Chapter 5, Problem 3CC

S&S Air’s Mortgage

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 $35 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 6.1 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.

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 3.5 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 $35 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.

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?

Summary Introduction

Case synopsis:

Company SS is an aircraft company which was formed by Person M and Person T. The owners of the company are satisfied by the work of Person C who has done the financial planning for the company. The owners of the company wish to expand their operations with their existing equipment but with a larger manufacturing facility.

Person M and Person T have found a suitable structure that is for sale and they believe that they can purchase and refurbish it for $35 million. The owners of the company now meet Person CV the loan officer of FUN Bank. The meeting is mainly to talk about about the mortgage options that are available for the company to fund the new facility.

Characters in the case:

• Company SS
• Person C
• Person M
• Person T
• Person CV
• FUN Bank

Adequate information:

• Person CV discusses about the 30-year mortgage loan and the 20-year mortgage loan.
• Person M asks Person CV about the smart loan.
• Person CV agrees with Person M about the smart loan and also states about the bullet loan or balloon payment.
• Person T asks Person CV about the interest-only loan.
• The thirty year mortgage monthly payment is $212,098.17.

To find: The number of period that the company takes to pay back the smart loan, assuming the 30-year traditional mortgage payments. The reason for the shortest period that is essential to pay back the traditional mortgage. The interest savings by the company.

Explanation of Solution

Given information:

Thirty-year mortgage:

• This loan can be paid in equal instalments.
• There is no closing cost for the loan as the company had a good relationship with the bank.
• The annual percentage rate for the loan is 6.1%.
• The twenty-year mortgage is also available with the same annual percentage rate.

Smart loan:

• The mortgage payment is made for every two weeks.
• It is one half of the traditional mortgage loan.
• The annual percentage rate is same as the traditional loan.
• The interest payments are saved in the smart loan.

Bullet loan or balloon payment:

• The great interest saving loan.
• The monthly payments are computed utilizing a 30 year traditional mortgage.
• For the above case the company will have a 5 year bullet where the company makes the mortgage payment for the traditional 30 year mortgage for the first 5 years.
• Immediately after the 60^th payment the bullet payment would be due.
• The remaining principal of the loan is the bullet payment.
• Person CV states that the remaining principal can be computed by the amortization table but it is the present values of the outstanding twenty five years of the mortgage payment of the 30-year mortgage.

Interest-only loan:

• Person CV states that the interest-only loan is offered by the bank with a term of 10 years and the annual percentage rate of 3.5%.
• The principal payments are not essential but the company has to make the interest payment on every month.
• At the end of the 10-year term the company must repay $35 million.

Formula to calculate the bi-weekly payments:

$\text{Bi-weekly payment}=\frac{30\text{-year traditional mortgage payment}}{2}$

Computation of the bi-weekly payment:

$\begin{array}{c}\text{Bi-weekly payment}=\frac{30\text{-year traditional mortgage payment}}{2}\\ =\frac{\$212,098.17}{2}\\ =\$106,049.09\end{array}$

Hence, the bi-weekly payment is $106,049.09.

The present value of annuity, the rate of interest, and the number of payments are known, and now it is essential to determine the number of periods for the payment of annuity. Note if the payment is made for every two weeks, then the total number of payments made is 26 payments for a year $\left(52/2\right)$. The number of periods can be determined by using the equation of the present value of annuity.

Formula to calculate present value of annuity:

$\text{Present value of annuity}=C\left\{\frac{\left[1-\left(\frac{1}{{\left(1+r\right)}^t}\right)\right]}{r}\right\}$

Note: C denotes the annual cash flow, r denotes the rate of exchange, and t denotes the period.

Compute the present value of annuity at 10% interest:

$\begin{array}{c}\text{Present value of annuity}=C\left\{\frac{\left[1-\left(\frac{1}{{\left(1+r\right)}^t}\right)\right]}{r}\right\}\\ \$35,000,000=\$106,049.09\left\{\frac{\left[1-\left(\frac{1}{{\left(1+\frac{0.061}{26}\right)}^t}\right)\right]}{\frac{0.061}{26}}\right\}\end{array}$

Now t can be found using the above equation:

$\begin{array}{c}\frac{1}{1.00235\text{t}}=1-\frac{\left[\left(\$35,000,000\right)\left(0.00235\right)\right]}{\$106,049.09}\\ 1.00235\text{t}=\frac{1}{0.2384}\\ 1.00235\text{t}=4.1950\\ \text{t}=\frac{\text{ln}4.1950}{\text{ln1}\text{.00235}}\end{array}$

$\text{t}=635.24\text{ periods}$

Hence, the number of periods is 635.24 periods.

Computation of the time that is essential to pay back the bi-weekly mortgage:

$\begin{array}{c}\text{Bi-weekly payoff}=\frac{635.24}{26}\\ =24.43\text{ years}\end{array}$

Note: There are 26 bi-weekly periods in a year.

Hence, the bi-weekly payoff can be made in 24.43 years.

The bi-weekly payment can be paid off quickly for two reasons that are as follows:

• One half of the payments quickly get to the bank that decreases the rate of interest that accrues every month.
• The company is actually paying the thirteen full payments every year (26 bi-weekly period amounts to 13 payments that are made monthly).

Computation of the total payments under the 30-year traditional mortgage loan:

$\begin{array}{c}30\text{-year total payments}=360\times 30\text{-year traditional mortgage payment}\\ =360\times \$212,098.17\\ =\$76,355,342.98\end{array}$

Hence, the thirty year total payments is $76,355,342.98.

Computation of the total payments under the bi-weekly mortgage loan:

$\begin{array}{c}\text{Bi-weekly total payments}=t\times \frac{\text{Bi-weekly payment}}{2}\\ =635.24\times \frac{\$106,049.09}{2}\\ =\$67,366,136.74\end{array}$

Hence, the bi-weekly total payment is $67,366,136.74.

Explanation:

The traditional answer for how much the bi-weekly mortgage saves is the variations between the two answers. The above computation proves to be the “pseudo interest” savings that is due to the different maturities of the loans. If the original rate of interest is 6.1% the cash flows present value will be still $35,000,000. More interest accrues in the thirty year traditional mortgage as it is longer but the present values will be the same as the present value of the bi-weekly mortgage. Thus, the two mortgage cash flows are equal. However, the bi-weekly mortgage is costly.

Formula to calculate the effective annual rate:

$\text{EAR}=1+{\left(\frac{\text{APR}}{\text{m}}\right)}^{\text{m}}-1$

Note: APR is the annual percentage rate, and m is the number of months.

Computation of the effective annual rate for the monthly mortgage:

$\begin{array}{c}\text{EAR}=1+{\left(\frac{\text{APR}}{\text{m}}\right)}^{\text{m}}-1\\ =1+{\left(\frac{0.061}{12}\right)}^{12}-1\\ =1+{\left(0.005083333333\right)}^{12}-1\\ =0.0627\end{array}$

Hence, the effective annual rate for the monthly mortgage is 0.0627 or 6.27%.

Computation of the effective annual rate for the bi-weekly mortgage:

$\begin{array}{c}\text{EAR}=1+{\left(\frac{\text{APR}}{\text{m}}\right)}^{\text{m}}-1\\ =1+{\left(\frac{0.061}{26}\right)}^{26}-1\\ =1+{\left(0.002346153846\right)}^{26}-1\\ =0.0628\end{array}$

Hence, the effective annual rate for the monthly mortgage is 0.0628 or 6.28%.