Question

Consider a perpetuity that pays $120 per year. Suppose that you bought this bond today for $4,000 and expect to sell it one year from today for $4,800. Calculate the initial current yield, expected capital gain, and expected rate of return of holding this bond for one year.

Answer 1

Question : Consider a perpetuity that pays $120 per year. Suppose that you bought this bond today for $4,000 and expect to sell it one year from today for $4,800. Calculate the initial current yield, expected capital gain, and expected rate of return of holding this bond for one year.

Solution : Initial current yield = ( interest earned / current price of the bond ) x 100

where, interest earned = perpetuity being received per year i.e. 20, current price of the bond $4000

So, intitial current yield = 120/4000 x 100 = 3%

Expected capital gain = (expected selling price - purchase price) / purchase price x 100

= (4800 - 4000 ) / 4000 x 100

   = 800/4000 x 100

= 0.20 x 100

= 20%

Expected holding return for holding this bond for one year = (capital gain + interest gain) / purchase price x 100

= 800 + 120 / 4000 x 100

= 920 / 4000 x 100

= 0.23 x 100

= 23%

Hence , for the bond with purchase prics = $4000 , selling price = $4800 and perpetuity = $120 per year,

Initial current yield = 3%

expected capital gain = 20%

expected holding period retuen = 23%