Investment appraisal decisions — practice questions

Quantitative comparison

Analysis

• NPV favours Beta (+$7 000 more value).
• Payback favours Alpha (3.2 < 4 target; Beta exceeds 4 years).
• ARR favours Alpha but is less reliable than NPV.

Recommendation (typical) Accept Beta if the firm prioritises shareholder wealth (NPV criterion) and can finance the longer capital lock-in. If the case stresses cash shortage, Alpha may be justified despite lower NPV — state this explicitly from the scenario.

Step 1: Calculate Appraisal Metrics for Each Project

Project X Calculations:

• Payback Period:
  • Cumulative cash flow after Year 2 = $150,000 +$180,000 = $330,000$
  • Amount needed to payback in Year 3 = $500,000 -$330,000 = $170,000$
  • Payback = 2 years + ($170,000 /$200,000) = 2.85 years
• Average Rate of Return (ARR):
  • Total Net Cash Flow = $150k +$180k + $200k +$150k + $100k =$780,000
  • Total Profit = Total Inflows - Initial Cost = $780,000 -$500,000 = $280,000$
  • Average Annual Profit = $280,000 / 5 years = $56,000
  • ARR = (Average Annual Profit / Initial Cost) * 100 = ($56,000 /$500,000) * 100 = 11.2%
• Net Present Value (NPV) at 10%: (Discount factors: Y1=0.909, Y2=0.826, Y3=0.751, Y4=0.683, Y5=0.621)
  • Y1: $150,000 * 0.909 =$136,350
  • Y2: $180,000 * 0.826 =$148,680
  • Y3: $200,000 * 0.751 =$150,200
  • Y4: $150,000 * 0.683 =$102,450
  • Y5 (incl. scrap): ($100,000 +$50,000) * 0.621 = $93,150$
  • Total PV of Inflows = $630,830$
  • NPV = $630,830 -$500,000 = **+$130,830**$

Project Y Calculations:

• Payback Period:
  • Cumulative cash flow after Year 3 = $120k +$130k + $140k =$390,000
  • Amount needed to payback in Year 4 = $400,000 -$390,000 = $10,000$
  • Payback = 3 years + ($10,000 /$120,000) = 3.08 years
• Average Rate of Return (ARR):
  • Total Net Cash Flow = $120k +$130k + $140k +$120k + $100k =$610,000
  • Total Profit = $610,000 -$400,000 = $210,000$
  • Average Annual Profit = $210,000 / 5 years = $42,000
  • ARR = ($42,000 /$400,000) * 100 = 10.5%
• Net Present Value (NPV) at 10%:
  • Y1: $120,000 * 0.909 =$109,080
  • Y2: $130,000 * 0.826 =$107,380
  • Y3: $140,000 * 0.751 =$105,140
  • Y4: $120,000 * 0.683 =$81,960
  • Y5: $100,000 * 0.621 =$62,100
  • Total PV of Inflows = $465,660$
  • NPV = $465,660 -$400,000 = **+$65,660**$

Step 2: Summarise and Analyse Results

Quantitative Analysis: Project X is superior on all three quantitative measures. It pays back faster, offers a higher average return, and most importantly, generates significantly more value for shareholders (NPV is almost double that of Project Y).

Step 3: Integrate Qualitative Factors and Make a Justified Recommendation

Qualitative Factors:

• Risk: Project X involves a new machine, which may have unforeseen technical issues and requires significant staff retraining, increasing implementation risk. Project Y is a software upgrade for existing equipment, which is likely lower risk.
• Strategic Fit: If Innovate Ltd.'s strategy is to be a market leader in production efficiency and technology, Project X is a better strategic fit. Project Y is more conservative, focusing on incremental improvement.

Recommendation: Innovate Ltd. should choose Project X.

Justification: Although Project X has a higher initial outlay and potentially higher implementation risk, its financial superiority is overwhelming. The NPV of +$130,830 is substantially higher than Project Y's, indicating it will add significantly more value to the business. This aligns with the primary corporate objective of maximising shareholder wealth. While the risks associated with a new machine are real, they can be mitigated through careful project management, phased implementation, and a comprehensive staff training program. The strategic benefit of adopting new, more efficient technology likely outweighs the short-term disruption. Therefore, based on a balanced consideration of both quantitative and qualitative factors, Project X is the recommended investment.