91Ó°ÊÓ

Question: The Robinson Corporation has $43 million of bonds outstanding that were issued at a coupon rate of 11¾ percent seven years ago. Interest rates have fallen to 10¾ percent. Mr. Brooks, the vice president of finance, does not expect rates to fall any further. The bonds have 17 years left to maturity, and Mr. Brooks would like to refund the bonds with a new issue of equal amount also having 17 years to maturity. The Robinson Corporation has a tax rate of 30 percent. The underwriting cost on the old issue was 2.4 percent of the total bond value. The underwriting cost on the new issue will be 1.7 percent of the total bond value. The original bond indenture contained a five-year protection against a call, with a 9 percent call premium starting in the sixth year and scheduled to decline by one-half percent each year thereafter. (Consider the bond to be seven years old for purposes of computing the premium.) Assume the discount rate is equal to the after-tax cost of new debt rounded up to the nearest whole number.

b. Calculate the present value of total outflows.

Step by step solution

01

Information available

Bond obligation = 43,000,000

Interest rate at the time of issue = 11¾%

Interest rate after decline = 10¾%

Time remaining of bonds = 17 years

Call premium on old issue =9%

Underwriting cost of new issue =1.7% of total bond value

Underwriting cost on old issue = 2.4% of total bond value

Tax rate = 30%

Discount rate = 8%

02

Calculation of present value of underwriting cost

The present value of the underwriting cost is $613,326

$$\begin{gathered} \mathit{A}\mathit{m}\mathit{o}\mathit{r}\mathit{t}\mathit{i}\mathit{z}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathbf{=}\frac{\mathbf{A}\mathbf{c}\mathbf{t}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{cos}\mathbf{t}}{\mathbf{Y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\mathbf{}\mathbf{r}\mathbf{e}\mathbf{m}\mathbf{a}\mathbf{i}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{g}}\mathbf{×}\mathit{T}\mathit{a}\mathit{x}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{7}\mathbf{\%}\mathbf{×}\mathbf{\$}\mathbf{43}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}}{\mathbf{17}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{731}\mathbf{,}\mathbf{000}}{\mathbf{17}}\mathbf{×}\mathbf{30}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{43}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{30}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{12}\mathbf{,}\mathbf{900} \\ \mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{f}\mathit{u}\mathit{t}\mathit{u}\mathit{r}\mathit{e}\mathbf{}\mathit{t}\mathit{a}\mathit{x}\mathbf{}\mathit{s}\mathit{a}\mathit{v}\mathit{i}\mathit{n}\mathit{g}\mathit{s}\mathbf{=}\mathit{A}\mathit{m}\mathit{o}\mathit{r}\mathit{t}\mathit{i}\mathit{z}\mathit{e}\mathit{d}\mathbf{}\mathbf{cos}\mathit{t}\mathbf{}\mathbf{×}\mathit{P}\mathit{V}{\mathit{A}}_{\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{8}\mathbf{\%}\mathbf{n}\mathbf{-}\mathbf{17}\mathbf{}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\mathbf{)}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{12}\mathbf{,}\mathbf{900}\mathbf{×}\mathbf{9}\mathbf{.}\mathbf{122} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{117}\mathbf{,}\mathbf{764} \\ \mathit{N}\mathit{e}\mathit{t}\mathbf{}\mathit{u}\mathit{n}\mathit{d}\mathit{e}\mathit{r}\mathit{w}\mathit{r}\mathit{i}\mathit{t}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathbf{cos}\mathit{t}\mathbf{}\mathbf{=}\mathit{A}\mathit{c}\mathit{t}\mathit{u}\mathit{a}\mathit{l}\mathbf{}\mathbf{cos}\mathit{t}\mathbf{}\mathbf{-}\mathit{P}\mathit{V}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{t}\mathit{h}\mathit{e}\mathbf{}\mathit{f}\mathit{u}\mathit{t}\mathit{u}\mathit{r}\mathit{e}\mathbf{}\mathit{t}\mathit{a}\mathit{x}\mathbf{}\mathit{s}\mathit{a}\mathit{v}\mathit{i}\mathit{n}\mathit{g}\mathit{s} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{7}\mathbf{\%}\mathbf{×}\mathbf{\$}\mathbf{43}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{)}\mathbf{-}\mathbf{\$}\mathbf{117}\mathbf{,}\mathbf{674} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{731}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{117}\mathbf{,}\mathbf{674} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{613}\mathbf{,}\mathbf{326} \end{gathered}$$

03

 Step 4: Calculation of present value of outflows

The present value of outflows is $3,171,826

$$\begin{gathered} \mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{o}\mathit{u}\mathit{t}\mathit{f}\mathit{l}\mathit{o}\mathit{w}\mathit{s}\mathbf{=}\mathit{c}\mathit{a}\mathit{l}\mathit{l}\mathbf{}\mathit{p}\mathit{r}\mathit{e}\mathit{m}\mathit{i}\mathit{u}\mathit{m}\mathbf{}\mathit{p}\mathit{a}\mathit{y}\mathit{m}\mathit{e}\mathit{n}\mathit{t}\mathbf{+}\mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{u}\mathit{n}\mathit{d}\mathit{e}\mathit{r}\mathit{w}\mathit{r}\mathit{i}\mathit{t}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathbf{cos}\mathit{t} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{558}\mathbf{.}\mathbf{500}\mathbf{+}\mathbf{\$}\mathbf{613}\mathbf{,}\mathbf{326} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{171}\mathbf{,}\mathbf{826} \end{gathered}$$

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