Electrical utility is offering a security, known as zero-coupon bond, for sale.

Question

Electrical utility is offering a security, known as zero-coupon bond, for sale. The terms of the security are investors pay $2,337.57 today to purchase the security, and the utility will pay the owner of the security $10,000 in ten years’ time. The government is offering a similar security; except that this Security will pay $500 each year for the duration of the security and in the last year will pay the full $10,000 plus the $500. The government is selling this security, known as a coupon bond, for $4, 787.76. Which one would you prefer?

Explanation / Answer

Coupon rate paid by coupon bond = $500/$4787076 x 100

= 10.44%

Zero Coupon Bond :

NPV of Zero Coupon Bond = $10000/PVF@10.44% - $2337.57

= $10000/(1/1.1044)10 - $2337.57

= $ 1,366.98

Coupon Bond :

NPV of Coupon Bond = PV of all coupon payments and principle repayment - $4787.76

= $500/(1/1.1044)1+$500/(1/1.1044)2+....+$500/(1/1.1044)10+$10000/(1/1.1044)10 - $4787.76

= $1,931.85

Coupon bond is more benefecial and it has to be preferred.

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