Question

Harpeth Valley Water District has a bond outstanding with a coupon rate of 4.03 percent and semiannual payments. The bond matures in 22 years, with a yield to maturity of 3.73 percent, and a par value of $5,000. What is the market price of the bond?

Multiple Choice

• $5,222.47

• $5,223.79

• $5,231.83

• $5,328.27

• $5,238.72

Answer 1

Given,

Coupon rate = 4.03%

Years to maturity = 22 years

Yield to maturity = 3.73% or 0.0373

Par value = $5000

Solution :-

Semi annual coupon payment (C) = $5000 x 4.03% x 1/2 = $100.75

Semi annual periods (n) = 22 years x 2 = 44

Semi annual yield to maturity (r) = 0.0373/2 = 0.01865

Now,

Market price of the bond

= C/r x [1 - (1 + r)^-n] + [par value x (1 + r)^-n]

= $100.75/0.01865 x [1 - (1 + 0.01865)^-44] + [$5000 x (1 + 0.01865)^-44]

= $100.75/0.01865 x [1 - (1.01865)^-44] + [$5000 x (1.01865)^-44]

= $100.75/0.01865 x [1 - 0.4435069818] + [$5000 x 0.4435069818]

= $100.75/0.01865 x 0.5564930182 + [$2217.534909]

= $3006.25584898 + $2217.534909

= $5223.79