A perpetuity is an annuity that pays a fixed cash amount indefinitely.

(a) Show that the price (present value) of a perpetuity paying an annual coupon is = where > 0 is the relevant market interest rate or yield.

(b) Consider a perpetuity that pays a $1 coupon every year and trades at $80. Calculate its yield .

(c) Suppose you bought 1,000 perpetuities at $80 each, and then that the yield calculated in (b) goes up in 25 basis points ( + 0.25%). Calculate your profit or loss(P&L)