Question: Bob Cratchit, a new analyst at Scrooge & Marley Inc., has prepared a capital budget for the Tiny Tim project. He is scheduled to present his analysis at a board meeting in one hour. Bob just received an email from his boss, Fred Fezziwig, indicating that the capital budget is missing a critical piece of machinery with a capital cost of 200000. The machine would be purchased at the outset of the project (Year 0). The machinery is in Class 8 with a depreciation rate of 20%. The machine will be sold for 160000 at the end of the two-year project. The tax rate is 35% and the weighted average cost of capital is 9%. No other element of the capital budget would be affected. Assume that all cash flows occur at year-end (except for the purchase of equipment). What is the reduction in NPV associated with the inclusion of the missing machinery? Round your answer to the nearest dollar.
1. **State the problem:**
Calculate the reduction in Net Present Value (NPV) due to adding a missing machinery costing $200000, depreciated at 20% per year, sold for $160000 after 2 years, with a tax rate of 35% and discount rate (WACC) of 9%.
2. **Key formulas and concepts:**
- Depreciation (straight-line or declining balance, here Class 8 implies declining balance at 20%)
- Tax shield from depreciation = Depreciation \times Tax rate
- After-tax salvage value = Salvage price \times (1 - Tax rate) if gain on sale
- NPV = Present value of cash inflows - Present value of cash outflows
3. **Calculate depreciation schedule:**
Year 0 purchase cost = $200000
Depreciation rate = 20% per year (declining balance)
Year 1 depreciation = $200000 \times 0.20 = $40000
Book value end Year 1 = $200000 - $40000 = $160000
Year 2 depreciation = $160000 \times 0.20 = $32000
Book value end Year 2 = $160000 - $32000 = $128000
4. **Calculate tax shield from depreciation:**
Year 1 tax shield = $40000 \times 0.35 = $14000
Year 2 tax shield = $32000 \times 0.35 = $11200
5. **Calculate after-tax salvage value:**
Sale price = $160000
Book value at sale = $128000
Gain on sale = $160000 - $128000 = $32000
Tax on gain = $32000 \times 0.35 = $11200
After-tax salvage value = $160000 - $11200 = $148800
6. **Calculate cash flows:**
Year 0: Outflow = -$200000
Year 1: Tax shield inflow = $14000
Year 2: Tax shield inflow + after-tax salvage = $11200 + $148800 = $160000
7. **Calculate present value of cash flows using discount rate 9%:**
$$PV = -200000 + \frac{14000}{(1+0.09)^1} + \frac{160000}{(1+0.09)^2}$$
Calculate each term:
$$\frac{14000}{1.09} \approx 12844.04$$
$$\frac{160000}{1.09^2} = \frac{160000}{1.1881} \approx 134622.52$$
Sum:
$$NPV = -200000 + 12844.04 + 134622.52 = -200000 + 147466.56 = -52533.44$$
8. **Interpretation:**
The inclusion of the missing machinery reduces the NPV by approximately $52533 (rounded to nearest dollar).
**Final answer:**
$$\boxed{\text{Reduction in NPV} = -52533}$$