Question

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?

S&S Air’s Mortgage ark Sexton and Todd Story, the owners of S&S Air, Inc., greatest Interest savings. At Todd's prompting, she goes IV Iwere impressed by the work Chris had done on finan on to explain a bullet loan. The monthly payments of a clal planning. Using Chris's analysis, and looking at the de bullet loan would be calculated using a 30-year tradi- mand for light alrcraft, they have decided that their existing tional mortgage. In this case, there would be a 5-year fabrication equipment is sufficient, but it is time to acquire bullet. This means that the company would make the a blgger manufacturing facility. Mark and Todd have Identi mortgage payments for the traditional 30-year mortgage fled a suitable structure that is currently for sale, and they for the first five years, but Immediately after the com- believe they can buy and refurbish it for about $35 million. pany makes the 60th payment, the bullet payment Mark, Todd, and Chris are now ready to meet with Christie would be due. The bullet payment is the remaining prin- Vaughan, the loan officer for First United National Bank cipal of the loan. Chris then asks how the bullet payment The meeting is to discuss the mortgage options available is calculated. Christie tells him that the remaining princi- to the company to finance the new facility. pal can be calculated using an amortization table, but it Christie begins the meeting by discussing a 30-year is also the present value of the remaining 25 years of mortgage. The loan would be repaid in equal monthly mortgage payments for the 30-year mortgage. Installments. Because of the previous relationship be- Todd also has heard of an interest-only loan and tween S&S Air and the bank, there would be no closing asks if this loan is available and what the terms would costs for the loan. Christie states that the APR of the be. Christie says that the bank offers an Interest-only loan would be 6.1 percent. Todd asks if a shorter mort loan with a term of 10 years and an APR of 3.5 percent. gage loan is available. Christie says that the bank does She goes on to further explain the terms. The company have a 20-year mortgage available at the same APR. would be responsible for making interest payments Mark decides to ask Christle about a "smart loan" he each month on the amount borrowed. No principal pay- discussed with a mortgage broker when he was refl ments are required. At the end of the 10-year term, the nancing his home loan. A smart loan works as follows: company would repay the $35 million. However, the Every two weeks a mortgage payment is made that is company can make principal payments at any time. The exactly one-half of the traditional monthly mortgage pay principal payments would work just like those on a tradi- ment. Christie informs him that the bank does have smarttional mortgage. Principal payments would reduce the loans. The APR of the smart loan would be the same as principal of the loan and reduce the interest due on the the APR of the traditional loan. Mark nods his head. He next payment. then states this is the best mortgage option available to Mark and Todd are satisfied with Christie's answers, the company because it saves Interest payments. but they are still unsure of which loan they should Christie agrees with Mark, but then suggests that a choose. They have asked Chris to answer the following bullet loan, or balloon payment, would result in the questions to help them choose the correct mortgage.

Answer 1

The 30-year loan payment will be:

PVA = C({1 – [1/(1 + r)] t } / r)
$35,000,000 = C{[1 – 1 / (1 + .061/12) 360] / (.061/12)}
C = $212,098.17

Payments Every two weeks, 52/2=26

Bi-weekly payment = $212,098.17 / 2

Bi-weekly payment = $106,049.09

Solving the present value of an annuity equation for the number of periods-

PVA = C({1 – [1/(1 + r)]t} / r)

$35,000,000 = $106,049.09{[1 – 1 / (1 + .061/26)t] / (.061/26)}

1/1.00235t= 1 – [($35,000,000)(.00235) / ($106,049.09)]

1.00235t= 1/.2384 = 4.1950

t = ln 4.1950 / ln 1.00235

T = 635.24 periods

Since they are 26 bi-weekly periods in a year, the time necessary to pay of the bi-weekly mortgage will

be:

Bi-weekly payoff = 635.24 / 26

= 24.43 years

how much the company saves is as follows:

The total payments under the 30-year traditional mortgage will be

30-year total payments = 360 × $212,098.17

30-year total payments = $76,355,342.98

And the total payments on the bi-weekly mortgage will be:

Bi-weekly total payments = 635.24 × ($106,049.09/2) = $67,366,136.74

Saving =$76,355,342.98 - $67,366,136.74=$89,89,206.24‬

The EAR of the monthly mortgage is

EAR = [1 + (APR / m)]m– 1

= [1 + (.061/12)]12– 1

= .0627 or 6.27%

And the EAR of the bi-weekly mortgage is:

EAR = [1 + (APR / m)]m– 1

= [1 + (.061/26)]26– 1

= .0628 or 6.28%

The bi-weekly mortgage is actually more expensive with the same APR.