“Exercise 1
Laptop plc. is planning on setting up a laptop repair centre. They estimate that:
The required investment will be
0.3m and the investments life is expected to be 5 years.
The investment is to be
depreciated using the straight line depreciation method and none of the costs
are expected to be recovered at the end of the 5 years.
Total revenues from repairs are
expected to be 200,000 in year one (one year from now), growing at 2.5% per
annum. Staffing costs are 90,000 per year.
Administrative, advertising and
general expenses associated with the centre are expected to be 20,000 per
year.
All costs are expected to
increase at 2.5% per annum.
The discount rate for ventures
of similar risk is 12%.
Laptop plc. faces a corporate
tax rate of 35%.

Calculate the NPV of this
project and determine whether it should be accepted or rejected.

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Investment

-300000

Revenues

200000

205000

210125

215378.1

220762.6

Total Costs

110000

112750

115568.8

118458

121419.4

Depreciation

60000

60000

60000

60000

60000

Total Income

30000

32250

34556.25

36920.16

39343.16

Taxes

10500

11287.5

12094.69

12922.05

13770.11

AT Income

19500

20962.5

22461.56

23998.1

25573.05

CF (add depr)

79500

80962.5

82461.56

83998.1

85573.05

PV

-300000

70982.14

64542.81

58694.51

53382.31

48556.45

R=0.12

NPV

-3841.78

Suppose you are told that
Laptop plc. is totally equity financed. The company has a beta equal to
1.2. Appropriate estimates for the risk free rate and the market risk
premium are 2% and 4%, respectively. Calculate the NPV of this project and
determine whether it should be accepted or rejected.

RCAPM

0.068

-300000

74438.2

70980.88

67692.07

64563.11

61585.83

NPV

39260.1

Suppose you are told that
Laptop plcs core business is not laptop repairs but production of laptop
components. The beta of companies in the laptop repair business is
generally around 2.5. Would you recommend accepting or rejecting the
project? [Explain your answer in no more than 100 words]
In no more than 200 words,
illustrate the concept of homemade leverage and explain the role it plays
in Modiglianis and Millers capital structure irrelevance result.

Exercise 2
Firms
A and B are identical except for their capital structure. A carries no debt,
whereas B carries 200 of debt on which it pays 6% interest rate. Assume no
transaction costs, no taxes, risk-free debt and perfect capital markets. The
relevant numbers are provided in the following table:

A

B

Value
of Firm

300(given)

400(given)

Debt

0(given)

200(given)

Equity

300

200

Earnings
before interest

30(given)

30(given)

Interest
payment

0

12

Interest
rate

Not
Applicable(given)

6%(given)

Earnings
after interest

30

18

Return
on Equity

10%

9%

Debt/Equity
Ratio

0

1

Cost
of Capital

10%

7.5%

Complete the
blank spaces in the table above.
State whether
each of the following statements is true or false

i.
To
reduce the companys cost of capital, the management of Company A should start
a programme of stock repurchases financed through the issue of new debt.
ii.
To
reduce the companys cost of capital, the management of Company B should issue
equity to reduce its debt burden.
iii.
Relative
to Company B, Company A is undervalued.
iv.
The
situation described in the table is the result of capital markets equilibrium.
v.
The
situation described in the table violates Modigliani-Miller Proposition 1.
Exercise 3
An
investor is uncertain about how much to invest in two risky assets. The first
asset (equity) yields an expected return of 12% and has a standard deviation
equal to 8%. The second asset (debt) yields an expected return of 6% and has a
standard deviation of 5%. The correlation coefficient between the returns is
-0.1.

Compute the expected
return and standard deviation of the following portfolios:

Portfolio

Percentage
in equity

Percentage
in debt

1

75

25

2

50

50

3

25

75

Portfolio

% in debt

% in eq

ExRet

Var

SD

3

0.75

0.25

0.075

0.001731

0.041608

2

0.5

0.5

0.09

0.002125

0.046098

1

0.25

0.75

0.105

0.003681

0.060673

Sketch the set of
portfolios composed of debt and equity in the mean-standard deviation
space and identify portfolios 1, 2 and 3.

