Question

164 PART 3 Valuation of Future Cash Flows CHAPTER CASE S&S Air's Mortgage M ark Sexton and Todd Story, the owners of S&S Air, Inc., IV Iwere impressed by the work Chris had done on finan- cial planning. Using Chris's analysis, and looking at the de- mand 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 identi- fied 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 be- tween 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 mort gage 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 refi- nancing his home loan. A smart loan works as follows: two weeks a mortgage payment is made that is exactly one-half of the traditional monthly mortgage pay- ment. 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 tradi- tional 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 com- pany makes the 60th payment, the bullet payment would be due. The bullet payment is the remaining prin- cipal of the loan. Chris then asks how the bullet payment is calculated. Christie tells him that the remaining princi- pal 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 also has 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 pay- ments 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 tradi- tional 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 a 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? 4. Assume S&S Air takes out a bullet loan under the terms described. What are the payments on the loan? 5. What are the payments for the interest-only loan? 6. Which mortgage is the best for the company? Are there any potential risks in this action?

Answer 1

Solution:

1.

For 20-year loan, the monthly payments are

PVA = PMT({1 – [1/(1 + r)] t } / r)

$35,000,000 = PMT{[1 – 1 / (1 + .061/12) 360] / (.061/12)}

PMT = $212,098.17

For 30-year loan, the monthly payments are

PVA = PMT({1 – [1/(1 + r)] t } / r)

$35,000,000 = PMT{[1 – 1 / (1 + .061/12) 240] / (.061/12)}

C = $252,774.22

2.

6-month Amortization table for 30-year mortgage
	Pmt	Principal	Interest	Balance
0				35000000.00
1	212098.17	34181.51	177916.7	34965818.49
2	212098.17	34355.26	177742.9	34931463.23
3	212098.17	34529.90	177568.3	34896933.32
4	212098.17	34705.43	177392.7	34862227.89
5	212098.17	34881.85	177216.3	34827346.04
6	212098.17	35059.17	177039	34792286.88

3.

Bi Weekly Payments	=212098.17/2
	106049.09
Present Value of Annuity	35000000.00
Annuity per period (PMT)	106049.09

Using the Present Value of Annuity Formula we get

PVA = PMT({1 – [1/(1 + r)]t} / r)

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

Solve for 't'

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

No. of bi-weekly periods in a year	26
No.of Years	=635.24 / 26
	24.43230769

It takes 24.43 years to pay off under a smart loan

Total Paymenst under the traditional loan

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

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

Total Payments under Bi weekly mortgage

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

Bi-weekly total payments = $67,366,136.74

Interest Savings

=76,355,342.98 -67,366,136.74

8989206.24

4.

Bullet Loan

The loan payments for the first 59 months are the same as the traditional 30-year mortgage, which is $212,098.17. This mortgage payment will be made in the 60th month as well, but the company will also make the bullet payment. The bullet payment can be found by using an amortization table, but the easier method is to find the present value of the remaining loan payments. The present value of the remaining loan payments in month 60 will be:

PVA = C({1 – [1/(1 + r)]t} / r)

PVA = $212,098.17{[1 – 1 / (1 + .061/12)300] / (.061/12)}

PVA = $32,609,016.11

So, the total payment in month 60 will be:

Month 60 payment = $212,098.17 + 32,609,016.11

Month 60 payment = $32,821,114.28