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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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