FINANCIAL MANAGEMENT CALCULATION

QUESTION

 

School of Business

 

 

 

BUACC3701:  Financial Management

 

 

 

 

Semester 1 – 2012

ASSIGNMENT

 

 

This assignment is to be completed in groups of three and carries 30 percent of the marks in this unit.

 

Question 1. (5 marks)

 

Brown Ltd operates outdoor amusement centres in a number of country towns. The company has decided to build another centre that is expected to generate a permanent increase in EBIT of $100,000 pa. Current EBIT is $350,000. Brown currently has a capital structure that utilises bonds, ordinary equity and preference shares. The $200,000 of issued bonds pay 8% pa. Preference shares pay an annual fixed dividend of $150,000. Currently 250,000 ordinary shares have been issued and are trading at $2 per share. The company pays tax at 30%.

 

a)     Brown needs to raise $500,000 to construct the new amusement centre. Assuming the company can issue new shares at the current market price, what is the impact on EPS if new shares are issued to fund the centre?

 

Solution :

 

Impact on EPS

 

350000 +100000 = 450000

 

Deduct interest = 450000-16000 = 434000

Deduct pref. Div= 434000-150000 = 284000

Deduct tax = 284000-85200 = 198800

Current EPS = 198800/250000 = 0.7952

New EPS = 198800/500000 =0.3976

 

 

 

b)     If new debt can be raised at a 10% interest rate, what is the impact on EPS of using debt rather than a new equity issue?

 

 

 

 

 

 

 

Solution :

 

Impact on EPS

 

350000 +100000 = 450000

 

Deduct interest = 450000-16000-50000 = 384000

 

Deduct pref. Div= 384000-150000 = 234000

Deduct tax = 234000-70200 = 163800

New EPS = 163800/2500000 = 0.6552

 

 

 

 

Brown Ltd depends on mainly on sunny weather to generate its expected EBIT. Using the information above together with the two following scenarios calculate the impact of the debt and equity financing alternatives if:

 

a)     Weather is good which will increase attendances and increase EBIT to $600,000

 

b)     Weather is poor which will decrease attendances and reduce EBIT to $320,000

 

c)     Calculate the indifference point

 

Solution :

 

If Weather is good

 

Impact of equity financing

New EBIT

950000

EBT

934000

After Pref

784000

Tax

235200

PAT

548800

Old EPS

2.1952

New EPS

1.0976

 

 

 

Impact of Debt finanacing

New EBIT

950000

EBT

934000

After Pref

784000

Tax

235200

PAT

548800

Old EPS

2.1952

New EPS

1.0976

 

If Weather is Bad

Equity Financing

New EBIT

670000

EBT

654000

After Pref

504000

Tax

151200

PAT

352800

Old EPS

1.4112

New EPS

0.7056

 

Debt Financing

New EBIT

670000

EBT

604000

After Pref

454000

Tax

136200

PAT

317800

Old EPS

1.2712

New EPS

1.2712


 

Question 2. (10 marks)

 

You are considering the following two stocks for your portfolio and have observed the following.

 

 

The risk free rate is 0.04 and you are considering investing 60% of your funds in Stock A and 40% in Stock B.

 

Calculate the following.

 

a)     Expected Return of Stock A (.25 mark)

b)     Expected Return of Stock B (.25 mark)

c)     Standard Deviation of Stock A (.5 mark)

d)     Standard Deviation of Stock B (.5 mark)

e)     Coefficient of Variation of Stock A (.25 mark)

f)      Coefficient of Variation of Stock B (.25 mark)

g)     Covariance of Stocks A and B (.5 mark)

h)     Correlation Coefficient of Stocks A and B (.5 mark)

i)      Portfolio Return (.25 mark)

j)      Portfolio Standard Deviation and Variance (1.25 mark)

k)     Weights of the Minimum Variance Portfolio (1.25 marks)

l)      Proof that these weights lead to the Minimum Variance Portfolio (1 mark)

m)   Weights of the Optimal Risky Portfolio with a risk-free asset (1 mark)

n)     Proof that these weights lead to the Optimal Risky Portfolio (1.25 marks)

  • o)     Discussion on what you would do with this portfolio (1 mark)

 

SOLUTION

 

a)     Expected Return of Stock A .

 

E(RA) = (0.13×0.35) + (0.09×0.35) + (-0.05×0.30) = 0.062 or 6.2%

 

b)     Expected Return of Stock B.

