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

 

b)     Expected Return of Stock B.

 

E(R_B) = (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(R_A) ]

 

= [0.075206/0.062] = 1.213006

 

 

 

f)      Coefficient of Variation of Stock B.

 

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

 

= [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

 

 

Cov_{AB     = 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)²  + 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

 

 

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

W_B         =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)²  + 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

 

 

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

 

b)     Expected Return of Stock B.

 

E(R_B) = (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(R_A) ]

 

= [0.075206/0.062] = 1.213006

 

 

 

f)      Coefficient of Variation of Stock B.

 

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

 

= [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

 

 

Cov_{AB     = 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)²  + 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

 

 

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

W_B         =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)²  + 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

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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 .