Question

A borrower has the following two financing options: 80% LTV fully amortizing CPM for 25 years at 8% or 90% LTV CPM loan at 9% with similar terms. The borrower is not planning to prepay the loan.

a. Compute the incremental cost of borrowing the additional 10% (any property value should works).

b. What is the incremental cost of borrowing the additional 10% if the lender charges 2 discount points additional on the 90% loan?

c. Redo (b) assuming the borrower prepays the loan after 5 years.

Answer 1

Assumed Value of porperty = $1000,000.

Option	Loan amount	Interest rate	Loan period (months)	Monthly payments
80% LTV	800,000.00	8%	300	(6,174.53)
90% LTV	900,000.00	9%	300	(7,552.77)
Difference	100,000.00			1,378.24

The borrower will pay $1378.24 per month more for 25 years (300 monthly payments) on $100,000 amount excess borrowed. The incremental cost therefore will be calculated as follows, using a financial calculator:

N=25*12=300, PMT=-1378.24, PV=$100,000, FV=0, CPT-->i/y = 1.35%, which is a monthly rate.

yearly rate = (1+0.0135)^12 - 1 = 17.46%

Monthly payments has been calculated as under:

• Option 1: N=3000, i/y=8/12=0.6667,PV=800,000, FV=0, CPT-->PMT=6174.53
• Option 1: N=3000, i/y=9/12=0.75,PV=900,000, FV=0, CPT-->PMT=7552.77

b.

Option	Loan amount	Points @2%	Net proceeds	Interest rate	Loan period (months)	Monthly payments
80% LTV	800,000.00	-	800,000.00	8%	300	(6,174.5)
90% LTV	900,000.00	18,000.00	882,000.00	9%	300	(7,552.8)
Difference			82,000.00			1,378.24

Now instead, the borrower will pay $1378.24 monthly on net incremental proceeds of $82,000. The incremental cost of which is:

N=300, PMT=-1378.24, PV=82,000, FV=0, CPT-->i/y=1.67%

Yearly incremental rate = (1+0.0167)^12 - 1= 21.97%

c. We need to calculate the loan balance after 5 years:

FV = PV(1+r)^n - (Payment*[((1+r)^n)-1]/r)

• Option 1: FV = 80000*(1+(0.08/12)^(5*12)) - 6174.53*(((1+(0.08/12))^(5*12))/(0.08/12) = 738,191.53
• Option 2: FV = 90000*(1+(0.09/12)^(5*12)) - 7552.77*(((1+(0.09/12))^(5*12))/(0.09/12) = 839,451.97
• Difference = 101,260.44

Now we need to calculate the i/y, with following info:

N=5*12=60, PMT=-1378.24, PV=82,000, FV=-101,260.44, CPT-->i/y=1.89%

Yearly incremental rate = (1+0.0189)^12 - 1= 25.26%