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- 12 Marks
Question
DDB Limited has decided to set up a factory to process groundnuts into oil. The feasibility studies cost them GH¢35,000. The consultants have advised that the initial outlay will be GH¢250,000; however, they were unable to estimate the cash inflow due to the uncertain economic environment.
Required:
Using NPV as an appraisal technique, you are required to calculate:
i) The constant cash inflow needed to break even if the cost of capital is 15% and the project is to last for 10 years.
(4 marks)
ii) By how much should the cash inflow increase to break even if the cost of capital is increased to 20%. (4 marks)
iii) If the cash inflow is GH¢45,000, for how long should the project run to break even if the cost of capital is 15%.
(4 marks)
Answer
i) Constant Cash Inflow Needed to Break Even at 15% Cost of Capital:
- Initial outlay: GH¢250,000
- Annuity factor (15% for 10 years): 5.019
- Break-even cash inflow (CF) = GH¢250,000 / 5.019 = GH¢49,810.72
(Total: 4 marks)
ii) Cash Inflow Increase Needed to Break Even at 20% Cost of Capital:
- Initial outlay: GH¢250,000
- Annuity factor (20% for 10 years): 4.192
- Break-even cash inflow (CF) = GH¢250,000 / 4.192 = GH¢59,637.40
- Increase in cash inflow = GH¢59,637.40 – GH¢49,810.72 = GH¢9,826.68
- Percentage increase = (GH¢9,826.68 / GH¢49,810.72) × 100 = 19.7%
(Total: 4 marks)
iii) Duration Needed to Break Even at 15% Cost of Capital with GH¢45,000 Cash Inflow:
- Initial outlay: GH¢250,000
- Given cash inflow: GH¢45,000
- Required annuity factor (AF) = GH¢250,000 / GH¢45,000 = 5.556
- This annuity factor lies between years 12 (5.421) and 13 (5.583)
- Interpolating between year 12 and year 13:
- (0.135 / 0.162) × 12 = 0.833 year
- Therefore, the project should run for 12 years and 10 months to break even.
(Total: 4 marks)
- Tags: Break-even Analysis, Cost of Capital, Discounted Cash Flow, NPV, Project evaluation
- Level: Level 2
- Topic: Discounted cash flow
- Series: NOV 2016
- Uploader: Dotse