Financial ManagementQuestion 5552 of 217
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5. What is the Discounted Payback period of the investment proposal ?

Options

A2.74 years
B2.87 years
C2.38 years
D2.48 years
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Correct Answer

✅ Option A — 2.74 years

All Options:

  • A2.74 years ✓
  • B2.87 years
  • C2.38 years
  • D2.48 years

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Detailed Solution & Explanation

Correct Answer: Option **A** Explanation: The Discounted Payback Period is the time required to recover the net initial investment from the cumulative discounted cash inflows of the project.
* Net Initial Investment to be recovered = ‘4,90,000\displaystyle ` 4,90,000 (as calculated in Question 4)
* Let's check the cumulative discounted cash inflows year-by-year:
* **End of Year 1:** Cumulative PV = ‘1,45,440\displaystyle ` 1,45,440
* **End of Year 2:** Cumulative PV = 1,45,440+1,58,179=‘3,03,619\displaystyle 1,45,440 + 1,58,179 = ` 3,03,619
* **End of Year 3:** Cumulative PV = 3,03,619+2,51,585=‘5,55,204\displaystyle 3,03,619 + 2,51,585 = ` 5,55,204 (which exceeds the initial outlay of ‘4,90,000\displaystyle ` 4,90,000)
Since the cumulative PV at the end of Year 3 (‘5,55,204\displaystyle ` 5,55,204) exceeds the net initial investment (‘4,90,000\displaystyle ` 4,90,000), the payback occurs during Year 3.
* Unrecovered investment at the end of Year 2 = 4,90,000−3,03,619=‘1,86,381\displaystyle 4,90,000 - 3,03,619 = ` 1,86,381
* Discounted cash inflow in Year 3 = ‘2,51,585\displaystyle ` 2,51,585
* Fraction of Year 3 required = fractextUnrecoveredInvestmenttextDiscountedInflowinYear3=frac1,86,3812,51,585approx0.74textyears\displaystyle \\frac{\\text{Unrecovered Investment}}{\\text{Discounted Inflow in Year 3}} = \\frac{1,86,381}{2,51,585} \\approx 0.74\\text{ years}
* textDiscountedPaybackPeriod=2textyears+0.74textyears=2.74textyears\\text{Discounted Payback Period} = 2\\text{ years} + 0.74\\text{ years} = 2.74\\text{ years}
Hence, **Option A** is the correct answer.

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