Chapter 13, Problem 8PA

Summary Introduction

(a)

To determine:

Value of bond.

Introduction:

Bond is a fixed return investment in which an individual gives money to an entity and entity in return gives fixed return to him over the period of time and par value of the bond too at maturity.

Explanation of Solution

Formula to calculate value of bond is,

$P=\left[{\displaystyle \sum _{t=1}^n\frac{C_t}{{\left(1+i\right)}^t}}\right]+\frac{FV}{{\left(1+i\right)}^n}$……..(1)

Where,

• P is value of bond.
• C is coupon rate.
• i is Required rate of return.
• n is number of years.
• FV is future value.

For 7 years:

Given,

C is 10%.

i is 8%.

n is 7 years.

FV is $1,000.

Substitute 10% for C, 8% fori, 7 years for n and $1,000 for FV in the above equation (1).

$\begin{array}{c}P=\frac{\$100}{{\left(1+0.08\right)}^1}+\frac{\$100}{{\left(1+0.08\right)}^2}+\mathrm{\dots }+\frac{\$100}{{\left(1+0.08\right)}^7}+\frac{\$1,000}{{\left(1+0.08\right)}^7}\\ =\$1,104.13\end{array}$

Value of bond is $1,104.13.

For 5 years:

Given,

C is 10%.

i is 8%.

n is 5 years.

FV is $1,000.

Substitute 10% for C, 8% fori, 5 years for n and $1,000 for FV in the above equation (1).

$\begin{array}{c}P=\frac{\$100}{{\left(1+0.08\right)}^1}+\frac{\$100}{{\left(1+0.08\right)}^2}+\mathrm{\dots }+\frac{\$100}{{\left(1+0.08\right)}^5}+\frac{\$1,000}{{\left(1+0.08\right)}^5}\\ =\$1,079.85\end{array}$

Value of bond is $1,079.85.

For 2 years:

Given,

C is 10%.

i is 8%.

n is 2 years.

FV is $1,000.

Substitute 10% for C, 8% fori, 2 years for n and $1,000 for FV in the above equation (1).

$\begin{array}{c}P=\frac{\$100}{{\left(1+0.08\right)}^1}+\frac{\$100}{{\left(1+0.08\right)}^2}++\frac{\$1,000}{{\left(1+0.08\right)}^2}\\ =\$1,035.67\end{array}$

Value of bond is $1,035.67.

Conclusion

Hence, Value of bond for 7, 5 and 2 year before maturity is $1,104.13, $1,079.85 and $1,035.67.

Summary Introduction

(b)

To determine:

Value of bond.

Explanation of Solution

For 7 years:

Given,

C is 6%.

i is 8%.

n is 7 years.

FV is $1,000.

Substitute 6% for C, 8% fori, 7 years for n and $1,000 for FV in the above equation (1).

$\begin{array}{c}P=\frac{\$60}{{\left(1+0.08\right)}^1}+\frac{\$60}{{\left(1+0.08\right)}^2}+\mathrm{\dots }+\frac{\$60}{{\left(1+0.08\right)}^7}+\frac{\$1,000}{{\left(1+0.08\right)}^7}\\ =\$895.9\end{array}$

Value of bond is $895.90.

For 5 years:

Given,

C is 6%.

i is 8%.

n is 5 years.

FV is $1,000.

Substitute 6% for C, 8% fori, 5 years for n and $1,000 for FV in the above equation (1).

$\begin{array}{c}P=\frac{\$60}{{\left(1+0.08\right)}^1}+\frac{\$60}{{\left(1+0.08\right)}^2}+\mathrm{\dots }+\frac{\$60}{{\left(1+0.08\right)}^5}+\frac{\$1,000}{{\left(1+0.08\right)}^5}\\ =\$920.1\end{array}$

Value of bond is $920.10.

For 2 years:

Given,

C is 6%.

i is 8%.

n is 2 years.

FV is $1,000.

Substitute 6% for C, 8% fori, 2 years for n and $1,000 for FV in the above equation (1).

$\begin{array}{c}P=\frac{\$60}{{\left(1+0.08\right)}^1}+\frac{\$60}{{\left(1+0.08\right)}^2}++\frac{\$1,000}{{\left(1+0.08\right)}^2}\\ =\$964.3\end{array}$

Value of bond is $964.3.

Conclusion

Hence, Value of bond for 7, 5 and 2 year before maturity is $895.90, $920.10 and $964.30.