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4. What is the Net Present Value of the investment proposal?

Options

A` 3,78,990.30
B` 4,54,980.60
C` 4,74,890.40
D` 3,89,260.70
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Correct Answer

✅ Option C — ` 4,74,890.40

All Options:

  • A` 3,78,990.30
  • B` 4,54,980.60
  • C` 4,74,890.40 ✓
  • D` 3,89,260.70

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Detailed Solution & Explanation

Correct Answer: Option **C** Explanation: The Net Present Value (NPV) of the investment proposal is calculated by subtracting the net initial investment from the total present value (PV) of cash inflows over the 5-year project life.
**1. Net Initial Investment (at Year 0):**
The cost of acquisition of the automated machine is ‘5,00,000\displaystyle ` 5,00,000. The existing old machine (which has a written down value of zero) can be sold immediately for ‘10,000\displaystyle ` 10,000.
textNetInitialInvestment=textCostofNewMachine−textSalvagevalueofOldMachine\\text{Net Initial Investment} = \\text{Cost of New Machine} - \\text{Salvage value of Old Machine}
textNetInitialInvestment=5,00,000−10,000=4,90,000\\text{Net Initial Investment} = 5,00,000 - 10,000 = 4,90,000
**2. Calculation of Cash Inflow after Taxes (CFAT) for Years 4 and 5:**
* **For Year 4:**
* textPBTtextYear4=3,11,000\\text{PBT}_{\\text{Year 4}} = 3,11,000 (calculated in Question 1)
* textPATtextYear4=3,11,000times(1−0.30)=2,17,700\\text{PAT}_{\\text{Year 4}} = 3,11,000 \\times (1 - 0.30) = 2,17,700
* textCFATtextYear4=2,17,700+90,000=3,07,700\\text{CFAT}_{\\text{Year 4}} = 2,17,700 + 90,000 = 3,07,700
* **For Year 5:**
* Additional Sales Units = 28,000\displaystyle 28,000 units, Selling Price = ‘35\displaystyle ` 35 per unit
* Sales Revenue = 28,000times35=‘9,80,000\displaystyle 28,000 \\times 35 = ` 9,80,000
* Variable Cost = 28,000times22=‘6,16,000\displaystyle 28,000 \\times 22 = ` 6,16,000
* Additional Fixed Cost = ‘35,000\displaystyle ` 35,000
* Savings in breakages = ‘20,000\displaystyle ` 20,000
* Depreciation = ‘90,000\displaystyle ` 90,000
* textPBTtextYear5=(9,80,000−6,16,000)−35,000+20,000−90,000=2,59,000\\text{PBT}_{\\text{Year 5}} = (9,80,000 - 6,16,000) - 35,000 + 20,000 - 90,000 = 2,59,000
* textPATtextYear5=2,59,000times(1−0.30)=1,81,300\\text{PAT}_{\\text{Year 5}} = 2,59,000 \\times (1 - 0.30) = 1,81,300
* textOperatingCFATtextYear5=1,81,300+90,000=2,71,300\\text{Operating CFAT}_{\\text{Year 5}} = 1,81,300 + 90,000 = 2,71,300
* In Year 5, the automated machine is sold at its residual value of ‘50,000\displaystyle ` 50,000. Thus, the total Cash Inflow in Year 5 is:
textTotalCFATtextYear5=2,71,300+50,000=3,21,300\\text{Total CFAT}_{\\text{Year 5}} = 2,71,300 + 50,000 = 3,21,300
**3. Present Value (PV) of Cash Inflows:**
* **Year 1:** 1,60,000times0.909=1,45,440\displaystyle 1,60,000 \\times 0.909 = 1,45,440
* **Year 2:** 1,91,500times0.826=1,58,179\displaystyle 1,91,500 \\times 0.826 = 1,58,179
* **Year 3:** 3,35,000times0.751=2,51,585\displaystyle 3,35,000 \\times 0.751 = 2,51,585
* **Year 4:** 3,07,700times0.683=2,10,159.10\displaystyle 3,07,700 \\times 0.683 = 2,10,159.10
* **Year 5:** 3,21,300times0.621=1,99,527.30\displaystyle 3,21,300 \\times 0.621 = 1,99,527.30
* textTotalPVofInflows=1,45,440+1,58,179+2,51,585+2,10,159.10+1,99,527.30=9,64,890.40\\text{Total PV of Inflows} = 1,45,440 + 1,58,179 + 2,51,585 + 2,10,159.10 + 1,99,527.30 = 9,64,890.40
**4. Calculation of NPV:**
textNPV=textTotalPVofCashInflows−textNetInitialInvestment\\text{NPV} = \\text{Total PV of Cash Inflows} - \\text{Net Initial Investment}
textNPV=9,64,890.40−4,90,000=4,74,890.40\\text{NPV} = 9,64,890.40 - 4,90,000 = 4,74,890.40
Hence, **Option C** is the correct answer.

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