Consider the following information as it relates to a perpetuity-style security: • Relevant rate of return observed in market = 6% per annum compounding half-yearly • A regular cash flow of $50 per half year will be paid in perpetuity, with the first cash flow occurring today Which of the following is closest to the PV of the cash flow stream expected of this perpetuity? a) $1,525.24 b) $1,618.12 c) $1,666.67 d) $1,716.67
Question
Consider the following information as it relates to a perpetuity-style security: • Relevant rate of return observed in market = 6% per annum compounding half-yearly • A regular cash flow of 1,525.24 b) 1,666.67 d) $1,716.67
Solution
The present value (PV) of a perpetuity can be calculated using the formula:
PV = C / r
where: C = Cash flow per period r = Discount rate per period
Given in the problem: C = $50 (cash flow per half year) r = 6% per annum compounding half-yearly = 6%/2 = 3% per half year = 0.03
Substituting these values into the formula:
PV = 1,666.67
So, the closest answer to the PV of the cash flow stream expected of this perpetuity is:
c) $1,666.67
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