Mathematics for FinancePYQ July 21Question 1577 of 512
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If the cost of capital be 12%\displaystyle 12\% per annual, then the net present value from given cash flow:\n\n| Year | Operating Profit (in thousands Rs.) |\n|---|---|\n| 0 | -100 |\n| 1 | 60 |\n| 2 | 40 |\n| 3 | 50 |

Options

A31048\displaystyle 31048
B34185\displaystyle 34185
C21048\displaystyle 21048
D24187\displaystyle 24187
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Correct Answer

✅ Option c — 21048\displaystyle 21048

All Options:

  • A31048\displaystyle 31048
  • B34185\displaystyle 34185
  • C21048\displaystyle 21048
  • D24187\displaystyle 24187

Detailed Solution & Explanation

The net present value (NPV\displaystyle NPV) is the sum of the present values of all cash flows: NPV=CF0+CF11+i+CF2(1+i)2+CF3(1+i)3NPV = CF_0 + \frac{CF_1}{1+i} + \frac{CF_2}{(1+i)^2} + \frac{CF_3}{(1+i)^3} Given: * CF0=−100\displaystyle CF_0 = -100 (in thousands) * CF1=60\displaystyle CF_1 = 60 * CF2=40\displaystyle CF_2 = 40 * CF3=50\displaystyle CF_3 = 50 * Interest rate (i\displaystyle i) = 12%\displaystyle 12\% p.a. = 0.12\displaystyle 0.12 Substituting the values: NPV=−100+601.12+40(1.12)2+50(1.12)3NPV = -100 + \frac{60}{1.12} + \frac{40}{(1.12)^2} + \frac{50}{(1.12)^3} NPV=−100+53.5714+31.8878+35.5890=21.0482 thousandsNPV = -100 + 53.5714 + 31.8878 + 35.5890 = 21.0482 \text{ thousands} This corresponds to Rs. 21,048\displaystyle 21,048. Hence, **Option C** is the correct answer.

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