Question

Tom wants to purchase a property for $300,000. He can borrow a 80% LTV fixed-rate loan, with 4.5% annual interest rate and a 3% origination fee. Or, he can borrow a 90% LTV fixed-rate loan, with 5.5% annual interest rate, and a 3% origination fee. Both loans have a 30 year amortization period. If he plans to prepay the loan at the end of 3rd year, what will be the incremental cost of borrowing for him to to borrow the additional 10% loan amount?

a-) 12.25%

b-) 14.47%

c.) 13.68%

d.) 10%

my answer was 12.25% with my calculation and it was wrong. Please advise . Thank you

Answer 1

The calculation involves finding the present value of increment cash outgo including origination fees and the amount prepaid at the end of the 3 year period. Cost of borrowing is equal to the interest rate at which the PV is equal to incremental loan amount.

                Total additional borrowing = $30,000

As per the PMT formula, for loan value of 240,000 at 4.5% for 30 years, PMT is 1,216.

Similarly, for 270,000 at 5.5% for 30 years, it is 1,533.

• Incremental monthly cash outgo = $317.
• Incremental prepaid amount at the end of 3 year = 30,619.

Present value of the total cash flow equals $30,000 for interest rate equal to 14.47%.

Hence cost of borrowing for incremental amount is 14.47%.

Present value formula = cash flow/(1+r/12)^N, where N is month.

Month	0	1	2	-----	35	36
Incremental cash flow	900.0	317.0	317.0	-----	317.0	30935.5
Present value	900.0	313.2	309.5	-----	208.4	20093.6
NPV	30000.7
Incremental borrowing	30000.0
Interest rate annual	14.47%