Question

A married couple are comparing the financing costs for the purchase of a $300,000 home.

The couple have good credit score of 790 and the required down payment, and as a result, can obtain a conventional mortgage loan with an 80 percent loan to value mortgage at a rate of 4.5% for a term of 30 year fixed rate mortgage. Closing costs for the conventional loan are 3% of the amount of the new mortgage.

Compute the following for the conventional mortgage loan:

Amount of the new mortgage loan__________   Amount of the Down Payment Required_________ +

Total Closing Costs required at Closing ___________ = Total Cash Outflow at Closing _______________

Monthly Mortgage Payment Required______________                  Annual Percentage Rate____________

Alternatively, the couple could obtain FHA mortgage financing with a 95 percent loan to value mortgage on the same property at the rate of 5.75% including the required FHA annual insurance premium for a 30 year fixed rate mortgage and 4.25% closing costs. However, with the FHA loan, an additional 1.75% is required at closing for the FHA mortgage insurance premium in addition to the 4.25% closing costs for a total cost of 6% of the new loan amount.

Compute the following for the FHA mortgage loan:

Amount of the new mortgage loan____________ Amount of the Down Payment Required__________ +

Total Closing Costs required at Closing ___________ = Total Cash Outflow at Closing ________________

Monthly Mortgage Payment including FHA Insurance: _____________   Annual Percentage Rate_______

What are the differences in the Conventional versus the FHA mortgage Loan Cash Outflow at Closing?

Conventional Loan Down Payment plus Closing Costs                                       ____________

(Less) FHA Loan: Down Payment plus Closing Costs                                           ____________

= Additional Cash Outflow for the Conventional Loan                                      ____________

Total FHA Monthly Mortgage Payment including the FHA Insurance          ____________

(Less) Conventional Monthly Mortgage Payment                                               ____________

= Difference in Total Monthly Mortgage Payments                                            ____________

What is the difference in the total Cash Outflows at Closing between the Conventional Home Mortgage Loan and the FHA Home Mortgage Loan?

Conventional Home Mortgage Cash Outflow at Closing?                                 ____________

(Less) FHA Home Mortgage Cash Outflow at Closing?                                       ____________

Additional Cash Outflow required for the Conventional Loan                        ____________

Total FHA monthly mortgage payment plus FHA Insurance Premium         ____________  

(Less) Conventional monthly mortgage payment                                                ____________

= Additional monthly costs with the FHA Home Mortgage Loan                   ____________

What is the Incremental cost of borrowing the additional funds?               _____________%

Answer 1

Purchase Price = $ 300000

Conventional Mortgage:

Interest Rate = 4.5 % per annum or 0.375 % per month, Loan Tenure = 30 years, Loan to Value Ratio = 80 %, Closing Costs = 3 % of the amount of mortgage

New Mortgage Loan = 0.8 x 300000 = $ 240000, Downpayment Required = 300000 - 240000 = $ 60000,

Closing Cost = 0.03 x 240000 = $ 7200

Total Cash Outflow at Closing = Closing Costs + Downpayment = 7200 + 60000 = $ 67200

Let the monthly mortgage payment be $ K

Therefore, 240000 = K x (1/0.00375) x [1-{1/(1.00375)^(360)}]

K = $ 1216.045

Annual Percentage Rate = (1.00375)^(12) - 1 = 0.04594 or 4.594 %

FHA Financing:

Interest Rate = 5.75 % per annum or 0.479167 % per month, Loan to Value Ratio = 95 %,Closing Costs = 6 % of the mortgage value, Tenure = 30 years

Loan Amount = 0.95 x 300000 = $ 285000

Let the monthly repayments be $ K

Therefore, 285000 = K x (1/0.00479167) x [1-{1/(1.00479167)^(360)}]

K = $ 1663.19

Amount of Mortgage = $ 285000

Amount of Downpayment = $ 15000

Total Closing Cost = 6 % of Mortgage Value = 0.06 x 285000 = $ 17100

Total Cash Outflow = 15000 + 17100 = $ 32100

Monthly Repayments = $ 1663.19

Annual Percentage Rate = (1.00479167)^(12) - 1 = 0.05904 or 5.904 %

Additional Cash flow for conventional mortgage = Total Cash Outflow under Conventional Mortgage - Total Cash Outflow under FHA = 67200 - 32100 = $ 35100

Difference in Monthly Mortgage Payments = Additional Monthly Cost of borrowing with the FHA Mortgage Loan = 1663.19 - 1216.045 = $ 447.145

Let the incremental cost of borrowing be r % per month.

Incremental Borrowing = 285000 - 240000 = $ 45000

Incremental EMI = 1663.19 - 1216.045 = $ 447.145

Therefore, 45000 = 447.145 x (1/r) x [1-{1/(1+r)^(360)}]

Using EXCEL's Goal Seek Function to solve the above equation, we get:

r = 0.00962 or 0.962 % per month

Therefore, incremental cost of borrowing = 0.962 x 12 = 11.544 % per annum