Question

1. Consider a bond that pays annually an 8% coupon with 20 years to maturity. The percentage change in the price of the bond if its yield to maturity increases from 5% to 7% is closest to? Set your decimal places to 4 in your financial calculator.

   a		19.50%
   b		24.22%
   c		-24.22%
   d		-19.50%

Answer 1

Lets assume face value of bond be $ 100

Price of bond if YTM is 5%

= $ 8 / 1.05¹ + $ 8 / 1.05² + $ 8 / 1.05³ + $ 8 / 1.05⁴ + $ 8 / 1.05⁵ + $ 8 / 1.05⁶ + $ 8 / 1.05⁷ + $ 8 / 1.05⁸ + $ 8 / 1.05⁹ + $ 8 / 1.05¹⁰ + $ 8 / 1.05¹¹ + $ 8 / 1.05¹² + $ 8 / 1.05¹³ + $ 8 / 1.05¹⁴ + $ 8 / 1.05¹⁵ + $ 8 / 1.05¹⁶ + $ 8 / 1.05¹⁷ + $ 8 / 1.05¹⁸ + $ 8 / 1.05¹⁹ + $ 108 / 1.05²⁰

= $ 137.3866 Approximately

Price of bond if YTM is 7%

= $ 8 / 1.07¹ + $ 8 / 1.07² + $ 8 / 1.07³ + $ 8 / 1.07⁴ + $ 8 / 1.07⁵ + $ 8 / 1.07⁶ + $ 8 / 1.07⁷ + $ 8 / 1.07⁸ + $ 8 / 1.07⁹ + $ 8 / 1.07¹⁰ + $ 8 / 1.07¹¹ + $ 8 / 1.07¹² + $ 8 / 1.07¹³ + $ 8 / 1.07¹⁴ + $ 8 / 1.07¹⁵ + $ 8 / 1.07¹⁶ + $ 8 / 1.07¹⁷ + $ 8 / 1.07¹⁸ + $ 8 / 1.07¹⁹ + $ 108 / 1.07²⁰

= $ 110.5940 Approximately

So the % change in price of the bond is

= ( $ 110.5940 - $ 137.3866) / $ 137.3866

= - 0.1950 or - 19.50% Approximately

so the correct answer is option d i.e. - 19.50%

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