Certainly! Let's break down the steps to compute Project A's accounting rate of return (ARR):
### Step 1: Calculate Total Income Over the Project's Life
The total income over the project's life can be computed by multiplying the annual income with the project life.
[tex]\[ \text{Total Income} = \$ 28,800 \times 5 = \$ 144,000 \][/tex]
### Step 2: Calculate Average Income Per Year
The average income per year is simply the total income divided by the project life.
[tex]\[ \text{Average Income} = \frac{\$ 144,000}{5} = \$ 28,800 \][/tex]
### Step 3: Calculate Depreciation Per Year
Depreciation is calculated by subtracting the salvage value from the initial investment and then dividing by the project life.
[tex]\[ \text{Depreciation} = \frac{\$ 285,000 - \$ 45,500}{5} = \frac{\$ 239,500}{5} = \$ 47,900 \][/tex]
### Step 4: Calculate Accounting Income Per Year
Accounting Income per year is determined by subtracting depreciation from the average income.
[tex]\[ \text{Accounting Income} = \$ 28,800 - \$ 47,900 = -\$ 19,100 \][/tex]
### Step 5: Calculate Average Investment
The average investment is calculated by taking the average of the initial investment and the salvage value.
[tex]\[ \text{Average Investment} = \frac{\$ 285,000 + \$ 45,500}{2} = \frac{\$ 330,500}{2} = \$ 165,250 \][/tex]
### Step 6: Calculate Accounting Rate of Return (ARR)
Finally, the accounting rate of return is computed by dividing the accounting income by the average investment and then converting it to a percentage.
[tex]\[ \text{ARR} = \left( \frac{-\$ 19,100}{\$ 165,250} \right) \times 100 \approx -11.56\% \][/tex]
Thus, Project A’s accounting rate of return (ARR) is approximately [tex]\(-11.56\%\)[/tex]. This indicates that the project would result in a negative return based on accounting income and average investment.
