Chapter 16, Problem 21P

a)

Summary Introduction

To determine: The annual financing cost.

Explanation of Solution

Computation:

$\begin{array}{c}\text{Interest cost}=\text{Loan amount}\times \text{Annual interest rate}\\ =\text{\$250,000}\times 9\text{\%}\\ =\$22,500\end{array}$

$\begin{array}{c}\text{Commitment fee}=\left(\$1,000,000-\$250,000\right)\times 0.5\%\\ =\$3,750\end{array}$

$\begin{array}{c}Usablefund=Loan\text{ amount}\times \left(1-\text{ compensating balance rate}\right)\\ =\text{\$250,000}\times \left(1-0.10\right)\\ =\$225,000\end{array}$

$\begin{array}{c}Annual\text{ financing cost}=\frac{\left(Interest\text{ cost}+\text{commitment fee}\right)}{Usablefunds}\times \frac{365}{365}\times 100\\ =\frac{\$22,500+\$3,750}{\$225,000}\times \frac{365}{365}\times 100\%\\ =11.67\%\end{array}$

Hence, the annual financing cost is 11.67%.

b)

Summary Introduction

To determine: The annual financing cost.

Explanation of Solution

Computation:

$\begin{array}{c}\text{Interest cost}=\text{Loan amount}\times \text{Annual interest rate}\\ =\text{\$500,000}\times 9\text{\%}\\ =\$45,000\end{array}$

$\begin{array}{c}\text{Commitment fee}=\left(\$1,000,000-\$500,000\right)\times 0.5\%\\ =\$2,500\end{array}$

$\begin{array}{c}Usablefund=Loan\text{ amount}\times \left(1-\text{ compensating balance rate}\right)\\ =\text{\$500,000}\times \left(1-0.10\right)\\ =\$450,000\end{array}$

$\begin{array}{c}Annual\text{ financing cost}=\frac{\left(Interest\text{ cost}+\text{commitment fee}\right)}{Usablefunds}\times \frac{365}{365}\times 100\\ =\frac{\$45,000+\$2,500}{\$450,000}\times \frac{365}{365}\times 100\%\\ =10.56\%\end{array}$

Hence, the annual financing cost is 10.56%.

c)

Summary Introduction

To determine: The annual financing cost.

Explanation of Solution

Computation:

$\begin{array}{c}\text{Interest cost}=\text{Loan amount}\times \text{Annual interest rate}\\ =\text{\$1,000,000}\times 9\text{\%}\\ =\$90,000\end{array}$

$\begin{array}{c}\text{Commitment fee}=\left(\$1,000,000-\$1,000,000\right)\times 0.5\%\\ =\$0\end{array}$

$\begin{array}{c}Usablefund=Loan\text{ amount}\times \left(1-\text{ compensating balance rate}\right)\\ =\text{\$1,000,000}\times \left(1-0.10\right)\\ =\$900,000\end{array}$

$\begin{array}{c}Annual\text{ financing cost}=\frac{\left(Interest\text{ cost}+\text{commitment fee}\right)}{Usablefunds}\times \frac{365}{365}\times 100\\ =\frac{\$90,000}{\$900,000}\times \frac{365}{365}\times 100\%\\ =10\%\end{array}$

Hence, the annual financing cost is 10%.