# Net Operating Loss Carry Forward

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Spring 1998
Problem 1
Bond Rating =                                BBB
Interest Rate =                                9.00%
After-tax Cost of Debt =                                      5.40%
Unlevered Beta = 1.06/(1+(1-0.4)(.1111)) =                                               0.993756211
Beta at 25% D/E Ratio = 0.99(1+0.6(.25)) =                                               1.142819643
Cost of Equity = 7% + 1.14 (5.5%) =                                         13.27%
Cost of Capital = 5.40% (.2) + 13.27% (.8) =                                                 11.70%

Problem 2
Change in Firm Value = (250 + 50) (.11-.10)(1.05)/(.10-.05) =                                            63
Change in stock price = 63/10 = \$ 6.30 (\$10.50 if you assume buyback at current price)

Problem 3
(100/250) (2) + (150/250) (X) = 5
Solve for X,                          X = 7 years

Spring 1999
Problem 1
Value of Bank Loan = 4 (PVA,7%,5) + 50/(1.07)^5 =                                            \$52.05
Value of Bonds Outstanding =                                                                 \$50.00
PV of Operating Leases = 10 (PVA,7%,7) =                                                     \$53.89
Market Value of Outstanding Debt=                                                           \$155.94

Market Value of Equity = 15* 10 =                                                           \$150.00
Debt Ratio = 155.94/(150+155.94) =                                                           50.97%

Cost of Equity = 6% + 1.2 (5.5%) =                                                           12.60%
Cost of Capital = 12.60%(.49) + 7% (1-.4)(.51) =                                              8.32%

Adjusted EBIT = 40 + 53.89*0.7 =                                            \$43.77
Adjusted BV of Capital = 50 + (50 + 50 + 53.89) =                                             203.89
Adjusted Return on Capital = 43.77 (1-.4)/203.89 =                                           12.88%

Problem 2
Change in Firm Value = 3 * 10 =                                                         \$30.00
Firm Value (Chg in WACC) (1.05)/(WACC(after)-.05) = 250 (Chg in WACC)(1.05)/(.10 -.05)= 30
Chg in WACC =                                              0.57%
WACC before =                                             10.57%
Ke (.8) + 8%(1-.4) (.2) = 10.57%
Cost of Equity before transaction = (.1057-.0096)/.8 =                                  12.01%

Problem 3
Value of firm before expansion = 300 + 70*10 =                                                         1000
Duration of assets after expansion = 7.5 (1000/1250) + 1 (250/1250) =
Weighted Duration of Assets has to be equal to 6.2years
(200/550)(1) + (100/550)(4) + (250/550) (X) =                                                    6.2
Solve for X
X = 11.24 years

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Spring 1999 (A)
Problem 1
PV of operating leases =                                                 \$      1,408
Straight Debt portion of convertible debt =                              \$      1,798
Total Debt =                                                             \$      3,206

Equity
Value of stock =                                                         \$      3,000
Value of conversion option = 2500-1798=                                  \$        702
Value of Equity =                                                        \$      3,702

Cost of Equity = 5.5% + 1.25(6.3%) =                                         13.375%
Cost of Debt (after-tax) = 7.5%(1-.4)=                                         4.50%
Cost of Capital = 13.375% (3702/6908) + 4.50% (3206/6908) =                                                     9.26%

Problem 2
Change in Firm Value =                                                             500
5000 (.10 - WACC after)/WACC after = 500
Solve for WACC after,
WACC after = 500/5500 =                                         9.09%
Cost of Equity after = 5.5% + 1 (6.3%) =                                         0.118
11.8(X) + 5% (1-X) = 9.09%
Solve for X,
X = (9.09-5)/6.8 =                                                60%
Debt to Capital ratio =                                           40%

Problem 3
Cody's should have long term debt: Negative coefficient suggests duration of 7.5 years
BAM should have floating rate debt: Oper income tends to move with inflation

Spring 2000
Problem 1
a. False. It has to be weighed off against the increase in both costs
b. True. It will reduce the marginal tax advantage of debt
c. True. The net operating loss carry forward will reduce the tax benefit of the debt. (No matter how the
the argument is structured, the firm without net operating losses will be able to borrow more money and get
a larger tax savings. The NOL will reduce the income available from which interest expenses can be deducted.
d. False. If you are more uncertain about future investment needs, you will value flexibility more and borrow less.

