where 
d periodic coupon payment of the bondr discount rate applied to the bondfor example if a perpetual bond pays 10 000 per year in perpetuity and the discount rate is assumed to be 4 the present value would be present value 10 000 0 04 250 000note that the present value of a perpetual bond is highly sensitive to the discount rate assumed since the payment is known as fact for example using the above example with 3 4 5 and 6 discount rates the present values are present value 3 10 000 0 03 333 333present value 4 10 000 0 04 250 000present value 5 10 000 0 05 200 000present value 6 10 000 0 06 166 667