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Question:
1. Allocate the joint costs to the two products soda and chlorine using:

(a) The sales value at the split-off method
(b) The physical measure method

2. Allocate the joint costs to the two products Soda and Basalt using the net realizable method .

3. What is the gross margin for each product under each of the three methods of allocation?
Answer:
Answer to Requirement 1

The net present value of a project refers to the difference between the present value of the inflow of cash and the present value of the outflow of cash over a period of time. NPV essentially reflects the profitability of an investment project. Furthermore, the internal rate of return refers to the discount rate that essentially values the net present value (NPV) of all cash flows in regards to a particular project that is equal to zero. It should be noted here that the NPV and IRR are derived from the same formula. The issue presented in the question is that the two projects have been considered, Project A and B. An initial investment of AED 11,000 is required. The cash inflows occur at the end of each year. Therefore, the following computations have been carried out on the basis of the given considerations (Magni & Martin, 2017).

Req.1:

 

 

Year

Project A

Project B

0

AED -11,000

AED -11,000

1

AED 1,000

AED 5,000

2

AED 2,000

AED 4,000

3

AED 3,000

AED 3,000

4

AED 4,000

AED 2,000

5

AED 5,000

AED 1,000

Required Rate of Return

8%

8%

NPV

AED 338.09

AED 1,473.26

IRR

9.00%

14.93%

The above table that has been presented shows the net present value and the internal rate of return computations for both of the projects. The table deduces that the internal rate of return and the Net present value of the projects are greater in case of Project B in comparison to Project A. Therefore, the project, which the Company should accept, is Project B.

Answer to Requirement 2

 

Project A

Project B

Year

Annual Cash Flow

Cumulative Cash Flow

Annual Cash Flow

Cumulative Cash Flow

0

AED -11,000

AED -11,000

AED -11,000

AED -11,000

1

AED 1,000

AED -10,000

AED 5,000

AED -6,000

2

AED 2,000

AED -8,000

AED 4,000

AED -2,000

3

AED 3,000

AED -5,000

AED 3,000

AED 1,000

4

AED 4,000

AED -1,000

AED 2,000

AED 3,000

5

AED 5,000

AED 4,000

AED 1,000

AED 4,000

Payback Period

4.20

2.67

The payback period for each project refers to the time period that is needed by an investment project for the purpose of deriving the projected returns from the respective investment ventures. The payback period for Project A is 4.20 years and that for Project B is2.67 years.

 


In case the Company has the policy of accepting projects with 3 years or less, the company should accept the Project B.

Answer to Question 2
Answer to Requirement 1

Particulars

2019 Beginning

2019 Ending

2020 Ending

2021 Ending

2022 Ending

2023 Ending

Cash Inflow:

 

 

 

 

 

 

Option 1

AED 0

AED 6,000,000

AED 6,825,000

AED 7,717,500

AED 9,261,000

AED 10,939,556

Option 2

AED 0

AED 6,400,000

AED 7,175,000

AED 8,017,500

AED 9,461,000

AED 13,039,556

Option 3

AED 5,000,000

AED 6,600,000

AED 7,375,000

AED 8,217,500

AED 9,661,000

AED 21,239,556

Cash Outflow:

 

 

 

 

 

 

Option 1

AED 0

AED 0

AED 0

AED -400,000

AED -1,200,000

AED -2,000,000

Option 2

AED -25,000,000

AED -3,000,000

AED -3,000,000

AED -3,000,000

AED -3,000,000

AED -3,000,000

Option 3

AED -40,000,000

AED -2,000,000

AED -2,000,000

AED -2,000,000

AED -2,000,000

AED -2,000,000

Answer to Requirement 2
Option 1

Option 1:

 

 

 

 

 

 

Particulars

2019 Beginning

2019 Ending

2020 Ending

2021 Ending

2022 Ending

2023 Ending

Expected Sales Unit

 

60000

65000

70000

80000

90000

Production Level

 

65000

65000

65000

65000

65000

Additional Sourced-Out Unit

 

0

0

5000

15000

25000

Selling Price p.u.

