Section C - Constructed Response

AquaNet Co is a public utility company evaluating the construction of a new water desalination plant. The project will last for 4 years.

Financial details:

1. Initial investment in plant and machinery is $50 million, payable immediately (Year 0).
2. The machinery will have a scrap value of $5 million at the end of Year 4.
3. Tax-allowable depreciation (capital allowances) is available at 25% per year on a reducing balance basis. A balancing charge or allowance will arise in Year 4.
4. Corporation tax is 30%, payable one year in arrears (i.e., Year 1 tax is paid in Year 2).
5. Expected sales volume is 10 million cubic meters of water per year.
6. Current selling price is $2.00 per cubic meter. This is expected to inflate by 4% per year.
7. Current variable costs are $0.80 per cubic meter. These are expected to inflate by 5% per year.
8. Fixed costs (excluding depreciation) are $3 million per year in current terms, inflating at 3% per year.
9. Working capital of $4 million is required immediately (Year 0) and will be fully recovered at the end of Year 4.
10. AquaNet's nominal after-tax cost of capital is 10%.

Required:
(a) Calculate the Net Present Value (NPV) of the desalination plant project. (14 marks)
(b) Discuss the difference between sensitivity analysis and expected value (probability) analysis in assessing project risk, and recommend which is more appropriate for AquaNet Co. (6 marks)

Part (a) NPV Calculation: 1. Inflated Cash Flows ($m): Year 1: Sales = 10 * 2.00 * 1.04 = 20.80. VC = 10 * 0.80 * 1.05 = 8.40. FC = 3 * 1.03 = 3.09. Net Op CF = 9.31 Year 2: Sales = 20.80 * 1.04 = 21.63. VC = 8.40 * 1.05 = 8.82. FC = 3.09 * 1.03 = 3.18. Net Op CF = 9.63 Year 3: Sales = 21.63 * 1.04 = 22.50. VC = 8.82 * 1.05 = 9.26. FC = 3.18 * 1.03 = 3.28. Net Op CF = 9.96 Year 4: Sales = 22.50 * 1.04 = 23.40. VC = 9.26 * 1.05 = 9.72. FC = 3.28 * 1.03 = 3.38. Net Op CF = 10.30 2. Tax on Operating CF (30%, paid in arrears): Year 2 (on Y1): -2.79 Year 3 (on Y2): -2.89 Year 4 (on Y3): -2.99 Year 5 (on Y4): -3.09 3. Capital Allowances (CA) & Tax Savings (30%): Cost = 50. Y1 CA = 50 * 25% = 12.50. Tax saving in Y2 = 3.75 Y2 CA = 37.50 * 25% = 9.38. Tax saving in Y3 = 2.81 Y3 CA = 28.12 * 25% = 7.03. Tax saving in Y4 = 2.11 Y4 Balancing Allowance = WDV (21.09) - Scrap (5.00) = 16.09. Tax saving in Y5 = 4.83 4. Other Flows: Y0: Initial Investment = -50.00. Working Capital = -4.00. Y4: Scrap = +5.00. Working Capital Recovery = +4.00. 5. Total Net Cash Flows & Discounting (10%): Y0: -54.00 * 1.000 = -54.00 Y1: 9.31 * 0.909 = 8.46 Y2: (9.63 - 2.79 + 3.75) = 10.59 * 0.826 = 8.75 Y3: (9.96 - 2.89 + 2.81) = 9.88 * 0.751 = 7.42 Y4: (10.30 - 2.99 + 2.11 + 5.00 + 4.00) = 18.42 * 0.683 = 12.58 Y5: (-3.09 + 4.83) = 1.74 * 0.621 = 1.08 NPV = -54.00 + 8.46 + 8.75 + 7.42 + 12.58 + 1.08 = -15.71 million. The project has a negative NPV and should be rejected. Part (b) Discussion: Sensitivity analysis assesses how much a single variable (e.g., sales volume, discount rate) can change before the project's NPV becomes zero. It is useful for identifying the most critical variables but ignores the probability of such changes occurring and assumes variables change in isolation. Expected value (EV) analysis assigns probabilities to different possible outcomes to calculate a weighted average return. It is useful for repeated decisions where the long-run average will be achieved. Recommendation: A desalination plant is a massive, one-off infrastructure project. EV is less appropriate because the project will only be undertaken once; the 'average' outcome will not occur. Sensitivity analysis is more appropriate for AquaNet to understand the risk boundaries of this specific, single investment.