Would a rational
risk-averse investor ever choose a portfolio entirely composed of debt?
Would a rational risk-averse investor ever choose a portfolio entirely
composed of equity? [Explain your answer in no more than 100 words]

Exercise 4

(Please answer all parts
of the question)

21st Century Cat is
a film producing company which is contemplating the production of a new film.
They estimate that:
The production of the film will
require an investment of 300,000 in year 0.
The distribution will generate
a stream of cash flows equal to 200,000 in year 1, and 100,000 in each of
years 2 and 3.
In year 3, the producer will
sell the rights to a tv broadcaster for 90,000.
Distribution costs will be
75,000 in year 1, and 50,000 in each of years 2 and 3.
Due to regulation aimed at
promoting cinema, all income generated by the project is tax-free.
a.
The
companys financial experts say that the appropriate discount factor for the
project is 10%. Calculate the NPV using this discount factor and determine
whether the project should be funded.

0

1

2

3

Initial
Inv

300

Revenues

200

100

190

Costs

75

50

50

Cash
Flows

-300

125

50

140

Discount
factor at 10% rate

1.1

1

0.909091

0.826446

0.751315

Discounted
Cash flows

-300

113.6364

41.32231

105.1841

NPV at
10%

-39.8573

b.
Assume
now that the company has a debt/equity ratio equal to one. The companys bonds
yield a 6% return, the companys beta is equal to 0.5, the market risk premium
is 5%, while the risk-free rate is 3%. Calculate the NPV of the project with
the new data.

Rcapm

0.055

Rwacc

0.0575

Discount
factor at 5.75% rate

1.0575

1

0.945626

0.894209

0.845588

Discounted
Cash flows

-300

118.2033

44.71047

118.3823

NPV at
5.75%

-18.7039

Exercise 5

(Please answer all parts
of the question)

An investor is uncertain about
how much to invest in two risky assets. The first asset (equity) yields an
expected return of 10% and has a standard deviation equal to 8%. The second
asset (debt) yields an expected return of 5% and has a standard deviation of
7%. The correlation coefficient between the returns is 0.1.
a.
Compute
the expected return and standard deviation of the following portfolios:

Portfolio

Percentage
in equity

Percentage
in debt

1

90

10

2

50

50

3

10

90

Equity

Debt

R

0.1

0.05

SD

0.08

0.07

Var

0.0064

0.0049

Portfolio

% in
equity

% in
debt

Expected
R

Var

SD

1

0.9

0.1

0.095

0.005

0.073

2

0.5

0.5

0.075

0.003

0.056

3

0.1

0.9

0.055

0.004

0.064

b.
In
the mean-standard deviation space, sketch the set of portfolios composed of
debt and equity and identify portfolios 1, 2, and 3 on your graph.

Would a rational
risk-averse investor ever choose portfolio 3? Would a rational risk-averse
investor ever choose portfolio 1? [Explain your answer in no more than 100
words]

