Question

Problem 6 An investor would like to purchase a $2,000,000 new apartment house and under consideration: Option 1 includes a 70% loan to value Option 2 includes an 80% loan to value mortgage for 15 years at 7 options financing has two mortgage for 15 years at 6.5% interest and 3% closing cost .5% interest and 4% closing Compute the APR for each mortgage option and the incremental cost of borr amount if option 2 is selected. the additional owing

Answer 1

All financials below are in $.

Cost of the house, C = 2,000,000

Under Option 1

LTV = 70%

Hence, loan amount = LTV x C = 70% x 2,000,000 = 1,400,000

Closing costs = 3% = 3% x 1,400,000 = 42,000

Effective amount disbursed, D = Loan amount - closing costs = 1,400,000 - 42,000 = 1,358,000

Assume monthly mortgage payments. We have to find the new APR of the loan based on effective amount disbursed. We will use the RATE function in excel. Inputs are:

Period = nos. of months in the term = 12 x 15 = 180

PMT = payment per period = PMT (Rate, Period, PV) = PMT (6.5% / 12, 180, - 1400000) = 12,195.50

PV = - Effective disbursed amount = - 1358000

FV = future value = 0

Hence, monthly effective rate of interest = RATE (Period, PMT, PV, FV) = RATE (180, 12195.50, -1358000, 0) = 0.5822%

Hence, APR = 12 x monthly rate = 12 x 0.5822% = 6.986%

Under Option 2

LTV = 80%

Hence, loan amount = LTV x C = 80% x 2,000,000 = 1,600,000

Closing costs = 4% = 4% x 1,600,000 = 64,000

Effective amount disbursed, D = Loan amount - closing costs = 1,600,000 - 64,000 = 1,536,000

Assume monthly mortgage payments. We have to find the new APR of the loan based on effective amount disbursed. We will use the RATE function in excel. Inputs are:

Period = nos. of months in the term = 12 x 15 = 180

PMT = payment per period = PMT (Rate, Period, PV) = PMT (7.5% / 12, 180, - 1600000) = 14,832.20

PV = - Effective disbursed amount = - 1536000

FV = future value = 0

Hence, monthly effective rate of interest = RATE (Period, PMT, PV, FV) = RATE (180, 14832.20, -1536000, 0) = 0.6810%

Hence, APR = 12 x monthly rate = 12 x 0.6810% = 8.173%

Incremental cost of borrowing:

Incremental amount borrowed = Effective disbursed amount under option 2 - that under option 1 = 1,536,000 - 1,358,000 = 178,000

Incremental PMT = 14,832.20 - 12,195.50 = 2,636.69

Incremental cost of borrowing per month = RATE (Period, PMT, -PV, FV) = RATE (180, 2636.69, -178000,0) = 1.3484%  

Hence, annualized incremental cost of borrowing = 12 x 1.3484% = 16.180%