You are a mortgage banker at Home Bank. One customer, Sean, wants to borrow money from your bank to finance his real estate investment project. The price for the real estate asset is $300,000. Sean wants to borrow a 80% loan to purchase the asset. You tell Sean that a constant payment, fully amortizing loan (FRM) with a 30 amortization period is available. The interest rate for the loan is 4.5%, which is the same as the market interest rate. Moreover, you will charge a loan origination fee of 3% for the loan.
(a) What is the monthly payment for the loan?
(b) What is the effective interest rate, assuming the mortgage is paid off after 30 years?
(c) If Sean plans to repay the loan after five years, what is the effective interest rate?
(d) If Sean wants to borrow a 90% loan, the loan rate will be 5.5%. Everything else being equal (i.e., he prepays the loan after 5 years, with the 3% loan fee), would you recommend him to borrow the 90% loan? [Hint: calculate incremental cost of borrowing]
(e) Suppose Sean can get a loan with a below-market interest rate from the builder. This fully amortizing FRM loan will have a 80% LTV, 4% interest rate, 30 years amortization period, and with no loan fees. At what price should the builder sell the asset to Sean in order to earn the market rate of interest (4.5%) on the loan? Assume that Sean would have the loan for the entire term of 30 years and the asset would normally sell for $300,000 without any special financing.