Question

An investor would like to purchase a $2,000,000 new apartment house and has two financing options under consideration:

Option 1 includes a 70% loan to value mortgage for 15 years at 6.5% interat and 3% closing costs.

Option 2 includes an 80% loan to value mortgage for 15 years at 7.5% interest and 4% closing costs.

Compute the APR for each mortgage option and the incremental cost of borrowing the additional amount if option 2 is selected.

Answer 1

Option 1

Value of home = $2,000,000

Value of loan = $2,000,000 × 70%

= $1,400,000

Value of loan is $1,400,000.

Closing cost = $1,400,000 × 3%

= $42,000.

Total amount need to borrow = $1,400,000 + $42,000

= $1,442,000.

Monthly payment on loan is calculated in excel and screen shot provided below:

Monthly payment is $12,561.37.

Effectively loan was $1,400,000 and pays $12,561.37.month. So Annual Percentage rate is calculated in excel and screen shot provided below:

Annual Percentage rate is 6.97%.

b.

Option 2

Value of home = $2,000,000

Value of loan = $2,000,000 × 80%

= $1,600,000

Value of loan is $1,600,000

Closing cost = $1,600,000 × 4%

= $64,000

Total amount need to borrow = $1,600,000 + $64,000

= $1,664,000.

Monthly payment on loan is calculated in excel and screen shot provided below:

Monthly payment is $15,425.49

Effectively loan was $1,600,000 and pays $15,425.49 per month. So Annual Percentage rate is calculated in excel and screen shot provided below:

Annual Percentage rate is 8.15%.

incremental cost of borrowing the additional amount if option 2 is selected is calculated below:

incremental cost of borrowing = 8.15% - 6.97%

= 1.18%

incremental cost of borrowing the additional amount if option 2 is selected is 1.18%.