Chapter 6, Problem 18P

a.

Summary Introduction

To identify: The interest on Treasury securities, and yield curve.

Yield:

Yield is the percentage of securities at which the return is provided by the company to its investors. Yield can be there in the form of dividend and interest.

Yield Curve:

The graphical representation of the expected return, provided by the company to its investors during the years is known as the yield curve.

Answer to Problem 18P

The items required for the calculation of interest rate are the real risk-free rate, inflation rate, and maturity risk premium.

Explanation of Solution

Given,

The risk free rate is 2% or 0.02.

Inflation rate for the first year is 7% or 0.07.

The inflation rate of second year is 5% or 0.05.

The inflation rate after two years is 3% or 0.03.

The maturity risk premium for the first year is 0.2% or 0.002 and it will increase by 0.2% every year till 1%.

Formula to calculate the interest rate,

$\text{r}=\text{r*}+\text{IP}+\text{MRP}$

Where,

• r is the corporate bond yield.
• r* is the risk free rate.
• IP is the inflation premium.
• MRP is the maturity risk premium.

Statement to show the calculation of interest rate

Maturity	Real Risk-Free Rate (%) (r*)	Inflation Rate (%) (IP)	Maturity Risk Premium (MRP)	Interest Rate on Treasury Bond $\left(\text{r}=\text{r*}+\text{IP}+\text{MRP}\right)$
1	2	7	0.2	9.20
2	2	5	0.4	7.40
3	2	3	0.6	5.60
4	2	3	0.8	5.80
5	2	3	1	6
10	2	3	1	6
20	2	3	1	6

Table (1)

The yield curve of the given data

Fig 1

• The x-axis represents the maturity.
• The y-axis represents the interest rate.
• The interest rates with their respective time period can be shown from the graph.

Conclusion

Hence, the interest of 1-year treasury securities is 9.20%, at 2-year treasury securities is 7.60%, 3-year treasury securities is 5.60%, 4-year treasury securities is 5.80% and thereafter is 6%.

b.

Summary Introduction

To identify: The interest rate on AAA rated securities, and the yield curve.

Answer to Problem 18P

The items required for the calculation of interest rate are real risk-free rate, inflation rate, and maturity risk premium.

Explanation of Solution

Explanation:

Given,

The risk free rate is 2% or 0.02.

Inflation rate for the first year is 7% or 0.07.

The inflation rate of second year is 5% or 0.05.

The inflation rate after two years is 3% or 0.03.

The maturity risk premium for the first year is 0.2% or 0.002 and it will increase by 0.2% every year till 1%.

The default risk premium is 1% which increases

Formula to calculate the interest rate,

$\text{r}=\text{r*}+\text{IP}+\text{MRP+DRP}$

Where,

• r is the corporate bond yield.
• r* is the risk free rate.
• IP is the inflation premium.
• MRP is the maturity risk premium.
• DRP is the default risk premium.

Statement to show the calculation of interest rate

Maturity	Real Risk-Free Rate (%) (r*)	Inflation Rate on Treasury Bond (%) (IP)	Maturity Risk Premium (%) (MRP)	Interest Rate on Treasury Bond $\left(\begin{array}{l}\text{r}=\text{r*}\\ +\text{IP}\\ +\text{MRP}\end{array}\right)$	Default Risk Premium (%) (DRP)	Interest Rate on AAA rated Bonds $\left(\begin{array}{l}\text{r}=\text{r*}+\text{IP}\\ +\text{MRP}+{\text{DRP}}_{\text{AAA}}\end{array}\right)$
1	2	7	0.2	9.20	1	10.20
2	2	5	0.4	7.40	2	9.40
3	2	3	0.6	5.60	2	7.60
4	2	3	0.8	5.80	3	8.80
5	2	3	1	6	4	10
10	2	3	1	6	5	11
20	2	3	1	6	5	11

Table (2)

The yield curve of the given data

Fig 2

• The x-axis represents the maturity.
• The y-axis represents the interest rate.
• The interest rates of treasury securities and AAA bonds with their respective time period can be shown from the graph.

Conclusion

Hence, the interest of 1-year AAA bond is 10.20%, at 2-year AAA bond is 9.40%, 3-year AAA bond is 7.60%, 4-year AAA bond is 8.80% 5-year AAA bond is 10% and thereafter it is 11%.

c.

Summary Introduction

To identify: The interest rate on lower rated bonds, and the yield curve.

Answer to Problem 18P

The items required for the calculation of interest rate are the inflation rate, real risk-free rate, and maturity risk premium.

Explanation of Solution

Given,

The risk free rate is 2% or 0.02.

Inflation rate for the first year is 7% or 0.07.

The inflation rate of second year is 5% or 0.05.

The inflation rate after two years is 3% or 0.03.

The maturity risk premium for the first year is 0.2% or 0.002 and it will increase by 0.2% every year till 1%.

The default risk premium is 1% which increases

Formula to calculate the interest rate,

$\text{r}=\text{r*}+\text{IP}+\text{MRP+DRP}$

Where,

• r is the corporate bond yield.
• r* is the risk free rate.
• IP is the inflation premium.
• MRP is the maturity risk premium.
• DRP is the default risk premium.

Statement to show the calculation of interest rate on AAA rated bonds

Maturity	Real Risk-Free Rate (%) (r*)	Inflation Rate on Treasury Bond (%) (IP)	Maturity Risk Premium (%) (MRP)	Default Risk Premium (%) (DRP)	Interest Rate $\left(\begin{array}{l}\text{r}=\text{r*}+\text{IP}\\ +\text{MRP}+{\text{DRP}}_{\text{AAA}}\end{array}\right)$
1	2	7	0.2	1	10.20
2	2	5	0.4	2	9.40
3	2	3	0.6	2	7.60
4	2	3	0.8	3	8.80
5	2	3	1	4	10
10	2	3	1	5	11
20	2	3	1	5	11

Table (3)

Statement to show the calculation of interest rate on lower rated bonds

Maturity	Real Risk-Free Rate (%) (r*)	Inflation Rate on Treasury Bond (%) (IP)	Maturity Risk Premium (%) (MRP)	Default Risk Premium on Lower rated Bonds (%) (DRP)	Interest Rate (%) $\left(\begin{array}{l}\text{r}=\text{r*}\\ +\text{IP}\\ +\text{MRP}\\ +{\text{DRP}}_{\text{LR}}\end{array}\right)$
1	2	7	0.2	2	11.2
2	2	5	0.4	3	10.40
3	2	3	0.6	4	9.60
4	2	3	0.8	5	10.80
5	2	3	1	5	11
10	2	3	1	6	12
20	2	3	1	7	13

Table (4)

The yield curve of the given data

Fig 2

• The x-axis represents the maturity.
• The y-axis represents the interest rate.
• The interest rates of Treasury securities, AAA bonds and lower rated bonds with their respective time period can be shown from the graph.

Conclusion

Hence, the interest of 1-year lower rated bond is 11.20%, at 2-year lower rated bond is 10.40%, 3-year lower rated bond is 9.60%, 4-year lower rated bond is 10.80% 5-year lower rated bond is 11%, 10-year lower rated bond is 12% and thereafter is 13%.