Question

Gross Return on a Loan Problem

1. (A.) What is the gross return on a loan if the bank requires the firm to hold 5.4 percent in compensating balances, current Federal Reserve’s reserve requirements are 5%, charges an origination fee of 0.0155 percent, the relevant firm’s risk premium is 3.1%, and the LIBOR is 2.6%?

(B.) What is the expected return to the loan if the probability of complete repayment of the loan is projected to be 88 percent?

2. (A.) What is the gross return on a loan if the bank requires the firm to hold 2.2 percent in compensating balances, charges an origination fee of 0.0125 percent, the relevant firm’s risk premium is 2.7%, and the LIBOR is 2.4%?

(B.) What is the expected return to the loan if the probability of complete repayment of the loan is 82 percent?

Answer 1

1.(A) Gross Return on loan=( LOF+BLR+CRP)/{1-CB(1-R)}

where, LOF is Loan originating fee, BLR is Base lending rate, CRP is Credit Risk Premium, CB is Compensating Balance and R is Reserve Requirement.

In this problem, LOF=0.000155, BLR= 0.026, CRP= 0.031, CB= 0.054, R= 0.05

Substituting these values,

Gross Return= (0.000155+0.026+0.031)/{1-0.054(1-0.05)}

= 0.057155/1-(0.054*0.95)

=0.057155/1-0.0513= 0.057155/0.9487

= 0.060245=6.02%

1.(B) Expected Return on a Loan= p*(1+GR)-1

where, p is the probability of complete repayment of loan, GR is the Gross Return.

Here, p=88%=0.88, GR=0.0602

So, substituting these values we get

Expected Return, E(r)= 0.88(1+0.0602)-1= 0.93298-1

= -0.067= -6.7%

2.(A) Similar to the previous case, this problem also can be solved.

Here LOF=0.000125, BLR=0.024, CRP= 0.027, CB= 0.022, R= 0.05

Substituting these values in the Gross Return formula,

GR= (0.000125+0.024+0.027)/{1-0.022(1-0.05)

= 0.051125/1-(0.022*0.95)= 0.051125/1-0.0209

= 0.051125/0.9791= 0.0522= 5.22%

2.(B) Similar to the previous problem we can find out the expected return.

Here, p=82%=0.88, GR= 0.0522

Substituting these values in the E(r) formula we get

E(r)= 0.82*(1+0.0522)-1

= 0.82*1.0522-1

= 0.8628-1

= -0.1372= -13.72%