Mathematics for FinancePYQ Sep 24Question 1564 of 512
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A Perpetuity has a cash flow of 625\displaystyle 625 and a required rate of return of 8%\displaystyle 8\%. If the cash flow is expected to grow at a constant rate of 4%\displaystyle 4\% per year, then the intrinsic value of this perpetuity (present value of growing perpetuity) is:

Options

A15,000\displaystyle 15,000
B15,625\displaystyle 15,625
C14,280\displaystyle 14,280
D16,667\displaystyle 16,667
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Correct Answer

✅ Option b — 15,625\displaystyle 15,625

All Options:

  • A15,000\displaystyle 15,000
  • B15,625\displaystyle 15,625
  • C14,280\displaystyle 14,280
  • D16,667\displaystyle 16,667

Detailed Solution & Explanation

The present value (PV\displaystyle PV) of a growing perpetuity is: PV=Ar−gPV = \frac{A}{r - g} Given: * Cash flow (A\displaystyle A) = 625\displaystyle 625 * Required rate of return (r\displaystyle r) = 8%\displaystyle 8\% p.a. = 0.08\displaystyle 0.08 * Growth rate (g\displaystyle g) = 4%\displaystyle 4\% p.a. = 0.04\displaystyle 0.04 Substituting the values: PV=6250.08−0.04=6250.04=15,625PV = \frac{625}{0.08 - 0.04} = \frac{625}{0.04} = 15,625 Hence, **Option B** is the correct answer.

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