Mathematics for FinanceMTP Nov 21Question 3961 of 507
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If the cost of capital be 12%\displaystyle 12\% per annum, then the Net Present Value (in nearest Rs.) from the given cash flow is given as (in thousands)Year: 0, 1, 2, 3Operating profit: (100), 60, 40, 50

Options

A34,048\displaystyle 34,048
B34,185\displaystyle 34,185
C51,048\displaystyle 51,048
D21,048\displaystyle 21,048
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Correct Answer

Option d21,048\displaystyle 21,048

All Options:

  • A34,048\displaystyle 34,048
  • B34,185\displaystyle 34,185
  • C51,048\displaystyle 51,048
  • D21,048\displaystyle 21,048

Detailed Solution & Explanation

The Net Present Value (NPV\displaystyle NPV) is: 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 is Rs. 21,048\displaystyle 21,048. Hence, **Option D** is the correct answer.

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