Question

Union Local School District has bonds outstanding with a coupon rate of 2.9 percent paid semiannually and 24 years to maturity. The yield to maturity on these bonds is 3.4 percent and the bonds have a par value of $10,000. What is the price of the bonds?

Answer 1

Answer: $4,642.37

The price of the bond is $4,642.37

Explanation:

Using the price of bond formula :

C × 1 - (1+r) *-n / r. + F / (1+r)*n

C = coupon rate = 2.9% of 10,000

= $290

n = 24years...... years to maturity

F = $10,000...... Face value/par value

r = yield to maturity = 3.4% = 0.034

Price of bond =

290 × 1–(1+0.034)*-24 /0.034

+ 10,000 / (1.034)*24

290× 1 - (1.034)*-24 / 0.034

+ 10,000 / (1.034)*24

290 × (1 - 0.448236347)

+ 4,482.36347

160.011459 + 4,482.36347

Price = $4,642.37 as the price of bond.

Answer 2

Answer:

Price of bond=$9,184.18

Explanation:

Explanation:

The value of the bond is the present value (PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV) discounted at the yield rate

Value of Bond = PV of interest + PV of RV

The value of bond for Local School District can be worked out as follows:

Step 1

PV of interest payments

Semi annul interest payment:

= 2.9% × 10,000× 1/2= 145

Semi-annual yield = 3.4/2 = 1.7%

Total period to maturity = (2 × 24) = 48 periods

PV of interest payment:

=145× (1- (1+0.017)^(-48)/0.017)

= 4,731.77

Step 2

PV of Redemption Value

= 10,000 × (1.017)^(-48)

= 4,452.40

Step 3

Price of bond

=4,731.77 + 4,452.40

=$9,184.1766