Question

THOAITIUm price you are willing to pay? Brighton, Inc. has bonds outstanding that will mature 12 years from today with a coupon interest rate of 6% paid semi-annually. If investors require 5% YTM for the next 3 years and 6% thereafter, what is the maximum price you are willing to pay?

Answer 1

The maximum price that we are willing to pay is computed as shown below:

N = 12 x 2

= 24

Coupon payment = $ 1,000 x 6% / 2 (Assumed a $ 1,000 bond )

= $ 30

YTM for first 6 periods = 5% / 2

= 2.5%

YTM for next 18 periods = 6% / 2

= 3%

So the price of the bond will be as follows:

= $ 30 / 1.025¹ + $ 30 / 1.025² + $ 30 / 1.025³ + $ 30 / 1.025⁴ + $ 30 / 1.025⁵ + $ 30 / 1.025⁶ + $ 30 / 1.03⁷ + $ 30 / 1.03⁸ +$ 30 / 1.03⁹ +$ 30 / 1.03¹⁰ +$ 30 / 1.03¹¹ +$ 30 / 1.03¹² +$ 30 / 1.03¹³ +$ 30 / 1.03¹⁴ +$ 30 / 1.03¹⁵ +$ 30 / 1.03¹⁶ +$ 30 / 1.03¹⁷ +$ 30 / 1.03¹⁸ +$ 30 / 1.03¹⁹ +$ 30 / 1.03²⁰ +$ 30 / 1.03²¹ +$ 30 / 1.03²² +$ 30 / 1.03²³ +$ 30 / 1.03²⁴ +$ 1,000 / 1.03²⁴

= $ 1,002.73 Approximately

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