Problem 2
Current cost of capital = Cost of equity (because firm has no debt) =                                            9.20%
Change in firm value = .1375 = (Cost of capital before - Cost of capital after)/Cost of capital after
0.1375 = (0.092 - Cost of capital after)/Cost of Capital after
Solving,
Cost of capital after = 0.092/(1+.1375) =                                                          8.09%
Cost of equity after = 10.48%
Cost of debt after = 4.5%
10.48% (1-X) + 4.5% (X) = 8.09%
Solving for X,
X = 40%

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Problem 3
Duration of assets =                                                  7
Existing Debt =                                                       1 (duration of this debt = 4 years)
New Debt =                                                            3
(1/(1+3)) (4) + (3/(1+3)) X = 7                                         ! Since the asset mix does not change, the duration remains 7.
Solving
Duration of new debt =                                                8
Proportion on new debt that has to be 2 year debt =                                                 25% (.25(2) + .75(10) = 8)

Spring 2001
Problem 1
a. Current Cost of Equity =                                     10.72% ! 5% + 1.04*5.5%                  ! If you decide to use the effective tax
Current cost of debt =                                           3.90%                                   has to be that you do not have enoug
Current cost of capital =                                        8.47% ! 10.72% (.67) + 3.9% (.33)       However, this will mean that the effec
If you did this, I gave you full credit.
b. New debt to capital ratio =                                                     50%
New debt to equity ratio =                                                    100.00%                    ! I gave full credit if you read the incre
Unlevered Beta =                                                                    0.8                  of the existing interest rate (I did take
New Beta =                                                                         1.28                  if you read it as 25%
New cost of equity =                                                         12.0400%                    ! You lost a point if you did not unleve
New after-tax cost of debt =                                                     4.05%
New Cost of capital=                                                             8.05%

c. Number of shares bought back =                                          21.7391304                    ! Since the price at which you were bu
c. Change in annual financing cost =                                             \$6.37                   cannot divide by the total number of s
Change in firm value =                                                          \$79.13
Change per share =                                                               \$0.59                   ! Transfer of wealth to stockholders s

Problem 2
Market value of the firm =                                                          2000 ! 1000/.5
Dollar debt at optimal of 25% =                                                      500 ! Don't increase the size of the firm. Otherwise, asset
Duration of debt at optimal
Let X be the proportion of the debt that is 5-year debt at optimal
X (4) + (1-X) (8) = 7
X = .25
The firm has to have \$ 125 million in 5-year debt and \$ 375 million in 10-year debt
It needs to pay off \$ 275 million of 5-year debt and \$ 225 million of 10 year debt.

Spring 2002
Problem 1
Part a: Current cost of capital
Beta =                                            1.15                                    Math error: -0.5
Cost of equity =                                9.85%                                     forgot to after-tax cost of debt: -0.5
Cost of capital =                               9.23% ! Debt ratio = 10%

Part b: New cost of capital
Unlevered beta =                             1.078125                                                    ! Forgot to adjust cost of equity : -
New levered beta =                        1.35535714 ! Don't forget to unlever and relever               ! Math errors: -0.5
New cost of equity =                           10.67%
New cost of capital =                           8.73%

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Part c
Borrow money over next 5 years and pay dividends
Its stockholders like dividends, because it has paid large dividends in the past
Its projects earn less than its cost of capital

Problem 2
Cost of capital before =                     9.00%
Cost of capital after                        8.00%
Change in firm value =                          824 ! Forgot to consider the effect of growth : -1 point
Increase in dollar debt to get to 25% =                                     1000
Number of shares bought back =                                               12.5
Number of shares left =                                                      37.5 ! Did not adjust the number of shares for buybac
Increase in value per share =                                       21.9733333 ( Remember that you cannot divide by 50 if you a

