Lion Corp. has a $4,000 par value bond outstanding with a coupon rate of 4.6 percent paid semiannually and 20 years to maturity. The yield to maturity on this bond is 2.1 percent. What is the dollar price of the bond

$5,627

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. Both of these cash flows discounted and added to calculate the value of the bond.

According to given data

Face value of the bond is $4,000

Coupon payment = C = $4,000 x 4.6% = $184 annually = $92 semiannually

Number of periods = n = 20 years x 2 = 40 period

Market Rate = 2.1% annually = 1.05% semiannually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond = 92 x [ ( 1 - ( 1 + 1.05% )^-40 ) / 1.05% ] + [ $4,000 / ( 1 + 1.05% )^40 ]

Price of the Bond = $2,992.30 + $2,634.95

Price of the Bond = $5,627.25

Price of the bond =$5626.2518

Explanation:

The price of a bond is the present value (PV) of the future cash inflows expected from the bond discounted using the yield to maturity.

The price of the bond can be calculated as follows:

PV of interest payment + PV of redemption Value

Step 1

PV of interest payment

Interest payment =( 4.6%× $4000)/2

=$ 92

Semi annual yield = 2.1/2 = 1.05 %

PV of interest payment

= 92× (1-(1.0105)^(-20×2))/0.0105)

= 2992.30

Step 2

PV of redemption value

= 4,000 × (1+0.0105)^(-20×2)

= 2633.948

Step 3

Price of bond

= $12992.30+ $2633.94

=$5626.2518

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