Question

Joseph's Company has just issued a 20-year, 9 percent coupon rate, $1,000-par bond that pays interest semiannually. Two years later, if the going rate of interest on the bond falls to 8 percent, what is the value of the bond?

            a.         $1,225.62

            b.         $1,135.90

            c.         $1,094.54

            d.         $1,116.52

            e.         $1,012.38

Answer 1

Current Value of the Bond

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

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $45 [$1,000 x 9.00% x ½]

Semi-annual Yield to Maturity = 4.50% [8.00% x ½]

Maturity Period = 36 Years [(20 Years – 2 Years) x 2]

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

= $45[PVIFA 4%, 36 Years] + $1,000[PVIF 4%, 36 Years]

= [$45 x 18.90828] + [$1,000 x 0.24367]

= $850.87 + $243.67

= $1,094.54

“Hence, the Current Value of the Bond will be (c). $1,094.54”

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.