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Union Local School District has bonds outstanding with a coupon rate of 4.6 percent paid semiannually...

Union Local School District has bonds outstanding with a coupon rate of 4.6 percent paid semiannually and 21 years to maturity. The yield to maturity on these bonds is 3.9 percent and the bonds have a par value of 5000.

What is the dollar price of each bond?

Expert Solution

Price of bond = C x [1-{1/ (1+r) ⁿ}/r] +M/(1+r)ⁿ

C = Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually

= ($ 5,000 x 4.6 %)/2 = $ 5,000 x 0.046 x ½ = $ 115

r = Rate of interest = 3.9 % or 0.039/2 = 0.0195 semiannually

n = No of periods to maturity = 21 years x 2 periods = 42

M = Face Value = $ 5,000

Bond Price = $ 115 x [1-{1/ (1+0.0195)⁴²}/0.0195 ] + $ 5,000/ (1+0.0195)⁴²

= $ 115 x [1-{1/ (1.0195)⁴²}/0.0195 ] + $ 5,000/ (1.0195)⁴²

= $ 115 x [1-(1/ 2.25042044535078)/0.0195] + $ 5,000/ 2.25042044535078

= $ 115 x [(1-0.444361409027336)/0.0195] + $ 2,221.80704513668

= $ 115 x (0.555638590972664/0.0195) + $ 2,221.80704513668

= $ 115 x 28.4942867165468 + $ 2,221.80704513668

= $ 3,276.84297240289 + $ 2,221.80704513668

= $ 5,498.65001753957 or $ 5,498.65

Dollar price of each bond $ 5,498.65

jeff jeffy answered 1 year ago

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