1. **State the problem:** We need to find 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: $$\frac{60000}{(1+0.10)^3} = \frac{60000}{1.331} = 45015.02$$ - Year 4: $$\frac{60000}{(1+0.10)^4} = \frac{60000}{1.4641} = 40922.75$$ 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 + 45015.02 = 149148.07 - After Year 4: 149148.07 + 40922.75 = 190070.82 5. **Determine discounted payback period:** The initial investment is 200000. After 4 years, cumulative discounted cash flow is 190070.82, which is less than 200000. So, the discounted payback period is more than 4 years. 6. **Conclusion:** The investment does not pay back within 4 years on a discounted basis at 10% discount rate. **Final answer:** Discounted payback period > 4 years.