# Investment Appraisal for ZebraToon plc ## Project Cash Flows | SAR Millions | Project A | Project B | |--------------|-----------|-----------| | Initial | (160) | (175) | | Year 1 | 40 | 80 | | Year 2 | 50 | 50 | | Year 3 | 50 | 40 | | Year 4 | 85 | 30 | Cost of Capital = **9%** --- ## 1. **Payback Period** **Definition:** The time taken for cumulative cash flows to equal the initial investment. ### **Project A** - Year 1: 40 - Year 2: 50 (Cumulative: 40+50=90) - Year 3: 50 (Cumulative: 90+50=140) - Year 4: 85 (Cumulative: 140+85=225) **Initial Outlay:** 160 After 3 years: 140 recovered Remainder: 160-140 = 20 Year 4 inflow: 85 Fraction of Year 4: \( \frac{20}{85} \approx 0.24 \) **Payback Period = 3.24 years** --- ### **Project B** - Year 1: 80 - Year 2: 50 (Cumulative: 80+50=130) - Year 3: 40 (Cumulative: 130+40=170) - Year 4: 30 (Cumulative: 170+30=200) **Initial Outlay:** 175 After 3 years: 170 recovered Remainder: 175-170 = 5 Year 4 inflow: 30 Fraction of Year 4: \( \frac{5}{30} \approx 0.17 \) **Payback Period = 3.17 years** --- ## 2. **Accounting Rate of Return (ARR)** **Formula:** \[\text{ARR} = \frac{\text{Average Annual Profit}}{\text{Initial Investment}} \times 100\] Assume no depreciation (since no scrap value or asset life given): Average Annual Cash Flow = Total Cash Flow / 4 ### **Project A** - Total Cash Inflow = 40+50+50+85 = 225 - Average = 225/4 = 56.25 - ARR = \( \frac{56.25}{160} \times 100 = 35.16\% \) ### **Project B** - Total Cash Inflow = 80+50+40+30 = 200 - Average = 200/4 = 50 - ARR = \( \frac{50}{175} \times 100 = 28.57\% \) --- ## 3. **Net Present Value (NPV)** \[ NPV = \sum \frac{\text{Cash Flow}_t}{(1+r)^t} - \text{Initial Investment} \] Where \( r = 9\% \) ### **Discount Factors at 9%:** | Year | Factor | |------|---------| | 1 | 0.9174 | | 2 | 0.8417 | | 3 | 0.7722 | | 4 | 0.7084 | --- ### **Project A** \[ \begin{align*} \text{NPV}_A &= (40 \times 0.9174) + (50 \times 0.8417) + (50 \times 0.7722) + (85 \times 0.7084) - 160 \\ &= 36.70 + 42.09 + 38.61 + 60.21 - 160 \\ &= 177.61 - 160 \\ &= \boxed{17.61} \end{align*} \] --- ### **Project B** \[ \begin{align*} \text{NPV}_B &= (80 \times 0.9174) + (50 \times 0.8417) + (40 \times 0.7722) + (30 \times 0.7084) - 175 \\ &= 73.39 + 42.09 + 30.89 + 21.25 - 175 \\ &= 167.62 - 175 \\ &= \boxed{-7.38} \end{align*} \] --- ## 4. **Internal Rate of Return (IRR)** Set NPV = 0, solve for r. Use interpolation between 2 rates. ### **Project A** Already positive at 9%. Try 15% (Discount Factors: 0.870, 0.756, 0.658, 0.572): \[ \begin{align*} \text{NPV}_{A,15\%} &= (40 \times 0.870) + (50 \times 0.756) + (50 \times 0.658) + (85 \times 0.572) - 160 \\ &= 34.80 + 37.80 + 32.90 + 48.62 - 160 \\ &= 154.12 - 160 = -5.88 \end{align*} \] - At 9%: NPV = 17.61 - At 15%: NPV = -5.88 \[ \text{IRR}_A = 9\% + \left(\frac{17.61}{17.61+5.88}\right) \times (15-9) = 9 + \left(\frac{17.61}{23.49}\right) \times 6 \approx 9 + 4.5 = \boxed{13.5\%} \] --- ### **Project B** NPV at 9% = -7.38 (already negative). Try 5% (Discount factors: 0.952, 0.907, 0.864, 0.823): \[ \begin{align*} \text{NPV}_{B,5\%} &= (80 \times 0.952) + (50 \times 0.907) + (40 \times 0.864) + (30 \times 0.823) - 175 \\ &= 76.16 + 45.35 + 34.56 + 24.69 - 175 \\ &= 180.76 - 175 = 5.76 \end{align*} \] - At 5%: NPV = 5.76 - At 9%: NPV = -7.38 \[ \text{IRR}_B = 5\% + \left(\frac{5.76}{5.76+7.38}\right) \times (9-5) = 5 + \left(\frac{5.76}{13.14}\right) \times 4 \approx 5 + 1.75 = \boxed{6.75\%} \] --- ## 5. **Critical Discussion & Recommendation** ### **Merits of Each Method** - **Payback Period**: Simple to use and understand. Ignores time value of money and cash flows after the payback period. - **ARR**: Easy to calculate. Based on accounting profits, not cash flows; ignores time value of money. - **NPV**: Considers time value of money and all cash flows; best measure of value added to the company. - **IRR**: Takes into account time value of money; gives the rate of return. Can be misleading if cash flows are non-standard or for mutually exclusive projects. ### **Result Discussion** - **Payback Period**: Both projects have similar payback periods (B is slightly faster). - **ARR**: Project A is higher. - **NPV**: Project A is positive (17.61), Project B is negative (-7.38). Project A adds value, B destroys value. - **IRR**: Project A has a higher IRR (13.5%) than the cost of capital (9%), B's IRR (6.75%) is below the cost of capital. ### **Recommendation** **Project A** should be undertaken as it has a positive NPV, a higher IRR than the cost of capital, and a higher ARR. **Project B** should be rejected as it has a negative NPV and a lower IRR than the cost of capital. --- ## **Summary Table** | Method | Project A | Project B | Decision | |------------------|-------------|-------------|--------------------| | Payback | 3.24 years | 3.17 years | Both similar | | ARR | 35.16% | 28.57% | Project A better | | NPV (SAR M) | 17.61 | -7.38 | Project A better | | IRR | 13.5% | 6.75% | Project A better | **Choose Project A.**