 

E(RB) = (0.16×0.35)+(0.02×0.35)+(-0.01×0.30) =0.06 or 6 %

 

 

c)     Standard Deviation of Stock A

 

VARA = [0.13(0.35-0.062)2] + [0.09(0.35-0.062) 2] + [-0.050(.30-0.062) 2] = 0.005656

STDA =√0.005656  = 0.075206

 

 

d)     Standard Deviation of Stock B

 

VARB= 0.16(0.35-0.06) 2+ 0.02(0.35-0.06) 2+-0.01(0.30-0.06) 2  =0.00553

 

STDB = √0.00553   = 0.074364

 

 

 

e)     Coefficient of Variation of Stock A.

 

Coefficient of Variation of Stock A = [STDA / E(RA) ]

 

= [0.075206/0.062] = 1.213006

 

 

 

f)      Coefficient of Variation of Stock B.

 

Coefficient of Variation of Stock B = [STDB / E(RB) ]

 

= [0.074364/0.06]×100 = 1.239399

 

 

g)     Covariance of Stocks A and B (.5 mark)

 

     

Deviations from
expected returns

Product of deviation
& probability
Probability Stock A Stock B Stock A Stock B  

0.35

0.13

0.16

0.068

0.1

0.00238

0.35

0.09

0.02

0.028

-0.04

-0.000392

0.3

-0.05

-0.01

-0.112

-0.07

0.002352

   E(R) =0.062  E(R ) =0.06    

0.00434

 

 

CovAB     = 0.00434

 

h)     Correlation Coefficient of Stocks A and B (.5 mark)

 

Correlation A,B = Covariance AB / STDA×STDB

= 0.00434 /0.075206×0.074364 = 0.78

 

i)      Portfolio Return

 

Probability Stock A Stock B

Combined Returns (%)

Expected Returns(%)

0.35

0.13

0.16

0.142

0.0497

0.35

0.09

0.02

0.062

0.0217

0.3

-0.05

-0.01

-0.034

-0.0102

     Portfolio Return =

0.0612

 

 

 

j)      Portfolio Standard Deviation and Variance

 

Probability Stock A Stock B

Combined Returns (%)

Expected Returns(%) Square of deviations
from expected return
Sqaure of deviations VARP

0.35

0.13

0.16

0.14

0.05

0.08

0.01

0.00

0.35

0.09

0.02

0.06

0.02

0.00

0.00

0.00

0.30

-0.05

-0.01

-0.03

-0.01

-0.10

0.01

0.00

      Portfolio Return =

0.06

   

0.01

 

 

Portfolio Variance = 0.01

Portfolio Standard Deviation = √0.07

 

 

 

k)     Weights of the Minimum Variance Portfolio (1.25 marks)

 

W* =VARB-COVAB /VARA+VARB-2COVAB

 

=0.0055-0.0043/0.0056+0.0055-2*0.0043

 

=0.48

W* = portion of investment in stock A

1       – W* = portion of investment in stock B = 1-0.48 = 0.52

 

 

 

 

 

l)      Proof that these weights lead to the Minimum Variance Portfolio

 

Variance with above weights =

VARP = 0.0056(0.48)+ 0.0055(0.52)2 +2(0.48)(0.52)(0.00434)  =0.0049

 

 

 

m)   Weights of the Optimal Risky Portfolio with a risk-free asset (1 mark)

 

=  Suppose stock B is risk free and giving the return of 0.04 or 4% as given in the question. Then STDB =0.08

 

 

WA             = 0.08-0.0043/0.0056+0.08-2*0.0043 = 0.98

WB         =1-0.98 = 0.02

 

 

 

n)     Proof that these weights lead to the Optimal Risky Portfolio (1.25 marks)

 

 

Variance with above weights is minimum as follows :

VARP = 0.0056(0.98)+ 0.08(0.02)2 +2(0.98)(0.02)(0.00434)  = 0.00558

 

  • o)     Discussion on what you would do with this portfolio (1 mark)

 

 

From the above calculation we can say that variance (0.0049) is less  in the portfolio when both are risky assets may be due to negative correlation than the variance (0.00558) in optimal risky portfolio.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 3. (15 marks)

 

Herbicide Ltd manufactures insecticide which is marketed in one and two litre bottles. The existing machinery owned by the company for the bottling of its product has now reached the end of its useful life, and the management of the company is deciding what equipment should be purchased to replace it. It is not necessary to replace the ancillary machinery which includes conveyor belts, washing and inspection machinery and other equipment.

