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 $65 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 4.89 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 since 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 would mean 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.

Todd has also heard of an interest-only loan and asks if this loan is available and what the terms would be. Christie says that the bank offers an interest-only loan with a term of 10 years and an APR of 3.85 percent. She goes on to further explain the terms. The company would be responsible for making interest payments each month on the amount borrowed. No principal payments are required. At the end of the 10-year term, the company would repay the $65 million. However, the company can make principal payments at any time. The principal payments would work just like those on a traditional mortgage. Principal payments would reduce the principal of the loan and reduce the interest due on the next payment.

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.

Questions:

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

2. Prepare an amortization table for the first six months of the traditional 30-year mortgage. How much of the first payment goes toward principal?

3. How long would it take for S&S Air to pay off the smart loan assuming 30-year traditional mortgage payments? Why is this shorter than the time needed to pay off the traditional mortgage? How much interest would the company save?

Answer 1

1. Loan = 65 million = 65000000, APR = 4.89%,

Calculating monthly payment for 30 year traditional mortgage

No of months = 30 x 12 = 360, monthly rate = APR/12 = 4.89%/12

We will use pmt function in excel to calculate the monthly payment

Formula to be used in excel: =pmt(rate,nper,-pv)

Using pmt function in excel we get monthly payment of traditional 30 year mortgage = 344577.40

Calculating monthly payment for 20 year traditional mortgage

No of months = 20 x 12 = 240, monthly rate = APR/12 = 4.89%/12

We will use pmt function in excel to calculate the monthly payment

Formula to be used in excel: =pmt(rate,nper,-pv)

Using pmt function in excel, we get monthly payment of traditional 20 year mortgage = 425031.27

2. We know that

Interest for a month = Beginning balance x monthly rate

Principal for the month = Monthly payment - interest for the month

Ending balance for a month = Beginning balance - Principal for the month

Beginning balance of a month = Ending balance of previous month

For example in first month

Beginning balance = 65000000, Interest = 6500000 x(4.89%/12) =264875.00 , Principal = 344577.40 - 264875.00 = 79702.40

Ending balance = 65000000 - 79702.40 = 64920297.60

So Beginning balance for second month = Ending balance of 1st month = 64920297.60

Similarly other values can be calculated for first 6 months and we get the following amortization schedule

Month	Beginning Balance	Monthly Payment	Interest	Principal	Ending Balance
1	65000000.00	344577.40	264875.00	79702.40	64920297.60
2	64920297.60	344577.40	264550.21	80027.19	64840270.41
3	64840270.41	344577.40	264224.10	80353.30	64759917.11
4	64759917.11	344577.40	263896.66	80680.74	64679236.38
5	64679236.38	344577.40	263567.89	81009.51	64598226.87
6	64598226.87	344577.40	263237.77	81339.63	64516887.24

Amount of first payment that goes towards the principal = 79702.40

3. For smart loan

Loan = 6500000

Two weekly payment amount = Monthly payment of traditional 30 year mortgage / 2 = 344577.40 / 2 = 172288.70

No of two weeks in a year = Weeks in a year / 2 = 52 / 2 = 26

Two weekly rate = APR / no of two weeks in a year = 4.89%/26

Using nper, we get no of two weeks to pay of smart loan = 658 two weeks

658 weeks = 650 + 8 = (650/26) years + 8 two weeks = 25 years and 8 two weeks

Smart loan can be repaid in 25 years and 8 two weeks

Time taken by smart loan is shorter because in smart loan as the the frequency of payments has increased, principal is being repaid more frequently than traditional loan. This consequently reduces the interest portion, larger percentage of periodic payments goes to towards principal payment as compared to traditional loan. This results in faster reduction of principal as compared to traditional loan. Also more total amount is being paid in a year in a smart loan as compared to traditional loan. This is shown below

Amount paid in year in traditional loan = 344577.40 x 12 = 4134928.80

Amount paid in year in smart loan = 172288.70 x 26 = 4479506.20

As more amount is being paid in year in smart loan, this also reduces decreases the balance of principal more quickly as compared to traditional loan. Hence the loan is repaid in shorter period of time

Calculating interest saved

Total payment in traditional loan = monthly payment x no of months = 344577.40 x 360 = 124047864

Total interest in traditional loan = Total payment in traditional loan - Loan = 124047864 - 65000000 = 59047864

Total payment in smart loan = two weekly payment amount x no of two weeks = 172288.70 x 658 = 113365964.60

Total interest in smart loan = Total payment in smart loan - Loan = 113365964.60 -65000000 = 48365964.60

Interest saved = Total interest in traditional loan -Total interest in smart loan = 59047864 - 48365964.60 = 10681899.40

Interest saved by the company = 10681899.40