1. **Problem Statement:** Calculate the discounted payback period for an investment costing 200000 with expected cash flows of 60000 each year for 4 years and a discount rate of 10%. 2. **Formula and Explanation:** The discounted payback period is the time it takes for the sum of the discounted cash flows to equal the initial investment. The present value (PV) of each cash flow is calculated as: $$PV = \frac{CF}{(1 + r)^t}$$ where $CF$ is the cash flow, $r$ is the discount rate, and $t$ is the year. 3. **Calculate discounted cash flows:** Year 1: $$\frac{60000}{(1+0.10)^1} = \frac{60000}{1.10} = 54545.45$$ Year 2: $$\frac{60000}{(1+0.10)^2} = \frac{60000}{1.21} = 49587.60$$ Year 3: $$\frac{60000}{(1+0.10)^3} = \frac{60000}{1.331} = 45051.41$$ Year 4: $$\frac{60000}{(1+0.10)^4} = \frac{60000}{1.4641} = 40955.83$$ 4. **Calculate cumulative discounted cash flows:** After Year 1: $54545.45$ After Year 2: $54545.45 + 49587.60 = 104133.05$ After Year 3: $104133.05 + 45051.41 = 149184.46$ After Year 4: $149184.46 + 40955.83 = 190140.29$ 5. **Find discounted payback period:** Initial investment = 200000 After 4 years, cumulative discounted cash flow is $190140.29$, which is less than 200000. We need to find the fraction of Year 4 to recover the remaining amount: Remaining amount after Year 3: $$200000 - 149184.46 = 50815.54$$ Fraction of Year 4: $$\frac{50815.54}{40955.83} = 1.24$$ Since this fraction is greater than 1, the payback period is more than 4 years, meaning the investment is not recovered within 4 years on a discounted basis. **Final answer:** The discounted payback period exceeds 4 years; the investment is not recovered within 4 years at a 10% discount rate.