 

AED 100

AED 105

AED 110

AED 116

AED 122

Initial Investment

AED 0

 

 

 

 

 

Sales Revenue

 

AED 6,000,000

AED 6,825,000

AED 7,717,500

AED 9,261,000

AED 10,939,556

Cost of Sourced Out Unit

 

AED 0

AED 0

AED -400,000

AED -1,200,000

AED -2,000,000

Net Operational Cash Flow

 

AED 6,000,000

AED 6,825,000

AED 7,317,500

AED 8,061,000

AED 8,939,556

Salvage Value

 

 

 

 

 

AED 0

Net Cash Flow

AED 0

AED 6,000,000

AED 6,825,000

AED 7,317,500

AED 8,061,000

AED 8,939,556

Discount Rate

10%

 

 

 

 

 

NPV

AED 25,135,745

 

 

 

 

 

Option 2

Option 2:

 

 

 

 

 

 

Particulars

2019 Beginning

2019 Ending

2020 Ending

2021 Ending

2022 Ending

2023 Ending

Expected Sales Unit

 

60000

65000

70000

80000

90000

Maximum Production Level

 

100000

100000

100000

100000

100000

Additional Production

 

40000

35000

30000

20000

10000

Normal Selling Price p.u.

 

AED 100

AED 105

AED 110

AED 116

AED 122

Lower Selling Price p.u.

 

AED 10

AED 10

AED 10

AED 10

AED 10

Initial Investment

AED -25,000,000

 

 

 

 

 

Normal Sales Revenue

 

AED 6,000,000

AED 6,825,000

AED 7,717,500

AED 9,261,000

AED 10,939,556

Sales at Lower Price

 

AED 400,000

AED 350,000

AED 300,000

AED 200,000

AED 100,000

Annual Operating Cost

 

AED -3,000,000

AED -3,000,000

AED -3,000,000

AED -3,000,000

AED -3,000,000

Net Operational Cash Flow

 

AED 3,400,000

AED 4,175,000

AED 5,017,500

AED 6,461,000

AED 8,039,556

Salvage Value

 

 

 

 

 

AED 2,000,000

Net Cash Flow

AED -25,000,000

AED 3,400,000

AED 4,175,000

AED 5,017,500

AED 6,461,000

AED 10,039,556

Discount Rate

10%

 

 

 

 

 

NPV

AED -3,674,756

 

 

 

 

 

Option 3

Option 3:

 

 

 

 

 

 

Particulars

2019 Beginning

2019 Ending

2020 Ending

2021 Ending

2022 Ending

2023 Ending

Expected Sales Unit

 

60000

65000

70000

80000

90000

Maximum Production Level

 

120000

120000

120000

120000

120000

Additional Production

 

60000

55000

50000

40000

30000

Normal Selling Price p.u.

 

AED 100

AED 105

AED 110

AED 116

AED 122

Lower Selling Price p.u.

 

AED 10

AED 10

AED 10

AED 10

AED 10

Cost of New Equipment

AED 40,000,000

 

 

 

 

 

Less: Sale of Old Equipment

AED 5,000,000

 

 

 

 

 

Initial Investment

AED -35,000,000

 

 

 

 

 

Normal Sales Revenue

 

AED 6,000,000

AED 6,825,000

AED 7,717,500

AED 9,261,000

AED 10,939,556

Sales at Lower Price

 

AED 600,000

AED 550,000

AED 500,000

AED 400,000

AED 300,000

Annual Operating Cost

 

AED -2,000,000

AED -2,000,000

AED -2,000,000

AED -2,000,000

AED -2,000,000

Net Operational Cash Flow

 

AED 4,600,000

AED 5,375,000

AED 6,217,500

AED 7,661,000

AED 9,239,556

Salvage Value

 

 

 

 

 

AED 10,000,000

Net Cash Flow

AED -35,000,000

AED 4,600,000

AED 5,375,000

AED 6,217,500

AED 7,661,000

AED 19,239,556

Discount Rate

10%

 

 

 

 

 

NPV

AED -4,114,470

 

 

 

 

 

The Net Present values of the three projects that have been computed shows the NPV of the three options. The NPV of option 1 reflects a positive value (AED 25,135,745) while the NPV of option 2 and that of option 3 reveals a negative figure of AED -3,674,756 and AED -4,114,470. This means that the option that should be used by the Company is Option 1. This is because it reflects a positive NPV. However, it should be noted here that the option 1 and the option 2 could also be considered by observing the following factors:

