Most annuities call for payments to be made over some finite period of time—for example, $100 per year for three years. However, some annuities go on indefinitely, or perpetually, and these are called perpetuities. The present value of a perpetuity is found by applying Equation 2-7.
PV(Perpetuity)
Payment
Interest rate i
Perpetuities can be illustrated by some British securities issued after the Napoleonic Wars. In 1815, the British government sold a huge bond issue and used the proceeds to pay off many smaller issues that had been floated in prior years to pay for the wars. Since the purpose of the bonds was to consolidate past debts, the bonds were called consols. Suppose each consol promised to pay $100 per year in perpetuity. (Actually, interest was stated in pounds.) What would each bond be worth if the opportunity cost rate, or discount rate, was 5 percent? The answer is $2,000:
$100
Suppose the interest rate rose to 10 percent; what would happen to the consol's value? The value would drop to $1,000:
$100
Thus, we see that the value of a perpetuity changes dramatically when interest rates change.
What happens to the value of a perpetuity when interest rates increase? What happens when interest rates decrease?
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