 

Machines Under Consideration

 

The new bottle filling and capping machines being considered are:

1.    The ‘Bottle-Snap’.

2.    The ‘Seal’.

3.    The ‘Zip Cap’.

4.    The ‘Screw-Top’.

 

The ‘Bottle-Snap’ is an improved version of the existing equipment to be retired. This machine has a nominal capacity of 370 bottles per minute (bpm) for one litre bottles, or 125 bpm for two litre bottles.

 

The ‘Seal’ is a similar machine to the above, except that it has a much larger capacity. Its nominal capacity is 600 one litre bpm or 280 two litre bpm.

The ‘Zip-Cap’ uses tear-off caps and operates at a maximum (nominal) rate of 350 one litre bpm. This machine could be used to fill and seal two litre bottles, but with a greatly reduced production rate.

 

The ‘Screw-Top’ can be used to reseal bottles after the initial opening. The nominal capacity of this machine is 200 two litre bpm. This machine could be used to fill and seal one litre bottles.

 

Departmental managers have determined the following average production capacities based on the preceding nominal (maximum) capacities of each machine.

 

Marketing Considerations

 

Management considers that either the ‘Crown’ or ‘Zip-Cap’ could be used for sealing the one litre bottles. ‘Screw-Tops’ are believed to be uneconomical for small bottles. Either ‘Crown’ or Screw-Top’s’ are considered suitable for the two litre bottles. Zip-Caps are thought to be unsuitable for two litre bottles.

 

 

The demand for pesticides is very seasonal and sales are highest during the summer months. Because of the large amount of storage space required in relation to value, it is uneconomical to build up large stocks during the cooler months for sale during periods of peak demand.  It is therefore necessary to employ labour at penalty rates for evening and weekend shift work during periods of peak demand.

 

Sales

 

The present annual sales volume of the company is approximately 1,600,000 24-bottle crates of one litre bottles, and 1,400,000 12-bottle crates of two litre bottles.

 

The current selling price per crate for the company’s insecticides is as follows:

  • $1.20 per 24-bottle crate of one litre bottles
  • $1.60 per 12-bottle crate of two litre bottles

 

The additional costs involved in the production of two litre ‘Screw-Top’ bottles would require a selling price of $1.75 per 12-bottle crate if this type of bottle were to be marketed.

 

Conventional or New Seals

 

The final choice has been narrowed down to five alternative proposals which are set out in Exhibit 1.

 

EXHIBIT 1

Identification of Alternatives

 

The four types of equipment being considered could be combined in five different ways to achieve the desired production capacities.

 

ALTERNATIVE A

This alternative would involve the acquisition of two ‘Bottle-Snap’ machines, one to be used to fill and seal one litre bottles and the used to fill and seal two litre bottles.  The use of two such machines has the advantage of flexibility (the one litre machine could be modified to produce two litre bottles and vice versa).

 

ALTERNATIVE  B

One ‘Seal’ could be used to produce both one litre and two litre bottles.  A change in the size of bottles processed, however, requires an extensive changeover of parts, taking approximately four hours. If this machine were installed, batch production and the holding of larger inventories of finished products would be required.

 

ALTERNATIVE  C

A ‘Zip-Cap’ machine could be used for the production of one litre bottles, and a ‘Bottle-Snap’ for two litre bottles. The latter could be used to produce one litre bottles if required.

 

ALTERNATIVE  D

The one litre bottles could be processed using a ‘Bottle-Snap’ while the two litre bottles could be produced with a ‘Scru-Top’. The former could be used to produce two litre ‘Seal’ bottles if required.

 

ALTERNATIVE  E

The final alternative is to produce one litre bottles using a ‘Zip-Cap’ and the two litre bottles using a ‘Scru-Top’.

 

Financial and Operating Data

The Accountant for the company has prepared a schedule showing the initial costs of the alternative machines, together with expected operating costs and other relevant data. This information is reproduced in Exhibit 2.

 

EXHIBIT 2

Identification of Costs

 

Notes

a          An initial investment allowance of 20 per cent is allowable for taxation purposes on the initial investment and installation costs.

Depreciation, at the rate of 20 per cent per annum (straight line), is allowable for tax purposes on all three items of expenditure required for acquisition, installation and parts inventory.

