Chapter 4: Q8BP (page 322)

Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 11 percent to 8 percent:
a. What is the bond price at 11 percent?
b. What is the bond price at 8 percent?
c. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent?

Short Answer

Expert verified

Bond price at 11% yield to maturity is $920.33
Bond price at 8% yield to maturity is $1,196.37
Percentage return on investment is 29.99%

Step by step solution

a.Computing annuity amount

$\begin{array}{rcl} C o u p o n A m o u n t & = & B o n d P a r V a l u e \times A n n u a l i n t e r e s t \\ = & $ 1, 000 \times 10 % \\ = & $ 100 \end{array}$

a.Computing bond price at 11 percent

Par value of bond (P) is $1,000.
Yield to maturity (r) is 11%.
Years to maturity (n) is 20.

$\begin{array}{rcl} B o n d P r i c e & = & C o u p o n \times \frac{[1 - \frac{1}{{(1 + r)}^{n}}]}{r} + \frac{P}{{(1 + r)}^{n}} \\ = & $ 100 \times \frac{[1 - \frac{1}{{(1 + 0.11)}^{20}}]}{0.11} + \frac{$ 1, 000}{{(1 + 0.11)}^{20}} \\ = & $ 100 \times 7.963 + 124.034 \\ = & $ 920.33 \end{array}$

b.Computing bond price at 8 percent

Par value of bond (P) is $1,000.
Yield to maturity (r) is 8%.
Years to maturity (n) is 20.
$\begin{array}{rcl} B o n d P r i c e & = & C o u p o n \times \frac{[1 - \frac{1}{{(1 + r)}^{n}}]}{r} + \frac{P}{{(1 + r)}^{n}} \\ = & $ 100 \times \frac{[1 - \frac{1}{{(1 + 0.08)}^{20}}]}{0.08} + \frac{$ 1, 000}{{(1 + 0.08)}^{20}} \\ = & $ 100 \times 9.818147 + 214.5482 \\ = & $ 1, 196.37 \end{array}$

c. Computigpercentage return on investment

$\begin{array}{rcl} P e r c e n t a g e R e t u r n & = & \frac{B o n d p r i c e a t 8 % - B o n d p r i c e a t 11 %}{B o n d p r i c e a t 11 %} \\ = & \frac{$ 1, 196.37 - $ 920.33}{$ 920.33} \\ = & 29.99 % \end{array}$

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Short Answer

Step by step solution

a.Computing annuity amount

a.Computing bond price at 11 percent

b.Computing bond price at 8 percent

c. Computigpercentage return on investment

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