Chapter 5: Discounted Cash Flow Valuation Of S&S Air's Mortg

Chapter 5: Discounted Cash Flow Valuation S&S Air's Mortgage

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This paper addresses the financial decision-making process for S&S Air, Inc., as they evaluate mortgage options to finance a new manufacturing facility. The decisions involve understanding different types of mortgage loans, calculating monthly payments, and analyzing amortization schedules, which are crucial components of discounted cash flow valuation and financial planning.

Introduction

S&S Air, Inc. is considering investing approximately $35 million to acquire and refurbish a manufacturing facility. To finance this investment, the company engages with a bank to explore suitable mortgage options. The key mortgage types discussed include traditional fixed-rate loans, "smart" loans, bullet loans, and interest-only loans. Understanding these loans' structures, amortization schedules, and payment calculations is essential for the company to make an informed decision aligned with its financial goals.

Types of Mortgage Loans and Their Features

1. Traditional Mortgages: These are fully amortizing loans with fixed monthly payments over a specified period, such as 20 or 30 years. The payments are calculated using the loan amount, interest rate, and amortization period. The bank offers a 30-year and a 20-year mortgage at an APR of 6.1%, with no closing costs.

2. Smart Loans: A variation of traditional mortgages, smart loans require payments every two weeks, with each payment being half of a monthly payment. This results in more frequent payments, accelerating principal repayment and reducing total interest paid, while maintaining the same APR.

3. Bullet Loans: These feature payments similar to a standard mortgage for the initial term (e.g., 5 years). After this period, the entire remaining principal balance—a balloon payment—is due immediately. The initial payments primarily cover interest, with minimal principal reduction.

4. Interest-Only Loans: The borrower makes monthly interest payments for the loan's duration, with the principal remaining unchanged until final repayment. The loan discussed has a 10-year term with an APR of 3.5%, after which the principal is payable in full, though partial prepayments are permitted.

Calculations of Mortgage Payments

1. Monthly payments for a 30-year traditional mortgage:

The monthly payment (PMT) is calculated using the formula:

PMT = P * [r(1 + r)^n] / [(1 + r)^n - 1]

Where:

- P = loan amount = $35,000,000

- r = monthly interest rate = annual rate / 12 = 0.061 / 12 ≈ 0.0050833

- n = total number of payments = 30 * 12 = 360

Plugging in the values:

PMT ≈ 35,000,000 [0.0050833 (1 + 0.0050833)^360] / [(1 + 0.0050833)^360 - 1]

Calculating:

- (1 + 0.0050833)^360 ≈ 6.0226

- Numerator: 0.0050833 * 6.0226 ≈ 0.030566

- Denominator: 6.0226 - 1 = 5.0226

- PMT ≈ 35,000,000 (0.030566 / 5.0226) ≈ 35,000,000 0.006085 ≈ $213,000

The approximate monthly payment for the 30-year mortgage is $213,000.

2. Monthly payments for a 20-year traditional mortgage:

Using the same formula, but with n = 20 * 12 = 240 payments:

(1 + 0.0050833)^240 ≈ 3.306

PMT ≈ 35,000,000 [0.0050833 3.306] / [3.306 - 1] ≈ 35,000,000 0.0168 / 2.306 ≈ 35,000,000 0.00728 ≈ $254,800

The approximate monthly payment for the 20-year mortgage is $254,800.

Amortization Schedule for the First Six Months of the 30-year Mortgage

To construct an amortization table for the first six months accurately, we calculate interest and principal portions of each payment:

Month 1:

• Interest: $35,000,000 * 0.0050833 ≈ $177,916
• Principal: $213,000 - $177,916 ≈ $35,084
• Remaining principal after Month 1: $35,000,000 - $35,084 ≈ $34,964,916

Month 2:

• Interest: $34,964,916 * 0.0050833 ≈ $177,693
• Principal: $213,000 - $177,693 ≈ $35,307
• Remaining principal: $34,964,916 - $35,307 ≈ $34,929,609

Repeating similar calculations for subsequent months, the principal portion gradually increases while interest decreases, illustrating amortization. The detailed schedule for the first six months would be as follows:

Month	Interest Payment	Principal Payment	Remaining Principal
1	$177,916	$35,084	$34,964,916
2	$177,693	$35,307	$34,929,609
3	$177,471	$35,529	$34,894,080
4	$177,248	$35,752	$34,858,328
5	$177,025	$35,975	$34,822,353
6	$176,803	$36,197	$34,786,156

In the first month, approximately $177,916 of the $213,000 payment goes toward interest, with about $35,084 reducing the principal.

Conclusion

Financial decision-making about mortgage options involves understanding the implications of loan duration, payment frequency, and repayment structure. The calculations show that shorter-term loans generally have higher monthly payments but lower total interest paid over the life of the loan. Alternative loan structures like smart loans, bullet loans, and interest-only loans provide flexibility and potential interest savings but come with different risks and obligations. A detailed amortization schedule illustrates how payments are allocated between interest and principal, helping S&S Air evaluate the most cost-effective and suitable mortgage option for their expansion plans.

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