  1. Annual fixed operating costs exclude depreciation.
  2. Variable operating costs exclude taxation expenses. “Normal” variable operating costs per crate are those estimated for production at normal rates of pay. “Penalty” variable operating costs per crate are those estimated for production during periods when penalty rates of pay apply (late shifts and weekends)

 


The Production Manager has prepared estimates of the total annual production hours required to meet expected sales for each of the five alternative proposals. These estimates are based on the expected average rate of production per hour, and separate ‘normal’ production hours from ‘penalty’ production hours. The Production Manager’s estimates are reproduced in Exhibit 3.

 

EXHIBIT 3

Production Hour Estimates

 

The company uses the net present value method in its capital budgeting decisions. The after tax required rate of return is 10%. Income tax rates for simplicity are 50%. Assume that any taxation implications occur at the time of the relevant cash flow or in the case of depreciation, in the year of the depreciation claim. Assume also that all cash flows take place at the end of each period and that inflation is zero.

 

Required

 

1)     Show the cash flows for each alternative proposal listed in Exhibit 1.

2)     Compute the Net Present Value, Payback Period and the Internal Rates of Return for each alternative.

3)     On the basis of your analysis in question 2, which of the alternatives would you recommend?

 

 

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

ALTERNATIVE A

 

 

Cash flows 1-7 years

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

-48000

-96000

           
Installation costs

-2500

-5000

           
Spare parts & accessories

-1000

-2000

           
Annual fixed operating costs

-18000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.148*601.25*2000

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

Per 12-Two litre bottles($) 1.543*601*668

-619722.805

-619722.805

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

Penalty                
Per 24 One litre bottles($) 1.156*400*2000

-924800

-924800

-924800

-924800

-924800

-924800

-924800

Per 12-Two litre bottles($) 1.551*400*1500

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$

3000

       

3000

   
Residual Value

6500

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1604135

             
Per 12-Two litre bottles($)

1400000

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

8-15 years cash flow

 

 

 

 

 

 

 

  Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                 
Initial Investment                
Installation costs                
Spare parts & accessories                
Annual fixed operating costs

-36000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($)

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

Per 12-Two litre bottles($)

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

Penalty                
Per 24 One litre bottles($)

-924800

-924800

-924800

-924800

-924800

-924800

-924800

-924800

Per 12-Two litre bottles($)

-930600

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$    

3000

       

3000

Residual Value              

6500

(end of 15 year life)                
Production                
Per 24 One litre bottles($)                
Per 12-Two litre bottles($)                
Sales Reveune                
Per 24 One litre bottles($)

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($)

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ALTERNATIVE B

 

 

 

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

65000

-65000

           
Installation costs

3500

-3500

           
Spare parts & accessories

1000

-1000

           
Annual fixed operating costs

25000

-25000

-25000

-25000

-25000

-25000

-25000

-25000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.153*1608000

-1274642

-1274642

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

Per 12-Two litre bottles($) 1.535*1411200

-771337.5

-771338

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

Penalty                
Per 24 One litre bottles($) 1.161*1608000

-1053259

-1053259

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

Per 12-Two litre bottles($) 1.543*1411200

-777672

-777672

-777672

-777672

-777672

-777672

-777672

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$

5500

       

5500

   
Residual Value

10000

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1608000

             
Per 12-Two litre bottles($)

1411200

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

    Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                   
Initial Investment

65000

               
Installation costs

3500

               
Spare parts & accessories

1000

               
Annual fixed operating costs

25000

-25000

-25000

-25000

-25000

-25000

-25000

-25000

-25000

Variable Opearting costs                  
Normal                  
Per 24 One litre bottles($) 1.153*1608000

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

Per 12-Two litre bottles($) 1.535*1411200

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

Penalty                  
Per 24 One litre bottles($) 1.161*1608000

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

Per 12-Two litre bottles($) 1.543*1411200

-777672

-777672

-777672

-777672

-777672

-777672

-777672

-777672

Overhaul and Repair of Equipment                  
Every 3 years$                  
Every 5 years$

5500

   

5500

       

5500

Residual Value

10000

             

10000

(end of 15 year life)                  
Production                  
Per 24 One litre bottles($)

1608000

               
Per 12-Two litre bottles($)

1411200

               
Sales Reveune                  
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

ALTERNATIVE C

 