Problem 3
a. Long term, Dollar, Fixed Rate, Straight                                         !   Heavy infrastructure: Long term
!   U.S. operations: Dollar
!   No pricing power: Fixed
!   Low growth: Straight
b. Long term, Mixed Currency, Floating Rate, Straight                              !   Brand Name: Long term
!   Worldwide operations: Mixed Currency
!   Pricing power: You can pass inflation through…
!   High margins and cashflows : Straight (Some o
c. Short term, Dollar, Fixed Rate, Convertible                                     !   Speedy Obsolescence: Short term
!   U.S. operations: Dollar
!   High Uncertainty: Floating (but Competitive Ind
!   High growth: Convertible

Spring 2003
Problem 1
Current cost of capital =                      9%
Current debt ratio =                          0.25
Current after-tax cost of debt =             0.036
Current cost of equity =                     0.108
Current beta =                                1.45

Unlevered beta =                               1.21
New levered beta =                             2.30               ! Debt = 3000; Equity = 2000; Stock buyback reduces the value

Cost of equity =                          14.18%

New cost of capital =                        8.19%

Change in firm value                      \$393.82 ! (.09 - .0819) (4000)/.0819                     ! If you had the NPV of the new in

Number of shares =                            100
Price at which bought back =               \$33.00
Number bought back =                  30.3030303 ! 1000/33
Number remaining =                    69.6969697

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Change in value per share =                   \$4.35 ! (393.82 - (33-30) (30.30))/69.70
Price per share after transaction =          \$34.35

Problem 2
Duration of existing debt =                    2.00

Duration of new debt =                         6.50

Currency break down
Dollar debt =                                  50%
Euro debt =                                    50% ! \$1 billion of Euro debt needed to get to \$ 1 billion (1/3 of total debt)

Spring 2004
Problem 1
New beta =                                     1.12
Cost of equity =                          0.093984

Interest coverage ratio =                      3.75
Rating =                              BB+
Cost of debt =                                 0.06
After-tax cost of debt =                      0.036

Cost of capital =                            7.08%

Problem 2
a. Value of firm =                             1050 ! 80*10+250
Cost of capital =                           10%
Cashflow last year =                           50            1050 = 50 (1+g)/ (Cost of capital -g)
Expected growth rate=                         0.05            1050 = 50 (1+g)/(.10-g)

b. Increase in value from recapitalization
Annual cost at current cost of capital =                       105
Annual cost at new cost of capital =                          94.5
Annual savings =                                              10.5
PV at expected growth rate =                                 262.5

c. If investors are rational, savings will accrue to all stockholders
Increase in value per share =                                3.28125
New stock price =                                           13.28125
Number of shares bought back =                           18.8235294
Number of shares left =                                  61.1764706

Problem 3
6 (150/500) + 8 (100/500) + X (250/500) = 10
Solving for X,
Duration of new bond =                     13.2

Since the firm has little pricing power, you would go with fixed rate debt
Since half of its revenues come from the EU region, half of its total debt of \$ 500 million should be in Euros
Hence the firm should use 100% Fixed rate, Euro debt

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Spring 2005
Problem 1
Value of unlevered firm =                                                 1000 !100 *10          !This firm has no debt. This is the

With \$250 million in debt, used to buy back stock
Value of levered firm =                                                   1025 ! 100 *10.25
Tax benefit from additional debt =                                         100 ! Tax rate * Dollar Debt

Value of levered firm = Value of unlevered firm + Tax benefit - (Probability of bankruptcy * Cost of bankruptcy)
1025 = 1000 + 100 - (X* .30*1000)
Probability of bankruptcy =                                                25%

Problem 2
Current market value of equity =                                                        4000
Market value of debt =                                                                  1000
Value of firm =                                                                         5000

Cost of capital = 10.44% = Cost of equity (.80) + 4.2% (.20)
Cost of equity =                                           0.12
Current beta =                                             1.75

After debt is repaid
New beta =                                          1.52173913
New cost of equity =                                    11.09% ! Equal to cost of capital

New firm value =                                      \$4,708.24 ! Change in firm value = (.1044-.1109) 5000/.1109

