Temple Corp. is considering a new project \vhose data are shown below. 'rhe equipment that would be used
has a 3-year tax life, would be depreciated by the straight-line method over its 3-year life, and would have a
zero salvage value. No new working capital would be required. Revenues and other operating costs are
expected to be constant over the project's 3-year life. What is the project's NPV?
Risk-adjusted WACC
Net investment cost (depreciable basis)
Straight-line depree. rate
Sales revenues, each year
Operating costs (exc!. deprec.), each year
Tax rate
10.0%
$65,000
33.3333%
$65,500
$25,000
35.0%
To calculate the Net Present Value (NPV) of the project, you need to discount the cash flows and subtract the initial investment cost.
Step 1: Calculate the annual after-tax cash flows:
Revenue per year = Sales revenues - Operating costs = $65,500 - $25,000 = $40,500
Tax expense per year = Revenue per year * Tax rate = $40,500 * 0.35 = $14,175
After-tax cash flow per year = Revenue per year - Tax expense per year = $40,500 - $14,175 = $26,325
Step 2: Calculate the present value of each year's cash flow:
PV of Year 1 cash flow = $26,325 / (1 + Risk-adjusted WACC)^1 = $26,325 / (1 + 0.1)^1 = $23,931.82
PV of Year 2 cash flow = $26,325 / (1 + Risk-adjusted WACC)^2 = $26,325 / (1 + 0.1)^2 = $21,755.65
PV of Year 3 cash flow = $26,325 / (1 + Risk-adjusted WACC)^3 = $26,325 / (1 + 0.1)^3 = $19,777.86
Step 3: Calculate the initial investment cost:
Depreciable basis = Net investment cost = $65,000
Annual depreciation expense = Depreciable basis * Straight-line depreciation rate = $65,000 * 0.333333 = $21,666.665
Total depreciation over 3 years = Annual depreciation expense * 3 = $21,666.665 * 3 = $64,999.995
Step 4: Calculate the NPV:
NPV = Sum of PV of cash flows - Initial investment cost
NPV = ($23,931.82 + $21,755.65 + $19,777.86) - $65,000 - $64,999.995
NPV = $65,465.33 - $65,000 - $64,999.995
NPV = -$533.665
The project's NPV is approximately -$533.665.
To calculate the project's NPV, we need to discount the project's cash flows at the risk-adjusted weighted average cost of capital (WACC) and subtract the initial investment cost.
The net investment cost (depreciable basis) is given as $65,000.
The straight-line depreciation rate is given as 33.3333%.
Sales revenues for each year are given as $65,500.
Operating costs (excluding depreciation) for each year are given as $25,000.
The tax rate is given as 35.0%.
First, let's calculate the depreciation expense for each year:
Depreciation expense per year = Net investment cost * Depreciation rate
Depreciation expense per year = $65,000 * 33.3333% = $21,666.65
Next, let's calculate the operating cash flow for each year:
Operating cash flow per year = Sales revenues - Operating costs - Depreciation expense
Operating cash flow per year = $65,500 - $25,000 - $21,666.65 = $18,833.35
Now, we can calculate the net cash flow for each year:
Net cash flow per year = Operating cash flow * (1 - Tax rate)
Net cash flow per year = $18,833.35 * (1 - 0.35) = $12,208.28
Next, let's discount the net cash flows at the risk-adjusted WACC:
Discounted cash flow per year = Net cash flow / (1 + WACC)^year
Discounted cash flow Year 1 = $12,208.28 / (1 + 0.10)^1 = $11,097.53
Discounted cash flow Year 2 = $12,208.28 / (1 + 0.10)^2 = $10,088.66
Discounted cash flow Year 3 = $12,208.28 / (1 + 0.10)^3 = $9,171.51
Finally, let's calculate the project's NPV by summing the discounted cash flows and subtracting the initial investment cost:
NPV = (-Net investment cost) + Sum of discounted cash flows
NPV = (-$65,000) + $11,097.53 + $10,088.66 + $9,171.51 = $-34,642.30
The project's NPV is -$34,642.30. This means that the project is expected to result in a negative net present value, indicating that it may not be a financially viable investment.