1-7 Year Cash out flows and Cash Inflows

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

-97500

           
Installation costs

-5000

           
Spare parts & accessories

-2000

           
Annual fixed operating costs

-36000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.151*1616877.5

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

Per 12-Two litre bottles($) 1.535*1400000

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

Penalty                
Per 24 One litre bottles($) 1.159*400*2000

-927200

-927200

-927200

-927200

-927200

-927200

-927200

Per 12-Two litre bottles($) 1.551*1411200

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$

6000

       

6000

   
Residual Value

6500

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1616877.5

             
Per 12-Two litre bottles($)

1400000

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

 

 

 

 

 

 

8-15 Years Cash flows

 

  Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                 
Initial Investment                
Installation costs                
Spare parts & accessories                
Annual fixed operating costs

-36000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($)

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

Per 12-Two litre bottles($)

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

Penalty                
Per 24 One litre bottles($)

-927200

-927200

-927200

-927200

-927200

-927200

-927200

-927200

Per 12-Two litre bottles($)

-930600

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$    

6000

       

6000

Residual Value              

6500

(end of 15 year life)                
Production                
Per 24 One litre bottles($)                
Per 12-Two litre bottles($)                
Sales Reveune                
Per 24 One litre bottles($)

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($)

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 


SOLUTION

 

School of Business

 

 

 

BUACC3701:  Financial Management

 

 

 

 

Semester 1 – 2012

ASSIGNMENT

 

 

 

Question 1. (5 marks)

 

a)     Solution :

 

Impact on EPS : Equity Financing

 

350000 +100000 = 450000

 

Deduct interest = 450000-16000 = 434000

 

Deduct pref. Div= 434000-150000 = 284000

 

Deduct tax = 284000-85200 = 198800

 

Current EPS = 198800/250000 = 0.7952

 

New EPS = 198800/500000 =0.3976

 

 

 

 

b)     Solution :

 

Impact on EPS: Debt Financing

 

350000 +100000 = 450000

 

Deduct interest = 450000-16000-50000 = 384000

Deduct pref. Div= 384000-150000 = 234000

 

Deduct tax = 234000-70200 = 163800

 

New EPS = 163800/2500000 = 0.6552

Solution :

 

If Weather is good

 

Impact of equity financing

New EBIT

950000

EBT

934000

After Pref

784000

Tax

235200

PAT

548800

Old EPS

2.1952

New EPS

1.0976

 

 

 

Impact of Debt finanacing

New EBIT

950000

EBT

934000

After Pref

784000

Tax

235200

PAT

548800

Old EPS

2.1952

New EPS

1.0976

 

If Weather is Bad

Equity Financing

New EBIT

670000

EBT

654000

After Pref

504000

Tax

151200

PAT

352800

Old EPS

1.4112

New EPS

0.7056

 

Debt Financing

New EBIT

670000

EBT

604000

After Pref

454000

Tax

136200

PAT

317800

Old EPS

1.2712

New EPS

1.2712


 

Question 2. (10 marks)

 

 

SOLUTION

 

a)     Expected Return of Stock A .

 

E(RA) = (0.13×0.35) + (0.09×0.35) + (-0.05×0.30) = 0.062 or 6.2%

 

b)     Expected Return of Stock B.

 

E(RB) = (0.16×0.35)+(0.02×0.35)+(-0.01×0.30) =0.06 or 6 %

 

 

c)     Standard Deviation of Stock A

 

VARA = [0.13(0.35-0.062)2] + [0.09(0.35-0.062) 2] + [-0.050(.30-0.062) 2] = 0.005656

STDA =√0.005656  = 0.075206

 

 

d)     Standard Deviation of Stock B

 

VARB= 0.16(0.35-0.06) 2+ 0.02(0.35-0.06) 2+-0.01(0.30-0.06) 2  =0.00553

 

STDB = √0.00553   = 0.074364

 

 

 

e)     Coefficient of Variation of Stock A.

 

Coefficient of Variation of Stock A = [STDA / E(RA) ]

 

= [0.075206/0.062] = 1.213006

 

 

 

f)      Coefficient of Variation of Stock B.

