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Business valuations and market efficiency

Question 8

Perpetuities

A payment of $5,800 is to be made every year for the foreseeable future, the
first payment occurring in one year’s time. The interest rate is 12%. Calculate
the PV of the perpetuity if:

(a) The value of the annuity remains constant

(b) The value of the perpetuity grows by 3% in the second year and remains
growing at that rate for the foreseeable future

(a) PV = FV × 1/r

PV = $5,800 × 1/0.12 = $48,333

(b) PV = FV × 1/(r – g)

PV = $5,800 × 1/(0.12 – 0.03) = $64,444

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