A bond has a par value of 1000 a time to maturity of 20 year

A bond has a par value of $1,000, a time to maturity of 20 years, and a coupon rate of 7.10% with interest paid annually. If the current market price is $710, what will be the approximate capital gain of this bond over the next year if its yield to maturity remains unchanged? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Capital gain ___$

Solution

Step-1:Calculation of yield to maturity Yield to Maturity = Average income / Average Investment = (Coupon+(Par Value-Current Price)/Life)/((Par Value + Current Price)/2) = (71+(1000-710)/20)/((1000+710)/2) = 10.00% Working: Par Value $    1,000 Coupon $    1,000 x 7.10% = $          71 Step-2:Calculation of Price after year 1 Price of coupon is the present value of cash flow from bond. Present Value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.10)^-19)/0.10 i 10% =         8.3649 n 19 Present Value of 1 = (1+i)^-n = (1+0.10)^-19 =         0.1635 Present Value of coupon $             71 x      8.3649 =      593.91 Present Value of Par Value $       1,000 x      0.1635 =      163.51 Price 1 year from now      757.42 Step-3:Calculation of Capital gain yield over the year Capital Gain yield = (Price after 1 - Current Price)/Current Price = (757.42-710)/710 = 6.68% Thus, Capital gain yield is 6.68%