Sierra Company is considering a long-term investment project called ZIP. ZIP will require an investment of $121,200. It will have a useful life of 4 years and no salvage value. Annual revenues would increase by $79,180, and annual expenses (excluding depreciation) would increase by $40,180. Sierra uses the straight-line method to compute depreciation expense. The company's required rate of return is 11%. Compute the annual rate of return.
To compute the annual rate of return for the ZIP project, you need to calculate the net cash flow for each year and then find the average rate of return over the project's useful life.
Step 1: Calculate the annual net cash flows
The formula for net cash flow is:
Net Cash Flow = Annual Revenues - Annual Expenses - Depreciation Expense
Given data:
Annual Revenues increase = $79,180
Annual Expenses increase = $40,180
Depreciation expense = Total investment / Useful life = $121,200 / 4 = $30,300
Using the formula:
Net Cash Flow = $79,180 - $40,180 - $30,300
Net Cash Flow = $8,700
So, the net cash flow for each year is $8,700.
Step 2: Calculate the total net cash flows
Since the net cash flow is the same for each year, we can simply multiply it by the useful life.
Total Net Cash Flows = Net Cash Flow × Useful life = $8,700 × 4
Total Net Cash Flows = $34,800
Step 3: Calculate the average annual net cash flow
The average annual net cash flow is equal to the Total Net Cash Flows divided by the useful life.
Average Annual Net Cash Flow = Total Net Cash Flows / Useful life = $34,800 / 4
Average Annual Net Cash Flow = $8,700
Step 4: Calculate the annual rate of return
The annual rate of return is the average annual net cash flow divided by the initial investment, and then multiplied by 100 to express it as a percentage.
Annual Rate of Return = (Average Annual Net Cash Flow / Initial Investment) × 100 = ($8,700 / $121,200) × 100
Annual Rate of Return ≈ 7.17%
Therefore, the annual rate of return for the ZIP project is approximately 7.17%.