Question

Mark Sexton and Todd Story, the owners of S&S Air, Inc., were impressed by the work Chris had done on financial planning. Using Chris's analysis, and looking at the demand for light aircraft, they have decided that their existing fabrication equipment is sufficient, but it is time to acquire a bigger manufacturing facility. Mark and Todd have identified a suitable structure that is currently for sale, and they believe they can buy and refurbish it for about $40 million. Mark, Todd, and Chris are now ready to meet with Christie Vaughan, the loan officer for First United National Bank. The meeting is to discuss the mortgage options available to the company to finance the new facility. Christie begins the meeting by discussing a 30-year mortgage. The loan would be repaid in equal monthly installments. Because of the previous relationship between S&S Air and the bank, there would be no closing costs for the loan. Christie states that the APR of the loan would be 8 percent. Todd asks if a shorter mortgage loan is available. Christie says that the bank does have a 20-year mortgage available at the same APR. Mark decides to ask Christie about a “smart loan” he discussed with a mortgage broker when he was refinancing his home loan. A smart loan works as follows: Every two weeks a mortgage payment is made that is exactly one-half of the traditional monthly mortgage payment. Christie informs him that the bank does have smart loans. The APR of the smart loan would be the same as the APR of the traditional loan. Mark nods his head. He then states this is the best mortgage option available to the company because it saves interest payments. Christie agrees with Mark, but then suggests that a bullet loan, or balloon payment, would result in the greatest interest savings. At Todd's prompting, she goes on to explain a bullet loan. The monthly payments of a bullet loan would be calculated using a 30-year traditional mortgage. In this case, there would be a 5-year bullet. This means that the company would make the mortgage payments for the traditional 30-year mortgage for the first five years, but immediately after the company makes the 60th payment, the bullet payment would be due. The bullet payment is the remaining principal of the loan. Chris then asks how the bullet payment is calculated. Christie tells him that the remaining principal can be calculated using an amortization table, but it is also the present value of the remaining 25 years of mortgage payments for the 30-year mortgage.

Mark and Todd are satisfied with Christie's answers, but they are still unsure of which loan they should choose. They have asked Chris to answer the following questions to help them choose the correct mortgage.

What are the monthly payments for a 30-year traditional mortgage? What are the payments for a 20-year traditional mortgage?

Answer 1

Answer 1:

Traditional mortgage:

Loan amount = $40 million = $40,000,000

Monthly interest = 8%/12

Duration = 30 years =30 * 12 months = 360 months

To get Monthly payment we can use excel function PMT:

= PMT (rate, nper, pv, fv, type)

= PMT (8%/12, 360, -40000000, 0, 0)

= $293,505.83

Monthly payments for a 30-year traditional mortgage = $293,505.83

Answer 2:

Duration = 20 years =20 * 12 months = 240 months

Monthly payment = = PMT (8%/12, 240, -40000000, 0, 0)

= $334,576.03

Monthly payments for a 30-year traditional mortgage = $334,576.03

-------------------------------------------------------------------------------------------------------------------------------------------------------------------

Note: The monthly payment can also be calculated using formula = EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

Monthly payments for a 30-year traditional mortgage = (40000000 * 8%/12 * (1 + 8%/12) ³⁶⁰) / ((1 + 8%/12) ³⁶⁰ - 1) = $293,505.83

Monthly payments for a 30-year traditional mortgage = (40000000 * 8%/12 * (1 + 8%/12) ²⁴⁰) / ((1 + 8%/12) ²⁴⁰ - 1) = $334,576.03​​​​​​​