Dr. Whitten has decided to purchase equipment that has a cost of $60,000 and will produce a pretax net cash inflow of $30,000 per year over its estimated useful life of six years. The equipment will have no salvage value and will be depreciated by the straight-line method. The tax rate is 50%. Determine Dr. Whitten’s approximate after-tax internal rate of return.
Assemble the assumptions in an orderly manner:
Assumption 1: initial cost of the investment = $60,000.
Assumption 2a: estimated annual net cash inflow the investment will generate = $30,000.
Assumption 2b: estimated annual net cash inflow the investment will generate after taxes =
$15,000 (e.g. 30,000 less 50% tax rate equals 15,000 net).
Assumption 3: useful life of the asset = 10 years.
Perform calculation
Step 1. Divide the initial cost of the investment ($15,000) by the estimated annual net cash
inflow after taxes it will generate ($15,000). The answer is a ratio amounting to 4.000.
Step 2. Now use the abbreviated look-up table for the Present Value of an Annuity of $1,
which is found at the back of the Examples and Exercises section. Find the line item for the
number of periods that matches the useful life of the asset (10 years in this case).
Step 3. Look across the 10 year line on the table and find the column that approximates the
ratio of 4.000 (as computed in Step 1). That column contains the interest rate representing the
rate of return. In this case the rate of return is 20%.
To determine Dr. Whitten's after-tax internal rate of return (IRR), we need to calculate the net cash inflows after taxes and find the discount rate that makes the net present value of those inflows equal to zero.
First, we need to calculate the annual after-tax net cash inflow. The pretax net cash inflow is $30,000 per year, and the tax rate is 50%. So, the annual after-tax net cash inflow can be calculated as:
After-tax net cash inflow = Pretax net cash inflow * (1 - tax rate)
= $30,000 * (1 - 0.50)
= $30,000 * 0.50
= $15,000
Next, we need to calculate the initial cost of the equipment in after-tax terms. Since there is no salvage value and the equipment will be depreciated by the straight-line method, the annual depreciation expense will be the initial cost divided by the useful life:
Annual depreciation expense = Initial cost / Useful life
= $60,000 / 6
= $10,000
Now, we can calculate the net cash inflows after-tax and after depreciation:
Net cash inflow after-tax and after depreciation = After-tax net cash inflow - Annual depreciation expense
= $15,000 - $10,000
= $5,000
To find the after-tax IRR, we need to find the interest rate that makes the net present value of the net cash inflows equal to zero. We can use a financial calculator or spreadsheet software to solve this. Alternatively, we can use the following steps for an approximation:
1. Assume a discount rate (e.g., 10%).
2. Calculate the present value of the net cash inflows after-tax and after depreciation using the assumed discount rate.
3. If the present value is greater than zero, decrease the discount rate. If the present value is less than zero, increase the discount rate.
4. Repeat steps 2 and 3 until the present value is close to zero.
5. The discount rate at which the present value is close to zero is the approximate after-tax IRR.
By applying this method, we can determine the approximate after-tax IRR for Dr. Whitten's investment.