Accounting Rate of Return (ARR):
ARR is calculated by dividing the average annual net income generated by the initial investment and expressing it as a percentage.
Step 1: Calculate the average annual net income generated.
Average annual net income = (Annual net income generated year 1 + Annual net income generated year 14) / 2
Average annual net income = ($59,040 + $59,040) / 2 = $59,040
Step 2: Calculate the ARR.
ARR = (Average annual net income / Initial investment) x 100
ARR = ($59,040 / $720,000) x 100 ≈ 8.18%
Payback Period:
The payback period is the time it takes for the initial investment to be recovered from the net cash flows.
Step 1: Calculate the annual net cash flows.
Annual net cash flows = Annual net income generated - Annual depreciation expense
Annual net cash flows = $59,040 - ($720,000 - $100,000) / 10
Annual net cash flows = $59,040 - $62,000 = -$2,960
Step 2: Calculate the payback period.
Payback period = Initial investment / Annual net cash flows
Payback period = $720,000 / $2,960 ≈ 243.24 years
Net Present Value (NPV):
NPV is calculated by discounting the net cash flows over the useful life of the investment at the cost of capital and subtracting the initial investment.
Step 1: Calculate the discount factor using the cost of capital (14%).
Discount factor (n=10, i=14%) = 1 / (1 + 0.14)^10 ≈ 0.20648
Step 2: Calculate the present value of each year's net cash flow and sum them up.
NPV = (Net cash flow year 1 x Discount factor year 1) + (Net cash flow year 2 x Discount factor year 2) + ... + (Net cash flow year 10 x Discount factor year 10) - Initial investment
NPV ≈ ($59,040 x 0.20648) + ($59,040 x 0.20648) + ... + ($59,040 x 0.20648) - $720,000
NPV ≈ $12,196.19
Without making any calculations, determine whether the IRR is more or less than 14%.
The Internal Rate of Return (IRR) is the discount rate at which the NPV becomes zero. Since the cost of capital provided (14%) is already greater than the ARR (8.18%), we can infer that the IRR is less than 14%.