Chapter 5, Problem 10P

a)

Summary Introduction

To determine: Discount yield on T-bill’s.

Explanation of Solution

Given information:

Par or face value is $100,000

Purchase price is $98,850

Days per year are 360 and 365

Days to maturity is 225

Calculation of discount yield:

$\begin{array}{c}\text{Discount}\text{yield}=\left[\frac{\left(\text{Par}\text{value}-\text{Purchase}\text{price}\right)}{\text{Par}\text{value}}\right]\times \left[\frac{360}{\text{Days}\text{to}\text{maturity}}\right]\\ =\left[\frac{\$100,000-\$98,850}{\$100,000}\right]\times \left[\frac{360}{\text{225}}\right]\\ =\$0.0115\times 1.6\\ =1.84\%\end{array}$

Therefore, discount yield is 1.84%

Calculation of bond equivalent yield:

$\begin{array}{c}\text{Bond equivalent}\text{yield}=\left[\frac{\left(\text{Par}\text{value}-\text{Purchase}\text{price}\right)}{\text{Purchase}\text{value}}\right]\times \left[\frac{365}{\text{Days}\text{to}\text{maturity}}\right]\\ =\left[\frac{\$100,000-\$98,850}{\$98,850}\right]\times \left[\frac{365}{\text{225}}\right]\\ =\$0.01163\times 1.622\\ =1.886\%\end{array}$

Therefore, discount yield is 1.886%

Calculation of effective annual yield:

$\begin{array}{c}\text{Effective annual return}={\left[1+\frac{\left(\text{Bond}\text{equivalent}\text{yield}\right)}{\left(\frac{\text{365}}{\text{Days}\text{to}\text{maturity}}\right)}\right]}^{\frac{365}{\text{Days}\text{to}\text{maturity}}}-1\\ ={\left[1+\frac{0.01886}{\left(\frac{\text{365}}{\text{225}}\right)}\right]}^{\frac{365}{225}}-1\\ =1.8918\%\end{array}$

Therefore, effective annual return is 1.8918%

b)

Summary Introduction

To determine: Discount yield on T-bill’s.

Explanation of Solution

Given information:

Par or face value is $100,000

Purchase price is $98,850

Days per year are 360 and 365

Days to maturity is 300

Calculation of discount yield:

$\begin{array}{c}\text{Discount}\text{yield}=\left[\frac{\left(\text{Par}\text{value}-\text{Purchase}\text{price}\right)}{\text{Par}\text{value}}\right]\times \left[\frac{360}{\text{Days}\text{to}\text{maturity}}\right]\\ =\left[\frac{\$100,000-\$98,850}{\$100,000}\right]\times \left[\frac{360}{\text{300}}\right]\\ =\$0.0115\times 1.2\\ =1.38\%\end{array}$

Therefore, discount yield is 1.38%

Calculation of bond equivalent yield:

$\begin{array}{c}\text{Bond equivalent}\text{yield}=\left[\frac{\left(\text{Par}\text{value}-\text{Purchase}\text{price}\right)}{\text{Purchase}\text{value}}\right]\times \left[\frac{365}{\text{Days}\text{to}\text{maturity}}\right]\\ =\left[\frac{\$100,000-\$98,850}{\$98,850}\right]\times \left[\frac{365}{\text{300}}\right]\\ =\$0.01163\times 1.2166\\ =1.4149\%\end{array}$

Therefore, discount yield is 1.4149%

Calculation of effective annual yield:

$\begin{array}{c}\text{Effective annual return}={\left[1+\frac{\left(\text{Bond}\text{equivalent}\text{yield}\right)}{\left(\frac{\text{365}}{\text{Days}\text{to}\text{maturity}}\right)}\right]}^{\frac{365}{\text{Days}\text{to}\text{maturity}}}-1\\ ={\left[1+\frac{0.014149}{\left(\frac{\text{365}}{\text{300}}\right)}\right]}^{\frac{365}{300}}-1\\ =1.4165\%\end{array}$

Therefore, effective annual return is 1.4165%