 

Coefficient of Variation of Stock B = [STDB / E(RB) ]

 

= [0.074364/0.06]×100 = 1.239399

 

 

g)     Covariance of Stocks A and B (.5 mark)

 

     

Deviations from
expected returns

Product of deviation
& probability
Probability Stock A Stock B Stock A Stock B  

0.35

0.13

0.16

0.068

0.1

0.00238

0.35

0.09

0.02

0.028

-0.04

-0.000392

0.3

-0.05

-0.01

-0.112

-0.07

0.002352

   E(R) =0.062  E(R ) =0.06    

0.00434

 

 

CovAB     = 0.00434

 

h)     Correlation Coefficient of Stocks A and B (.5 mark)

 

Correlation A,B = Covariance AB / STDA×STDB

= 0.00434 /0.075206×0.074364 = 0.78

 

i)      Portfolio Return

 

Probability Stock A Stock B

Combined Returns (%)

Expected Returns(%)

0.35

0.13

0.16

0.142

0.0497

0.35

0.09

0.02

0.062

0.0217

0.3

-0.05

-0.01

-0.034

-0.0102

     Portfolio Return =

0.0612

 

 

 

j)      Portfolio Standard Deviation and Variance

 

Probability Stock A Stock B

Combined Returns (%)

Expected Returns(%) Square of deviations
from expected return
Sqaure of deviations VARP

0.35

0.13

0.16

0.14

0.05

0.08

0.01

0.00

0.35

0.09

0.02

0.06

0.02

0.00

0.00

0.00

0.30

-0.05

-0.01

-0.03

-0.01

-0.10

0.01

0.00

      Portfolio Return =

0.06

   

0.01

 

 

Portfolio Variance = 0.01

Portfolio Standard Deviation = √0.07

 

 

 

k)     Weights of the Minimum Variance Portfolio (1.25 marks)

 

W* =VARB-COVAB /VARA+VARB-2COVAB

 

=0.0055-0.0043/0.0056+0.0055-2*0.0043

 

=0.48

W* = portion of investment in stock A

1       – W* = portion of investment in stock B = 1-0.48 = 0.52

 

 

 

 

 

l)      Proof that these weights lead to the Minimum Variance Portfolio

 

Variance with above weights =

VARP = 0.0056(0.48)+ 0.0055(0.52)2 +2(0.48)(0.52)( 0.00434)  =0.0049

 

 

 

m)   Weights of the Optimal Risky Portfolio with a risk-free asset (1 mark)

 

=  Suppose stock B is risk free and giving the return of 0.04 or 4% as given in the question. Then STDB =0.08

 

 

WA             = 0.08-0.0043/0.0056+0.08-2*0.0043 = 0.98

WB         =1-0.98 = 0.02

 

 

 

n)     Proof that these weights lead to the Optimal Risky Portfolio (1.25 marks)

 

 

Variance with above weights is minimum as follows :

VARP = 0.0056(0.98)+ 0.08(0.02)2 +2(0.98)(0.02)( 0.00434)  = 0.00558

 

  • o)     Discussion on what you would do with this portfolio (1 mark)

 

 

From the above calculation we can say that variance (0.0049) is less  in the portfolio when both are risky assets may be due to negative correlation than the variance (0.00558) in optimal risky portfolio.

 

Question 3. (15 marks)

 

 

SOLUTION

 

 

 

 

 

CASH FLOWS

 

 

 

 

ALTERNATIVE A

 

 

Cash flows 1-7 years

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

-48000

-96000

           
Installation costs

-2500

-5000

           
Spare parts & accessories

-1000

-2000

           
Annual fixed operating costs

-18000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.148*601.25*2000

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

Per 12-Two litre bottles($) 1.543*601*668

-619722.805

-619722.805

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

Penalty                
Per 24 One litre bottles($) 1.156*400*2000

-924800

-924800

-924800

-924800

-924800

-924800

-924800

Per 12-Two litre bottles($) 1.551*400*1500

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$

3000

       

3000

   
Residual Value

6500

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1604135

             
Per 12-Two litre bottles($)

1400000

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

8-15 years cash flows

 

 

  Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                 
Initial Investment                
Installation costs                
Spare parts & accessories                
Annual fixed operating costs

-36000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($)

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

Per 12-Two litre bottles($)

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

-619722.81

Penalty                
Per 24 One litre bottles($)

-924800

-924800

-924800

-924800

-924800

-924800

-924800

-924800

Per 12-Two litre bottles($)

-930600

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$    

3000

       

3000

Residual Value              

6500

(end of 15 year life)                
Production                
Per 24 One litre bottles($)                
Per 12-Two litre bottles($)                
Sales Reveune                
Per 24 One litre bottles($)

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($)

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ALTERNATIVE B

 

 

 