  • The production level of 65,000 units with the existing equipment has been sourced out at a cost of AED 80 per unit.
  • Moreover, the excess capacity in any of the five years period could be used for meeting the demands of other companies at a lower price. The lower price would result in ten dirhams per unit.
  • Therefore, in order to derive a positive net present value in case of Option 2 and Option 3 the lower price should be more than 10 dirhams per unit.
Answer to Question 3
Answer to Requirement 1(a)

Requirement 1.a:

Particulars

Amount

Cost of Material

AED 1,500,000

Conversion Cost

AED 500,000

Joint Cost

AED 2,000,000

 

Salt

Chlorine

Production (ton)

1500

1000

Market Selling Price per ton

AED 50

AED 150

Sales Value

AED 75,000

AED 150,000

Allocation of Joint Cost

AED 666,667

AED 1,333,333

Answer to Requirement 1 (b)

Requirement 1.b:

Particulars

Amount

Cost of Material

AED 1,500,000

Conversion Cost

AED 500,000

Joint Cost

AED 2,000,000

 

Salt

Chlorine

Production (ton)

1500

1000

Allocation of Joint Cost

AED 1,200,000

AED 800,000

Answer to Requirement 2

Particulars

Amount

Cost of Material

AED 1,500,000

Conversion Cost

AED 500,000

Joint Cost

AED 2,000,000

 

Salt

Basalt

Production (ton)

1500

1000

Market Selling Price per ton

AED 50

AED 250,000

Sales Value

AED 75,000

AED 250,000,000

Further processing cost

 

AED -90,000

Net Realizable Value

AED 75,000

AED 249,910,000

Allocation of Joint Cost

AED 600

AED 1,999,400

Answer to Question 3

Gross Margin under Split-Off Method:

 

 

Particulars

Soda

Chlorine

Basalt

Sales Revenue

AED 75,000

0

AED 250,000,000

Cost of Material & Conversion

AED -666,667

AED -1,333,333

 

Transfer Cost

 

AED 1,333,333

AED -1,333,333

Processing Cost

 

 

AED -90,000

Gross Margin

AED -591,667

AED 0

AED 248,576,667

Gross Margin %

-788.89%

0.00%

99.43%

Gross Margin under Physical Measure Method:

 

 

Particulars

Soda

Chlorine

Basalt

Sales Revenue

AED 75,000

AED 0

AED 250,000,000

Cost of Material & Conversion

AED -1,200,000

AED -800,000

 

Transfer Cost

 

AED 800,000

AED -800,000

Processing Cost

 

 

AED -90,000

Gross Margin

AED -1,125,000

AED 0

AED 249,110,000

Gross Margin %

-1500.00%

0.00%

99.64%

Gross Margin under NRV Method:

 

 

Particulars

Soda

Chlorine

Basalt

Sales Revenue

AED 75,000

AED 0

AED 250,000,000

Cost of Material & Conversion

AED -600

AED 0

AED -1,999,400

Transfer Cost

 

AED 0

AED 0

Processing Cost

 

 

AED -90,000

Gross Margin

AED 74,400

AED 0

AED 247,910,600

Gross Margin %

99.20%

0.00%

99.16%

 
 
References

Arjunan, K. C. (2017). IRR Performs Better than NPV: A Critical Analysis of Cases of Multiple IRR and Mutually Exclusive and Independent Investment Projects.

Ioana, A. D. R. I. A. N. (2016, February). Theoretical and experimental elements of investment business in Romania. In Economics and Education ISI Proceedings of the 12th International Conference on Educational Technologies (EDUTE ‘16), Proceedings of the 10th International Conference on Business Administration,(ICBA ‘16) (pp. 88-98).

Liu, J., Jin, F., Xie, Q., & Skitmore, M. (2017). Improving risk assessment in financial feasibility of international engineering projects: A risk driver perspective. International Journal of Project Management, 35(2), 204-211.

Magni, C. A., & Martin, J. (2017). The Reinvestment Rate Assumption Fallacy for IRR and NPV.

Rodrigues, S., Torabikalaki, R., Faria, F., Cafôfo, N., Chen, X., Ivaki, A. R., ... & Morgado-Dias, F. (2016). Economic feasibility analysis of small scale PV systems in different countries. Solar Energy, 131, 81-95.

Sultana, N. (2015). Conflicting Result between NPV and IRR: Which one is better?. International Journal of Research in Business and Technology, 7(1), 873-877.

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