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Present Value Comparison

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Present Value Comparison


1. **State the problem:** We need to compare the present values of two payment options using a discount rate of 11.5% per year. 2. **Formula for Present Value (PV):** $$PV = \frac{FV}{(1 + r)^t}$$ where $FV$ is the future value, $r$ is the discount rate, and $t$ is the time in years. 3. **Calculate PV for Option A:** - Payment today: Rs. 550000 (no discount since $t=0$) - Payment in 2 years: Rs. 600000 $$PV_{A2} = \frac{600000}{(1 + 0.115)^2} = \frac{600000}{1.115^2} = \frac{600000}{1.243225} \approx 482438.68$$ Total PV for Option A: $$PV_A = 550000 + 482438.68 = 1032438.68$$ 4. **Calculate PV for Option B:** - Payment today: Rs. 300000 - Payment in 1 year: Rs. 850000 $$PV_{B1} = \frac{850000}{1.115} \approx 762331.84$$ Total PV for Option B: $$PV_B = 300000 + 762331.84 = 1062331.84$$ 5. **Compare the two options:** $$Difference = PV_B - PV_A = 1062331.84 - 1032438.68 = 29893.16$$ 6. **Conclusion:** Option B has a higher present value by approximately Rs. 29893.16. This means Option B is financially better when considering the time value of money at an 11.5% discount rate.