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Internal Rate Return C2Cd0F

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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)