Problem 3
a. Current asset duration = 0.75(10) + 0.25 (5) =                                         8.75

b. Expected asset duration if tourism business doubles = (0.75/1.25)(10) + (0.5/1.25) (5) =
To solve for duration of new debt
(.5/.75)*6+(.25/.75)*X = 8                                     ! New debt issue = 0.25

Duration of new debt =                                  12

Fall 2006
Problem 1
a. Cost of equity = 4.5% + 1.00*4% =                                    8.50%
Cost of capital = 8.5% (.9) + 5% (.1) =                                                8.15%

b. With change in tax status and leverage
Unlevered beta =                                            0.9 ! 1/ (1+(1-0)(1/9))
New levered beta =                                         1.44 ! 0.9 (1+(1-.4)(50/50))
Cost of equity =                                        10.26%
Cost of capital =                                        6.93% ! 10.26% (.5)+6%(1-.4)(.5)

c. Change in firm value, assuming 3% growth rate
Savings in costs each year =                                           \$12.20 ! 1000 (.0815-.0693)
Increase in firm value =                                              \$310.43 ! 12.20/(.0693-.03)
Firm value after transaction =                                      \$1,310.43

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Price paid on transaction
For equity = 11.5*90=                                             \$1,035.00
For debt =                                                          \$100.00
Total price paid =                                                \$1,135.00

Value gained in transaction =                                       \$175.43

Prtoblem 2
Duration of assets after divestiture =                                  8.25

Duration of debt after transactiion
Let the proportion of 10-year bonds after the repayment be X
X(10) + (1-X) (2) = 8.25
Solving for X,
X=                                       0.78125
Dollar debt after repayment = 8 -4 = 4                         ! Repaid \$ 4 billion of debt
10-year bonds after the repayment =                                    3.125
2-year bonds after the repayment =                                     0.875
Repaid amounts
10-year bonds =                                                        2.875
2-year bonds =                                                         1.125

Spring 2007
Problem 1
8.44%
a. Cost of capital at existing debt ratio = ! 13%(.4)+9%(1-.4)(.6)
b.
Beta at current cost of equity =           2 ! (13-5)/4
Unlevered beta =                      1.0526
New Debt to Equity Ratio =           42.86% ! (600-300)/(400+300)
Levered Beta =                    1.3233083
New cost of equity                   10.29%
New cost of capital                   8.29%

Problem 2
a. Change in firm value =          \$11.11 ! (80+20)(.10-.09)/.09
b. Number of shares bought back =       6
\$6.00
Share of firm value to buy back shares ! 6* \$1/share
\$5.11
Share of firm value to remaining shares
Number of shares remaining           14 ! 20-6
Value increase per remaining share\$0.37

Problem 3
Duration of existing assets =                 8 ! 2(5/20)+10(15/20)
Duration of existing debt =                   8

Duration after transaction            6.8 ! 2(5/12.5)+10(7.5/12.5)
To estimate the duration of the new debt
8(5/10) + X(5/10) = 6.8
Duration of new debt =                5.6

Spring 2008

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Problem 1
Old debt to equity =                         0%
Current beta =                              1.00 ! Cost of equity is 9%; Rf =5% and Risk premium =4%
New debt to equity =                    42.86% ! 600/1400; Debt used to buy back stock
New beta =                               1.2571
New cost of equity =                    10.03%
New after-tax cost of debt =             3.60%
Debt Ratio =                            30.00% ! 600/ (600 +1400)
Cost of capital =                       8.100%

Problem 2
Current cost of capital =                  12%
New cost of capital =                   10.00%
Market value of firm =                    1000 ! 200 + 800
Annual cost savings =                        20
PV of savings (with g=4%) =         333.333333 ! 20/ (.1-.04): Okay if you used (1+g)
New firm value =                    1333.33333

b. Value of firm =                  1333.33333
- Debt =                                   500 ! Paid off \$ 300 million out of \$ 800 million
Value of equity =                   833.333333
Number of shares =                           30
Value per share =                        \$27.78

