Question

The Florida Investment Fund buys 58 bonds of the Gator Corporation through a broker. The bonds pay 10 percent annual interest. The yield to maturity (marketrate of interest) is 12 percent. The bonds have a 10-year maturity.

Using an assumption of semiannual interest payments:

a.Compute the price of a bond (refer to “Semiannual Interest and BondPrices” in Chapter 10 for review if necessary).

b.Compute the total value of the 58 bonds.

Short answer

a. Price of bond equals $885.30.

b. Total value of 58 bonds equals $51,347.40.

Step-by-step solution

Computation of coupon payment

Assuming the par value of the bond = $1,000

Semi-annual interest rate equals 6% (12% / 2).

Semi-annual periods equals 20 (10 x 2).

$\begin{array}{rcl}\mathbf{Coupon}& \mathbf{=}& \mathbf{Parvalue}\mathbf{\times }\mathbf{Semi}\mathbf{-}\mathbf{annualcoupanrate}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{5}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{50}\\ & & \end{array}$

Computation of price of bond

$\begin{array}{rcl}\mathbf{Priceperbond}& \mathbf{=}& \mathbf{CouponPayment}\mathbf{\times }\left(\frac{1-{\left(1+r\right)}^{-n}}{r}\right)\mathbf{+}\frac{\mathbf{FaceValue}}{{\left(1+r\right)}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{50}\mathbf{\times }\left(\frac{1-{\left(1+0.06\right)}^{-10\times 2}}{0.06}\right)\mathbf{+}\frac{\mathbf{1}\mathbf{,}\mathbf{000}}{{\left(1+0.06\right)}^{\mathbf{10}\mathbf{\times }\mathbf{2}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{885}\mathbf{.}\mathbf{30}\\ & & \end{array}$

 Step 3: (b) Computation of Price of 58 bonds

$\begin{array}{rcl}\mathit{P}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathit{o}\mathit{f}\mathbf{58}\mathit{b}\mathit{o}\mathit{n}\mathit{d}\mathit{s}& \mathbf{=}& \mathit{P}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathit{o}\mathit{f}\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{l}\mathit{e}\mathit{b}\mathit{o}\mathit{n}\mathit{d}\mathbf{\times }\mathit{N}\mathit{o}\mathbf{.}\mathit{o}\mathit{f}\mathit{b}\mathit{o}\mathit{n}\mathit{d}\mathit{s}\\ & \mathbf{=}& \mathbf{\$}\mathbf{885}\mathbf{.}\mathbf{30}\mathbf{\times }\mathbf{58}\\ & \mathbf{=}& \mathbf{\$}\mathbf{51}\mathbf{,}\mathbf{347}\mathbf{.}\mathbf{40}\\ & & \end{array}$