Consider an FI holds two loans with the following characteristics: $\begin{array}{c|c|c|c|c|c|}
\hline \text { Loan i } & \text { Weight I } & \begin{array}{c}
\text { Annual spread between loan rate and Fl's } \
\text { cost of funds }
\end{array} & \begin{array}{c}
\text { Annual fees } \
\text { Loss to Fl given } \
\text { default }
\end{array} & \begin{array}{c}
\text { Lected default } \
\text { frequency }
\end{array} \
\hline 1 & 0.45 & 3.5 \% & 1.5 \% & 30 \% & 4 \% &\mathrm { P } _ { 12 } =-0.20\
\hline 2 & 0.55 & 4.5 \% & 2.0 \% & 25 \% & 3 \% \
\hline
\end{array}$
What is the return on the loan portfolio (round to two decimals)?
A)3.80%
B)5.75%
C)9.55%
D)4.87%

Question

Consider an FI holds two loans with the following characteristics: $\begin{array}{c|c|c|c|c|c|}
\hline \text { Loan i } & \text { Weight I } & \begin{array}{c}
\text { Annual spread between loan rate and Fl's } \
\text { cost of funds }
\end{array} & \begin{array}{c}
\text { Annual fees } \
\text { Loss to Fl given } \
\text { default }
\end{array} & \begin{array}{c}
\text { Lected default } \
\text { frequency }
\end{array} \
\hline 1 & 0.45 & 3.5 \% & 1.5 \% & 30 \% & 4 \% &\mathrm { P } _ { 12 } =-0.20\
\hline 2 & 0.55 & 4.5 \% & 2.0 \% & 25 \% & 3 \% \
\hline
\end{array}$
 What is the return on the loan portfolio (round to two decimals)?
A)3.80%
B)5.75%
C)9.55%
D)4.87%

Quizplus · Accepted Answer

The return on the loan portfolio can be calculated by considering the weight of each loan, the spread between the loan rate and the FI's cost of funds, the annual fees, the loss given default, and the expected default frequency. The formula for the return on each loan is: $$ \text{Return} = (\text{Spread} + \text{Fees} - (\text{Loss given default} \times \text{Expected default frequency})) \times \text{Weight} $$ For Loan 1: $$ \text{Return}_1 = (3.5\% + 1.5\% - (30\% \times 4\%)) \times 0.45 = (5\% - 1.2\%) \times 0.45 = 3.8\% \times 0.45 = 1.71\% $$ For Loan 2: $$ \text{Return}_2 = (4.5\% + 2.0\% - (25\% \times 3\%)) \times 0.55 = (6.5\% - 0.75\%) \times 0.55 = 5.75\% \times 0.55 = 3.16\% $$ Adding the returns of both loans: $$ \text{Total Return} = \text{Return}_1 + \text{Return}_2 = 1.71\% + 3.16\% = 4.87\% $$

Consider an FI Holds Two Loans with the Following Characteristics