Question

A developer is offering $110,000 loans on new properties at 9% for 25 years. However, her current required rate of return for the project is 9.5%. The property would normally sell for $110,000 without any special financing.

A. At what price should the builder sell the properties to earn, in effect the required rate of return on the loan? Assume that the builder would have the loan for the entire term of 25 years.

B. How would the answer change in (A.) if the property is expected to be sold after 10 years and the loan repaid?

Answer 1

Part (a)

PV of the loan = - PV (Rate, Nper, PMT, FV) = - PV (9.5%, 25, 9% x 110000, 110000) =  104,809

Hence, the price the builder should sell the properties to earn, in effect the required rate of return on the loan = Normal sale price + Loan amount - NPV = 110,000 + 110,000 - 104,809 = $ 115,191

Part (b)

PV of the loan = - PV (Rate, Nper, PMT, FV) = - PV (9.5%, 10, 9% x 110000, 110000) =   106,547

Hence, the price the builder should sell the properties = Normal sale price + Loan amount - NPV = 110,000 + 110,000 - 106,547 = $ 113,453