Question

Assume the bank’s borrowing rate is 2% per annum. A business applies for 12 million loan for a project and plans to repay the loan in one year. A loan officer estimates the payoff from the project will be 30 million with 70% probability and 10 million with 30% probability. If a loan defaults, on average, a bank can get 60% of the salvage value. If the bank requires 3% return on its loans, what would be the loan rate?

Answer 1

Let Y be the bank's Borrowing Amount

It is given in the question the payoff from the project will be as follows:

=(30 million X 70%) + (10 million X 30%)

= 24 million

So the estimated payoff the project will be 20 million.

And, in case of default of payment, the Bank is assured to get 60% of the salvage value, which is

=24 million X 60%

= 14.40 million

Now, Calculating the Amount payable on Bank Borrowing @ 2%

=(1.02)*Y

Therefore the net amount realised by Bank

= 14.40 million - (1.02*Y) ....eq (1)

and the bank is expecting the return of 3% on its loan, equals to 12*3%

=0.36 million (2)

Solving for Y, equations (1) and (2)

14.40 million-(1.02*Y) = 0.36 million

Therefore Y= 13.76 million

Now calculating the Interest rate(r) compounded monthly for 1 year on Banks' Loan

12*(1+r)¹² = 14.40

or (1+r)¹²  = 1.20

we get r=83% compounded monthly or 7% compounded annually

The Banks' Loan rate would be 7%