Consider an FI that holds two loans with the following characteristics: $$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline \text { Loan i } & \text { Weight I } & \begin{array} { c }
\text { Annual } \
\text { loan rate }
\end{array} & \begin{array} { c }
\text { Annual Fl's cost of } \
\text { funds }
\end{array} & \text { Annual fees } & \begin{array} { c }
\text { Loss to Fl given } \
\text { default }
\end{array} & \begin{array} { c }
\text { Expected default } \
\text { frequency }
\end{array} & \
\hline 1 & 0.30 & 10.0 \% & 4.5 \% & 2.0 \% & 25 \% & 4 \% & P _ { 12 } = - 0.25 \
\hline 2 & 0.70 & 11.0 \% & 5.0 \% & 1.5 \% & 20 \% & 3 \% & \
\hline
\end{array}$$ What is the return on the loan portfolio (round to two decimals)?

Question

Consider an FI that holds two loans with the following characteristics: $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline \text { Loan i } & \text { Weight I } & \begin{array} { c } 
\text { Annual } \
\text { loan rate }
\end{array} & \begin{array} { c } 
\text { Annual Fl's cost of } \
\text { funds }
\end{array} & \text { Annual fees } & \begin{array} { c } 
\text { Loss to Fl given } \
\text { default }
\end{array} & \begin{array} { c } 
\text { Expected default } \
\text { frequency }
\end{array} & \
\hline 1 & 0.30 & 10.0 \% & 4.5 \% & 2.0 \% & 25 \% & 4 \% & P _ { 12 } = - 0.25 \
\hline 2 & 0.70 & 11.0 \% & 5.0 \% & 1.5 \% & 20 \% & 3 \% & \
\hline
\end{array}$$ What is the return on the loan portfolio (round to two decimals)?

Quizplus · Accepted Answer

The return on the loan portfolio can be calculated by considering the weighted average of the returns from each loan, taking into account the loan rates, costs of funds, annual fees, and the expected losses due to defaults. The calculation is as follows:For Loan 1:- Effective return = Annual loan rate + Annual fees - Annual FI's cost of funds - (Loss to FI given default * Expected default frequency)- Effective return = 10.0% + 2.0% - 4.5% - (25% * 4%)- Effective return = 12.0% - 4.5% - 1.0% = 6.5%For Loan 2:- Effective return = 11.0% + 1.5% - 5.0% - (20% * 3%)- Effective return = 12.5% - 5.0% - 0.6% = 6.9%Weighted average return on the portfolio = (0.30 * 6.5%) + (0.70 * 6.9%) = 1.95% + 4.83% = 6.78%Therefore, the return on the loan portfolio is 6.78%.

Consider an FI That Holds Two Loans with the Following