Here is anyother way to get to the same solution
Increase in firm value =            \$333.33
Discount on stock offered =         \$100.00 ! The discount on the private placement
Remaining value savings =           \$233.33
/ Number of shares=                  \$30.00
Increase in value per share=          \$7.78
Added tos hare price =               \$27.78

Duration of assets                            7.5           3
Weighted duration =                             6              ! 7.5(100/150)+3 (50/150)
Existing debt New debt
Value                                          25          50
Duration                                        5X
Solving for duration of new debt
5 * (25/75) + X (50/75) = 6
Duration of new debt =                     6.50

Spring 2009
Problem 1
a. Existing cost of capital
Weoight
Estimated value         Cost       Risk measure
Debt                                      600          0.6      6.00% BB
Equity                                    400          0.4    17.68%        2.28
Capital                                  1000                 10.67%

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b. New cost of capital
New debt ratio =                                 30.00%
New D/E ratio =                               0.4285714
Unlevered beta =                                     1.2
New levered beta =                            1.5085714

Weight    Cost       Risk Measure
Debt                               30.00%      3.90% A
Equity                             70.00% 0.1305143 1.5085714
10.31%

Problem 2
Current cost of equity = Current cost of capital =             10.00%
If investors are rationa, all shares get an equal portion of increase in firm value
Increase in firm value =                                           100 ! Since investors are rational,
all shares gain \$1.00.
Solving for cost of capital after,
(Cost of capital before - Cost of capital after)*Existing firm value/ Cost of capital after =100
(.10-Cost of Capital after)*1000/ cost of capital after = 100
Cost of capital after =                            9.09%

Beta after =                                        1.4 ! Lever the beta, using new debt/equity ratio
Cost of equity after=                          12.400%
12.4% (.6) + X(1-.4) (.4) = .0909
Pre-tax cost of debt =                            6.88%

I kept the firm value constant at 1000 in the example above. If you use 1100 as firm value, the answers will b
D/E ratio after =                            0.5714286
Beta after =                                 1.3428571
Cost of equity after =                          12.06%
12.06% (700/1100) + X (1-.4) (400/1100)= .0909
Pre-tax cost of debt =                           6.49%

Problem 3
Weighted duration of assets after cash is used =                   8.4 !   Weighted average of just operating asset
Duration of the debt has to be equal to this after the debt is paid off:   (since cash is being used for retiring deb
X (10) + (1-X) (0) = 8.4
84% of the debt has to be 10-year zero coupon debt.
Total debt outstanding after debt retirement =                   1300 !    Debt outstnading before - Debt repaid
!0-year zero coupon debt =                                       1092 !    84% of outstanding debt
10-year coupon debt to be paid off =                              108 !    Long term debt repaid
Short trm debt to be paid off =                                     92 !   Short term debt repaid

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Alternatively, you can assume that the bank debt is at market value

Market Value of Debt =                  153.94

If you do this, the cost of debt will be a weighted average of 7% and
8%, the cost of debt will be around 7.5%.

29.925

6.2

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Common errors
1. Reversed the cost of capital before and after in
firm value change calculation.
2. Computed change in firm value incorrectly
3. Did not use after-tax cost of debt
4. Other math errors.

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32.6086956

Common errors
change to.
ange, the duration remains 7.                 2. Tried to change asset duration (why?)
3. Set up new debt incorrectly (had two unknowns with
one equation)
25(2) + .75(10) = 8)                           4. Other errors.

If you decide to use the effective tax rate, the rationale
as to be that you do not have enough operating income to cover your interest expenses.
owever, this will mean that the effective tax rate should be 10% in part b (since debt is doubled)
you did this, I gave you full credit.

I gave full credit if you read the increase as 0.25%
f the existing interest rate (I did take off half a point                        78.2608696
You lost a point if you did not unlever and relever betas

Since the price at which you were buying back the stock was given, you
annot divide by the total number of shares outstanding.

