A lender is considering what terms to allow on a loan. Current market terms are

Question

A lender is considering what terms to allow on a loan. Current market terms are 6.25 percent interest for 25 years, and the borrower, Rich, has requested a loan of $2,800,000. The lender believes that extra credit analysis and careful loan control will have to be exercised because Rich has never borrowed such a large sum before. In addition, the lender expects that market rates will move upward very soon, perhaps even before the loan is closed. To be on the safe side, the lender decides to extend to Rich a FRM commitment for $2,500,000 at 6.25 percent interest for 25 years; however, the lender wants to charge a loan origination fee to make the mortgage loan yield 6.6 percent. a. What origination fee should the lender charge? b. What fee should be charged if it is expected that the loan that will be repaid after 7 years?

Explanation / Answer

(a) Original Loan Amount = $ 2500000, Actual Loan Yield = 6.6 % and Promised Loan Yield = 6.25 %

Loan Tenure = 25 years

Let the actual annual payments be $ K (the mortgage is assumed to be repaid in equal annual repayments)

Therefore, 2500000 = K x (1/0.066) x [1-{1/(1.066)^(25)}]

K = $ 206853.6 approximately.

At the promised yield rate, these annual repayments will include the value of the loan amount plus the origination fees.

Therefore, total repayment = 206853.6 x (1/0.0625) x [1-{1/(1.0625)^(25)}] = $ 2582616

Origination Fee = Total Repayment - Loan Amount = 2582616 - 2500000 = $ 82616

(b) If the loan is to be repaid in 7 years instead of 25 everything esle remains same except for the number of compounding periods (number of annual repayments).

Promised Yield = 6.25 % and Actual Yield = 6.6 %

Let the annual repayments be $ M

2500000 = M x (1/0.066) x [1-{1/(1.066)^(7)}]

M = $ 457434.3

At the promised yield rate, these annual repayments will include the value of the loan amount plus the origination fees.

Therefore, total repayment = 457434.3 x (1/0.0625) x [1-{1/(1.0625)^(7)}] = $ 2531037

Origination Fees = Total Repayment - Loan Amount = 2531037 - 2500000 = $ 31037

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