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

65000

-65000

           
Installation costs

3500

-3500

           
Spare parts & accessories

1000

-1000

           
Annual fixed operating costs

25000

-25000

-25000

-25000

-25000

-25000

-25000

-25000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.153*1608000

-1274642

-1274642

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

Per 12-Two litre bottles($) 1.535*1411200

-771337.5

-771338

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

Penalty                
Per 24 One litre bottles($) 1.161*1608000

-1053259

-1053259

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

Per 12-Two litre bottles($) 1.543*1411200

-777672

-777672

-777672

-777672

-777672

-777672

-777672

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$

5500

       

5500

   
Residual Value

10000

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1608000

             
Per 12-Two litre bottles($)

1411200

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                   
Initial Investment

65000

               
Installation costs

3500

               
Spare parts & accessories

1000

               
Annual fixed operating costs

25000

-25000

-25000

-25000

-25000

-25000

-25000

-25000

-25000

Variable Opearting costs                  
Normal                  
Per 24 One litre bottles($) 1.153*1608000

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

-1274641.5

Per 12-Two litre bottles($) 1.535*1411200

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

-771337.5

Penalty                  
Per 24 One litre bottles($) 1.161*1608000

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

-1053259.2

Per 12-Two litre bottles($) 1.543*1411200

-777672

-777672

-777672

-777672

-777672

-777672

-777672

-777672

Overhaul and Repair of Equipment                  
Every 3 years$                  
Every 5 years$

5500

   

5500

       

5500

Residual Value

10000

             

10000

(end of 15 year life)                  
Production                  
Per 24 One litre bottles($)

1608000

               
Per 12-Two litre bottles($)

1411200

               
Sales Reveune                  
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

ALTERNATIVE C

 

1-7 Year Cash out flows and Cash Inflows

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

-97500

           
Installation costs

-5000

           
Spare parts & accessories

-2000

           
Annual fixed operating costs

-36000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.151*1616877.5

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

Per 12-Two litre bottles($) 1.535*1400000

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

Penalty                
Per 24 One litre bottles($) 1.159*400*2000

-927200

-927200

-927200

-927200

-927200

-927200

-927200

Per 12-Two litre bottles($) 1.551*1411200

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$

6000

       

6000

   
Residual Value

6500

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1616877.5

             
Per 12-Two litre bottles($)

1400000

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

 

 

 

 

 

 

8-15 Years Cash flows

 

  Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                 
Initial Investment                
Installation costs                
Spare parts & accessories                
Annual fixed operating costs

-36000

-36000

-36000

-36000

-36000

-36000

-36000

-36000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($)

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

Per 12-Two litre bottles($)

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

-2418241.3

Penalty                
Per 24 One litre bottles($)

-927200

-927200

-927200

-927200

-927200

-927200

-927200

-927200

Per 12-Two litre bottles($)

-930600

-930600

-930600

-930600

-930600

-930600

-930600

-930600

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$    

6000

       

6000

Residual Value              

6500

(end of 15 year life)                
Production                
Per 24 One litre bottles($)                
Per 12-Two litre bottles($)                
Sales Reveune                
Per 24 One litre bottles($)

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($)

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ALTERNATIVE D

1-7 Years Cash flows

 

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

154000

-154000

           
Installation costs

7000

-7000

           
Spare parts & accessories

4000

-4000

           
Annual fixed operating costs

38000

-38000

38000

-38000

38000

-38000

38000

-38000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.148*601.25*2000

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

Per 12-Two litre bottles($) 1.645*601.25*668

-660689.58

-660689.58

-660689.58

-660689.58

-660689.58

-660689.58

-660689.58

Penalty                
Per 24 One litre bottles($)

1622358

-1622358

1622358

-1622358

1622358

-1622358

1622358

-1622358

Per 12-Two litre bottles($)

0

0

0

0

0

0

0

0

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$

3000

       

3000

   
Residual Value

6500

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1604135

             
Per 12-Two litre bottles($)

1401000

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

   

357482.4

3843198

522482.4

3843198

525482.4

3843198

522482.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1-8 Years cash flows

 

  Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                 
Initial Investment                
Installation costs                
Spare parts & accessories                
Annual fixed operating costs

38000

-38000

38000

-38000

38000

-38000

38000

-38000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($)

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

-1380470

Per 12-Two litre bottles($)

-660689.58

-660689.58

-660689.58

-660689.58

-660689.58

-660689.58

-660689.58

-660689.58

Penalty                
Per 24 One litre bottles($)

1622358

-1622358

1622358

-1622358

1622358

-1622358

1622358

-1622358

Per 12-Two litre bottles($)