Transfer of wealth to stockholders selling back stock = (11.50-10)*21.739

ax cost of debt: -0.5

Forgot to adjust cost of equity : -1
Math errors: -0.5

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! Closely held, outperformed: Not target of a takeover - No immediacy
! ROC < Cost of capital : Don't invest
! History of paying dividends: Pay more dividends

the number of shares for buyback : -1
at you cannot divide by 50 if you are buying back at the current price)

ucture: Long term            0.25 points off for each mistake

erations: Mixed Currency
You can pass inflation through… Hence, floating rate debt
and cashflows : Straight (Some of you made the argument for convertible because of intangibility of asset, but the cashflows are predictable
escence: Short term

nty: Floating (but Competitive Industry: Fixed - So, I gave credit for both)

Stock buyback reduces the value of equity

If you had the NPV of the new investment, you can add that on.

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billion (1/3 of total debt)

d be in Euros

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This firm has no debt. This is the unlevered firm value.             1. Tried to force cost of capital approach through: -2 to -3
2. Wrong bankrupcty cost: -0.5 to -1
3. Other errors: -0.5 to -1
!Note that the stock price increases on the announcement to reflect what the firm will be worth after the transaction

t of bankruptcy)

1. Error in estimating current cost of equity: -0.5
2. Did not unlever beta: -0.5
3. Estimated new cost of equity wrong: -0.5
4. Used old cost of equity instead of capital in computing firm value ch
5. Did not compute PV of annual savings: -0.5
6. Did not compute increase in firm value at all: -1

4-.1109) 5000/.1109

Current Balance Sheet                                   1. Weighted businesses incorrectly: -0.5
Transporation      0.75 Debt                        0.5 2. Did not compute new weights after bu
Tourism            0.25 Equity                      0.5 3. Did not compute new dollar debt corre
4. Mixed up asset and debt durations: -1
New Balance Sheet
Transporation         0.75 Debt                    0.75 ! Issued 0.25 of debt to fund doubling of
Tourism                0.5 Equity                   0.5

! Mechanical errors: -0.5
! Tax effect: -0.5

!   Unlevered with tax rate: -0.5
!   Relevered with wrong debt to equity: -0.5
!   Forgot to tax effect cost of debt: -0.5
!   Wrong debt ratio: -0.5

! Okay if you used (1+g) in numerator
! Change in firm value incorrect: -1 to -1.5

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! Gan/Loss on Sale: -1 to -1.5

! Duration for assets computed incorrectly: -1.5 to -2

! Dolalr debt after restructuring incorrect: -1
! Breakdown of debt after restructuring: -1 to -1.5

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1. Did not adjust the cost of equity at all: -1.5 points
2. Error in beta estimation: -0.5 to -1 point
3. Weights incorrect: -0.5 point
4. Forgot to after-tax cost of debt: -0.5 point

1. Cost savings per year incorrect: -0.5 point
2. PV of savings incorrect: -1 point
3. Math errors: -0.5 point each

1. Divided by existing number of shares: -1 point
2. Error in computing per share value: -.5 to -1 point

1. Asset duration incorrect: -0.5 to -1.5 points (depending)
2. Debt duration incorrect: -0.5 to -1 point
3. Math error: -0.5 point

! Wrong cost of debt : -.5
! Math error: -.5

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!   Wrong debt ratio: -0.5 to -1
!   Forgot to unlever and relever beta: -1
!   Used Debt to capital ratio to lever beta: -0.5
!   Wrong cost of cebt : -.5

! Firm value computed incorrectly: -1
! Did not lever beta: -1
ors are rational,        ! Error in setting up new WACC: -.5 to -1

after =100

w debt/equity ratio

irm value, the answers will be different.

! Computed beta of assets including cash: -1
verage of just operating assets
debt)
s being used for retiring(Cash is used up after the transaction)
Did not comptue the new debt level right: -1
Other math errors: -.5 point
tanding debt

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sset, but the cashflows are predictable and brand name has high marketable value)

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l approach through: -2 to -3

e worth after the transaction

cost of equity: -0.5

y wrong: -0.5
ead of capital in computing firm value change: -0.5
ual savings: -0.5
n firm value at all: -1

. Did not compute new weights after business changed: -0.5
. Did not compute new dollar debt correctly: -0.5
. Mixed up asset and debt durations: -1

Issued 0.25 of debt to fund doubling of tourism business

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