Exercise 1Laptop
plc. is planning on setting up a laptop repair centre. They estimate that: The required investment will be
0.3m and the investments life is expected to be 5 years. The investment is to be
depreciated using the straight line depreciation method and none of the costs
are expected to be recovered at the end of the 5 years. Total revenues from repairs are
expected to be 200,000 in year one (one year from now), growing at 2.5% per
annum. Staffing costs are 90,000 per year. Administrative, advertising and
general expenses associated with the centre are expected to be 20,000 per
year. All costs are expected to
increase at 2.5% per annum. The discount rate for ventures
of similar risk is 12%. Laptop plc. faces a corporate
tax rate of 35%.Year 0Year 1Year 2Year 3Year 4Year 5Investment-300000Revenues200000205000210125215378.1220762.6Total Costs110000112750115568.8118458121419.4Depreciation6000060000600006000060000Total Income300003225034556.2536920.1639343.16Taxes1050011287.512094.6912922.0513770.11AT Income 1950020962.522461.5623998.125573.05CF (add depr)7950080962.582461.5683998.185573.05PV-30000070982.1464542.8158694.5153382.3148556.45R=0.12NPV-3841.78RCAPM0.068-30000074438.270980.8867692.0764563.1161585.83NPV39260.1Exercise 2Firms
A and B are identical except for their capital structure. A carries no debt,
whereas B carries 200 of debt on which it pays 6% interest rate. Assume no
transaction costs, no taxes, risk-free debt and perfect capital markets. The
relevant numbers are provided in the following table:ABValue
of Firm 300(given)400(given)Debt0(given)200(given)Equity300200Earnings
before interest30(given)30(given)Interest
payment012Interest
rateNot
Applicable(given)6%(given)Earnings
after interest3018Return
on Equity10%9%Debt/Equity
Ratio01Cost
of Capital10%7.5%i.
To
reduce the companys cost of capital, the management of Company A should start
a programme of stock repurchases financed through the issue of new debt. ii.
To
reduce the companys cost of capital, the management of Company B should issue
equity to reduce its debt burden.iii.
Relative
to Company B, Company A is undervalued.iv.
The
situation described in the table is the result of capital markets equilibrium.v.
The
situation described in the table violates Modigliani-Miller Proposition 1. Exercise 3An
investor is uncertain about how much to invest in two risky assets. The first
asset (equity) yields an expected return of 12% and has a standard deviation
equal to 8%. The second asset (debt) yields an expected return of 6% and has a
standard deviation of 5%. The correlation coefficient between the returns is
-0.1.PortfolioPercentage
in equityPercentage
in debt175252505032575Portfolio% in debt% in eqExRetVarSD30.750.250.0750.0017310.04160820.50.50.090.0021250.04609810.250.750.1050.0036810.060673Exercise 421st Century Cat is
a film producing company which is contemplating the production of a new film.
They estimate that: The production of the film will
require an investment of 300,000 in year 0. The distribution will generate
a stream of cash flows equal to 200,000 in year 1, and 100,000 in each of
years 2 and 3. In year 3, the producer will
sell the rights to a tv broadcaster for 90,000. Distribution costs will be
75,000 in year 1, and 50,000 in each of years 2 and 3. Due to regulation aimed at
promoting cinema, all income generated by the project is tax-free.a.
The
companys financial experts say that the appropriate discount factor for the
project is 10%. Calculate the NPV using this discount factor and determine
whether the project should be funded.0123Initial
Inv300Revenues200100190Costs755050Cash
Flows-30012550140Discount
factor at 10% rate1.110.9090910.8264460.751315Discounted
Cash flows-300113.636441.32231105.1841NPV at
10%-39.8573b.
Assume
now that the company has a debt/equity ratio equal to one. The companys bonds
yield a 6% return, the companys beta is equal to 0.5, the market risk premium
is 5%, while the risk-free rate is 3%. Calculate the NPV of the project with
the new data.Rcapm0.055Rwacc0.0575Discount
factor at 5.75% rate1.057510.9456260.8942090.845588Discounted
Cash flows-300118.203344.71047118.3823NPV at
5.75%-18.7039Exercise 5An investor is uncertain about
how much to invest in two risky assets. The first asset (equity) yields an
expected return of 10% and has a standard deviation equal to 8%. The second
asset (debt) yields an expected return of 5% and has a standard deviation of
7%. The correlation coefficient between the returns is 0.1.a.
Compute
the expected return and standard deviation of the following portfolios:PortfolioPercentage
in equityPercentage
in debt190102505031090Equity DebtR0.10.05SD0.080.07Var0.00640.0049Portfolio% in
equity% in
debtExpected
RVarSD10.90.10.0950.0050.07320.50.50.0750.0030.05630.10.90.0550.0040.064b.
In
the mean-standard deviation space, sketch the set of portfolios composed of
debt and equity and identify portfolios 1, 2, and 3 on your graph. “