Internal Rate Return C2Cd0F
1. **State the problem:**
We need to find the internal rate of return (IRR) for a machine costing 8000, with a 10-year life, zero salvage value, annual savings of 1554 before taxes and depreciation, straight-line depreciation, and a 35% tax rate.
2. **Formula and concepts:**
The IRR is the discount rate $r$ that makes the net present value (NPV) of cash flows zero:
$$0 = -\text{Initial Cost} + \sum_{t=1}^{10} \frac{\text{After-tax cash flow}_t}{(1+r)^t}$$
3. **Calculate depreciation:**
Straight-line depreciation per year:
$$\frac{8000 - 0}{10} = 800$$
4. **Calculate taxable income:**
Annual savings before taxes and depreciation = 1554
Taxable income = savings - depreciation = $1554 - 800 = 754$
5. **Calculate tax:**
Tax = $754 \times 0.35 = 263.9$
6. **Calculate after-tax savings:**
After-tax savings = $1554 - 263.9 = 1290.1$
7. **Calculate after-tax cash flow:**
Add back non-cash depreciation:
$$1290.1 + 800 = 2090.1$$
8. **Set up IRR equation:**
$$0 = -8000 + \sum_{t=1}^{10} \frac{2090.1}{(1+r)^t}$$
9. **Solve for $r$:**
This is the IRR, the rate $r$ that satisfies:
$$8000 = 2090.1 \times \frac{1 - (1+r)^{-10}}{r}$$
Using trial or financial calculator, the IRR is approximately 9.79%.
**Final answer:** 9.79% (option b)