Question

The Nickelodeon Manufacturing Co. has a series of $1000 par value bonds outstanding. Each bond pays interest semi-annually and carries an annual coupon rate of 7%. Some bonds are due in 3 years while others are due in 10 years. If the required rate of return on bonds is 10%, what is the current price of
a. The bonds with 3 years to maturity
b. The bonds with 10 years to maturity?
Please show all work and formulas without use of financial calculator

Answer 1

(a)-Price of the Bond with 3 Years to maturity

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 = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 5.00% [10.00% x ½]

Maturity Period = 6 Years [3 Years x 2]

Price of the Bond = Present Value of the Coupon payments + Present Value of Face Value

= $35[PVIFA 5.00%, 6 Years] + $1,000[PVIF 5.00%, 6 Years]

= [$35 x 5.07569] + [$1,000 x 0.74622]

= $177.64 + $746.22

= $923.86

(b)-Price of the Bond with 10 Years to maturity

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 = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 5.00% [10.00% x ½]

Maturity Period = 20 Years [10 Years x 2]

Price of the Bond = Present Value of the Coupon payments + Present Value of Face Value

= $35[PVIFA 5.00%, 20 Years] + $1,000[PVIF 5.00%, 20 Years]

= [$35 x 12.46221] + [$1,000 x 0.37689]

= $436.18 + $376.89

= $813.07

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.