0

0

0

0

0

0

0

0

Overhaul and Repair of Equipment                
Every 3 years$                
Every 5 years$    

3000

       

3000

Residual Value              

6500

(end of 15 year life)                
Production                
Per 24 One litre bottles($)                
Per 12-Two litre bottles($)                
Sales Reveune                
Per 24 One litre bottles($)

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($)

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

3843198

522482.4

3846198

522482.4

3843198

522482.4

3843198

531982.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ALTERNATIVE E

 

 

    Year 1 Year 2 Year 3 Year 4 Year 5 Year6 Year 7
    Cashflows            
Initial Investment

155500

-155500

           
Installation costs

7000

-7000

           
Spare parts & accessories

4000

-4000

           
Annual fixed operating costs

38000

-38000

38000

-38000

38000

-38000

38000

-38000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($) 1.151*586.25*2758

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

Per 12-Two litre bottles($) 1.645*586.25*758

-2659763.5

-2659763.5

-2659763.5

-2659763.5

-2659763.5

-2659763.5

-2659763.5

Penalty                
Per 24 One litre bottles($)

1623759

-1623759

1623759

-1623759

1623759

-1623759

1623759

-1623759

Per 12-Two litre bottles($)

0

0

0

0

0

0

0

0

Overhaul and Repair of Equipment                
Every 3 years$

5000

   

-5000

   

-5000

 
Every 5 years$

3000

       

-3000

   
Residual Value

15000

             
(end of 15 year life)                
Production                
Per 24 One litre bottles($)

1604135

             
Per 12-Two litre bottles($)

1401000

             
Sales Reveune                
Per 24 One litre bottles($) 1600000*1.24

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($) 1400000*1.60

2240000

2240000

2240000

2240000

2240000

2240000

2240000

   

-2125048

1364970

-1963548

1364970

-1961548

1359970

-1958548

 

 

 

 

 

 

 

 


  Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15
                 
Initial Investment                
Installation costs                
Spare parts & accessories                
Annual fixed operating costs

38000

-38000

38000

-38000

38000

-38000

38000

-38000

Variable Opearting costs                
Normal                
Per 24 One litre bottles($)

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

-1861026

Per 12-Two litre bottles($)

-2659763.5

-2659763.5

-2659763.5

-2659763.5

-2659763.5

-2659763.5

-2659763.5

-2659763.5

Penalty                
Per 24 One litre bottles($)

1623759

-1623759

1623759

-1623759

1623759

-1623759

1623759

-1623759

Per 12-Two litre bottles($)

0

0

0

0

0

0

0

0

Overhaul and Repair of Equipment                
Every 3 years$  

-5000

   

-5000

   

-5000

Every 5 years$    

-3000

       

-3000

Residual Value              

15000

(end of 15 year life)                
Production                
Per 24 One litre bottles($)                
Per 12-Two litre bottles($)                
Sales Reveune                
Per 24 One litre bottles($)

1984000

1984000

1984000

1984000

1984000

1984000

1984000

1984000

Per 12-Two litre bottles($)

2240000

2240000

2240000

2240000

2240000

2240000

2240000

2240000

 

1364970

-1963548

1361970

-1958548

1359970

-1958548

1364970

-1951548

LF36

“The presented piece of writing is a good example how the academic paper should be written. However, the text can’t be used as a part of your own and submitted to your professor – it will be considered as plagiarism.

But you can order it from our service and receive complete high-quality custom paper.  Our service offers   ACCOUNTING essay sample that was written by professional writer. If you like one, you have an opportunity to buy a similar paper. Any of the academic papers will be written from scratch, according to all customers’ specifications, expectations and highest standards.”

Please  Click on the  below links to Chat Now  or fill the Order Form !

order-now-new                                                                                  chat-new (1) 

 

 

NPV based on the above cash flows :

 

 

 

Alternate A = $485,673.08

 

Alternative B = $3,337,600.00

Alternate C =$3,337,600.00

Alternate D = 4,621,800.00

ALTERNATIVE E = $572,645.58

 

 

 

 

 

 

 

REFERENCES

 

Porterfield,James C.T. (1965). investment Decision and Capital Costs,Prentice-Hall.

 

Reichelstein, S. (1997): Investment Decisions and Managerial Performance Evaluation, in: Review of Accounting Studies, 2 (2), p. 157-180.

 

 

 

On the basis of above calculation NPV is highest in Alternative E and payback is also shortest in the same .