Question

In: Finance

A bond has a 10-year maturity, an 4% annual coupon rate, with quarterly coupons paid, and...

A bond has a 10-year maturity, an 4% annual coupon rate, with quarterly coupons paid, and a par value of $1,000. The annual discount rate is 8%. What should be the bond’s price?

Solutions

Expert Solution

Price of the Bond

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $5,000

Quarterly Coupon Amount = $10 [$1,000 x 4% x ¼]

Quarterly Yield to Maturity = 2% [4% x ¼]

Maturity Period = 40 Years [10 Years x 4 Quarters]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $10[PVIFA 2%, 40 Years] + $1,000[PVIF 2%, 40 Years]

= [$10 x 27.35548] + [$1,000 x 0.45289]

= $273.56 + $452.89

= $726.45

“Therefore, the Price of the Bond = $726.45”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)n} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.   


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