Question

consider a consol/perpetuity that pays $100 every period forever. If current yield on the consol was 4% in period t and increased to 5% in period t+1. During this period, the inflation rate was 2%. Then what is the real rate of return for someone who bought it in period t and sold it in period t+1?

(In word format preferred)

Answer 1

current yield = annual income / current price

in year t, current price = annual income/current yield
current price = 100/0.04 = 2500

in year t+1, current price = annual income/current yield
current price = 100/0.05 = 2000

buying cost = 2500
selling price = 2000
interest income = 100

real rate of return = (2000+100 - 2500*(1.02))/2500 = -18%