected growth rate =    3%
Cost of capital =        10%

Reinvestment rate =       50.00%

FCFF next year =          \$9.27 ! I gave full credit even if you missed the (1+g)
\$132.43
Value of operating assets =                                                              ! 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
1            2             3
Net Income              -10           -5        10
- Reinvestment          10            5         5
= FCFE                  -20           -10       5
Cost of equity          20%           16%       12%

a. Terminal value
Return on equity =            12%                                                          ! Reinvestmeent rate not computed: - 1 pt
Expected growth rate
=                            4%
Reinvestment rate =      33.33%
Net income in year 4      \$10.40
Reinvestment in year
4=                            \$3.47
FCFE in year 4 =              \$6.93
Terminal value of
equity =                  \$86.67 ! The reinvestment rate has to be re-estimated with ROE = Cost of equtiy

b. Value of equity
today
1             2          3
FCFE                    -\$20.00       -\$10.00     \$5.00                                    ! No compounded cost of equity: -1 point
Terminal value                                   \$86.67
Compounded cost of
equity                    1.2           1.392   1.55904 ! Use compounded cost of equity since r changes
Present value           -\$16.67        -\$7.18   \$58.80
Value of equity today
=                         \$34.95
Exercise proceeds =        \$4.00 ! Exercise price * 2                                      ! Double counted shares: -1 point
Number of shares =         12.00 ! Includes options but not expected future share issues   ! Did not compute exercise value: -1 point
Value per share =          \$3.25

Fall 2008
Problem 1
Year                           Current           1              2              3
Expected growth                                 8%             8%             8%
EBIT (1-t)                     \$300.00        \$324.00        \$349.92        \$377.91
+ Depreciation                  \$50.00         \$54.00         \$58.32         \$62.99
- Cap Ex                       \$175.00        \$189.00        \$204.12        \$220.45
- Change in WC                  \$75.00         \$81.00         \$87.48         \$94.48
FCFF                           \$100.00        \$108.00        \$116.64        \$125.97

a. Reinvestment rate =       66.67%        ! (Net Cap Ex + Change in WC)/ EBIT (1-t)
Growth rate =              8.00%
Return on capital =       12.00%
b.
Reinvestment rate =          33.33%           ! g/ ROC                   ! Cashflows grow 4% a year forever after year 5, but if the return on capital stays at 12%,
FCFF in year 4 =             \$262.02       ! 377.91 (1.04) (1-.33)       the reinvstment rate has to be reestimated.
Terminal value              \$4,367.00      ! 262.02/(.10-.04)                                         ! Used cash flow in year 3 to growt at 4%: -1 point
c. & d.                                                                                               ! Did not use 10% as discount rate: -0.5 point
FCFF                                          \$108.00        \$116.64       \$4,492.97
Cost of capital                                 12%            11%            10%                                                   ! Discounted at year-specific cost of capital: -0.5 point
Cumulated WACC                                  1.12          1.2432        1.36752    ! Discount at cumulated WACC                 ! Mistake on minority interest: -0.5 to -1 point
Present value                                  \$96.43         \$93.82       \$3,285.49                                                ! Other errors: -0.5 point
Value of firm               \$3,475.74
+ Cash                         400
- Debt                        1000                       I also gave full credit if you used the treasury stock approach.           ! Used weird combinatiions of treasury stock and option
- Minority interest            500        ! 250 * 2      Add exercise value of \$ 400 million (20*20 to numerator)                   approaches: -0.5 to -1 point
Value of equity             \$2,375.74                     and divide by 100 million shares
Value of options                200
\$2,175.74
Value of equity in common stock
Value per shaer               \$27.20

e.
False. (The cash wll be discounted only if investstor expect the firm to waste the cash.                                             ! ALL OR NOTHING
This firm has a return on captial > Cost of captial. I would expect investors to trust the
management of this firm.

f.
EBIT (1-t) of diversted stores =               \$30.00
Cost of capital =                               10%                                                                                  ! Estimated a reinvstment even though growth was zero:
Value of stores =                             \$300.00     ! With no growth, we can assume EBIT (1-t) = FCFF                          ! Did not net out proceeds: -0.5 point
Divestiture proceeds =                          250
Net effect on value =                         -\$50.00     ! Sold for less than these stores are worth
Effect on value/share =                    -\$0.63      ! Value per share will decrease

Fall 2009
Problem 1
1          2               3 Terminal year
EBIT                            -\$100.00    \$100.00         \$150.00        154.5 ! Ignored NOL: -1 point
Taxes                              \$0.00      \$0.00          \$40.00          61.8 ! Failed to accumulate losses: -0.5 points
EBIT (1-t)                      -\$100.00    \$100.00         \$110.00          92.7 ! Did not compute FCFF: -1 point
Reinvestment                     \$100.00    \$150.00          \$50.00       23.175
FCFF                            -\$200.00    -\$50.00          \$60.00       69.525
Terminal value                                              \$993.21
Cumulated Cost of capital          \$1.15       \$1.29          \$1.42               ! Did not cumulate discount rates: -1 point
PV                              -\$173.91     -\$38.82        \$743.38
NOL                              \$150.00      \$50.00          \$0.00

Capital invested                 \$572.50    \$722.50         \$772.50                ! Did not compute ROC in year 3: -1 point
! Errors on reinvestment rate: -1 point
Return on capital in terminal year =                        12.00%                 ! Errors on terminal value computation: -0.5 to -1 point
Reinvestment in terminal year =                             25.00%

Value of operating assets =                 \$530.64
+ Cash                                       \$80.00                                ! Did not add cash: -1 point
+ Value of cross holding                    \$100.00 40*2.5                         ! Did not compute minority holding value: -1 point
- Expected lawsuit liability                 \$25.00 ! .25*100                      ! Did not subtract out lawsuit liability: -1 point
Value of equity                             \$685.64

Value of equity =                           \$685.64                                ! Any mistake: -1 point
+ Exercise proceeds                         \$60.00
/ Number of diluted shares                      110
Value per share today =                       \$6.78
ould solve this problem

esent value of the excess returns.

in year 5; NOLs are gone….

3%/10% = 30%

e terminal value
ashflows and the terminal value
umber of shares

s EBITDA does

up on the quiz, this is what the solution would have looked like.

in year 5; NOLs are gone….

3%/10% = 30%

e terminal value
ashflows and the terminal value
then compute the

d it on. The interest rate is a decoy and does not play a role in the valuation.
(it shows up below the operating income line). Add estimated market value = 80 *2.5
ou counted a 100% in your operating income, you have to subtract estimated market value: 120* 2
ter even if some of this debt belongs to Ajax Leasing

o first before you can use the equation. I was very, very easygoing about

nce you have high growth.
e is to equity investors
nvestment; -1 point

alculated: - 1 point
ot computed: - 1 pt

of equity: -1 point

cise value: -1 point
tal stays at 12%,

t year-specific cost of capital: -0.5 point
inority interest: -0.5 to -1 point

ombinatiions of treasury stock and option

einvstment even though growth was zero: -0.5 top -1 point
ut proceeds: -0.5 point

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