A \(1,000 par value bond was issued 25 years ago at a 12 percent coupon rate. It currently has 15 years remaining to maturity. Interest rates on similar obligations are now 8 percent.

a. What is the current price of the bond? (Look up the answer in Table 16-2.)

b. Assume Ms. Bright bought the bond three years ago when it had a price of \)1,050. What is her dollar profit based on the bond’s current price?

c. Further assume Ms. Bright paid 30 percent of the purchase price in cash and borrowed the rest (known as buying on margin). She used the interest payments from the bond to cover the interest costs on the loan. How much of the purchase price of $1,050 did Ms. Bright pay in cash?

d. What is Ms. Bright’s percentage return on her cash investment? Divide the answer to part b by the answer to part c.

e. Explain why her return is so high.

Step by step solution

01

Step 1:(a) Computation of bond value

$$\begin{gathered} \mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\left(C\right)\mathbf{=}\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathbf{}\mathit{V}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{\times }\mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathbf{}\mathit{R}\mathit{a}\mathit{t}\mathit{e} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{12}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{120} \end{gathered}$$

$$\begin{gathered} \mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathbf{}\mathit{V}\mathit{A}\mathit{l}\mathit{u}\mathit{e}\mathbf{=}\mathit{C}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+r\right)}^t}}\right]}{\mathbf{r}}\mathbf{+}\frac{\mathbf{F}}{{\left(1+r\right)}^{\mathbf{t}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{120}\mathbf{\times }\frac{\left[1-{\displaystyle \frac{1}{{\left(1+0.08\right)}^{15}}}\right]}{\mathbf{0}\mathbf{.}\mathbf{08}}\mathbf{+}\frac{\mathbf{1}\mathbf{,}\mathbf{000}}{{\left(1+0.08\right)}^{\mathbf{15}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{342}\mathbf{.}\mathbf{38} \end{gathered}$$

02

Computation of profit

$$\begin{gathered} \mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{=}\mathit{C}\mathit{u}\mathit{r}\mathit{r}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{-}\mathit{P}\mathit{u}\mathit{r}\mathit{c}\mathit{h}\mathit{a}\mathit{s}\mathit{e}\mathit{d}\mathbf{}\mathit{P}\mathit{r}\mathit{i}\mathit{c}\mathit{e} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{342}\mathbf{.}\mathbf{38}\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{050} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{292}\mathbf{.}\mathbf{38} \end{gathered}$$

03

Computation of price paid in cash

$$\begin{gathered} \mathit{P}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{p}\mathit{a}\mathit{i}\mathit{d}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{c}\mathit{a}\mathit{s}\mathit{h}\mathbf{=}\mathit{C}\mathit{a}\mathit{s}\mathit{h}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{\times }\mathit{P}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{050}\mathbf{\times }\mathbf{30}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{315} \end{gathered}$$

04

Computation of percentage return on her cash investment

$$\begin{gathered} \mathit{R}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathbf{}\mathit{o}\mathit{n}\mathbf{}\mathit{c}\mathit{a}\mathit{s}\mathit{h}\mathbf{}\mathit{I}\mathit{n}\mathit{v}\mathit{e}\mathit{s}\mathit{t}\mathit{m}\mathit{e}\mathit{n}\mathit{t}\mathbf{=}\frac{\mathbf{D}\mathbf{o}\mathbf{l}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{}\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{t}}{\mathbf{P}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{}\mathbf{p}\mathbf{a}\mathbf{i}\mathbf{d}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{292}\mathbf{.}\mathbf{38}}{\mathbf{315}}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{92}\mathbf{.}\mathbf{82}\mathbf{\%} \end{gathered}$$

05

High returns

The bonds owned by her are for a long time period and she is paying 30% of the cash price are actual price paid in cash which helped her to acquire higher returns.

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