(a) When the council is described as “risk averse,” it means that they are cautious and prefer to avoid taking on unnecessary risks. Expected values help in this context by providing a quantitative measure of the potential outcomes of an investment. By calculating expected values, the council can assess the potential returns and make more informed decisions based on the likelihood of different scenarios.

(b) To calculate the expected value of the annual contribution due to the refurbishment work, we multiply each demand level’s increase in contribution by its respective probability:

Expected value = (High demand × High probability) + (Medium demand × Medium probability) + (Low demand × Low probability) Expected value = (£250,000 × 0.25) + (£200,000 × 0.40) + (£150,000 × 0.35) Expected value = £62,500 + £80,000 + £52,500 Expected value = £195,000

Therefore, the expected value of the annual contribution due to refurbishment work is £195,000.

© To calculate net present value (NPV), we need to discount each year’s expected cash flow using a discount rate of 6%. The NPV formula is:

NPV = Σ(Ct / (1+r)^t)

Where Ct is the cash flow at time t and r is the discount rate.

For simplicity, let’s assume a perpetuity with an annual cash flow equal to our calculated expected value (£195,000):

NPV = [£195,000 / (1+0.06)] + [£195,000 / ((1+0.06)^2)] + [£195,000 / ((1+0.06)^3)] + …

Using this perpetual formula for NPV calculation:

NPV = (£195,000 / 0.06) NPV ≈ £3,250,000

The internal rate of return (IRR) is the discount rate at which the NPV becomes zero. To calculate IRR, we can use a financial calculator or spreadsheet software. Assuming an annual cash flow of £195,000:

IRR ≈ 10.56%

Therefore, the net present value (NPV) of the proposed refurbishment scheme is approximately £3,250,000, and the internal rate of return (IRR) is approximately 10.56%.

(d) Sensitivity analysis shows how sensitive a project’s outcome is to changes in certain variables. In this case, we will analyze the sensitivity of the project to changes in the initial cost and discount rate.

(i) Sensitivity to Initial Cost: We can assess how changes in the initial cost impact NPV and IRR by recalculating them with different values for the initial cost. This helps understand if small variations in costs significantly affect project viability.

(ii) Sensitivity to Discount Rate: By varying the discount rate, we can observe how it affects NPV and IRR. This helps assess if changing interest rates or alternative financing options could significantly alter project feasibility.

(e) Advantages of Sensitivity Analysis:

• It allows decision-makers to understand how uncertainties in key variables affect project outcomes.
• It provides insights into potential risks and opportunities associated with different scenarios.
• It assists in identifying critical factors that have a significant impact on project performance.

Disadvantages of Sensitivity Analysis:

• It assumes that changes in variables are independent when they may be correlated in reality.
• It does not consider interactions between multiple variables simultaneously.
• The results are based on assumptions and estimates, so they may not accurately reflect actual outcomes.

Overall, sensitivity analysis provides valuable information for decision-making but should be used alongside other techniques and judgment to make informed choices regarding investments.


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