Pricing And Valuation Analysis Of Fixed Rate Mortgages

Pricing and Valuation Analysis of Fixed Rate Mortgages

Pyramid Mortgage Finance Company (PMFC)

I. Executive Summary

Pyramid Mortgage Finance Company (PMFC) originated four balloon mortgages of $500,000, each amortized over 25 years and an original term of 11 years. We have analyzed several elements of these mortgages. Through the analysis, we have identified several issues with the current mortgage portfolio and have offered recommendations. The analysis included appropriate pricing of the mortgages, structure of the mortgage offerings in relation to handling of discount points, potential liquidation of the mortgages and hedging opportunities.

Key findings that contributed to our recommendations include:

• PFMC could hedge against rising interest rate risk and have the potential to realize gains if interest rates decrease.

• Although selling the mortgages would incur an initial loss of capital, the funds from the sale could be invested at the current market rate of 8.5% to garner high yields.

Based on these conclusions, we recommend that PFMC sell the mortgages unless they can guarantee they can receive an 8.5% or higher constant return on the payments they receive from the mortgages.

II. Purpose of Analysis

Purpose: The critical questions that need to be addressed in the PMFC portfolio include, but are not limited to:

• Were the mortgages properly priced a year ago?

• Since PMFC is in need of cash, should the mortgages be liquidated?

• If the mortgages should be liquidated, what is the maximum liquidation value or price of the mortgages?

• What is the appropriate mechanism to use to hedge interest rate risk associated with the mortgage investment if they are to be kept in PMFC's portfolio?

To address these issues, several scenarios have been prepared and the relevant information, such as annual percentage rate, effective yield amongst others, was calculated. We then compared these numbers to their counterparts in the original issuance of the four balloon mortgages. Based on this analysis, recommendations are offered to help resolve the issues of the PMFC mortgage portfolio.

Models: This report was created analyzing the current situation of the PMFC mortgage portfolio and creating alternative analytic models that explore the areas where the PMFC portfolio is lacking.

Data Sources: Group Case #1: 6F:214 Real Estate Finance and Investment by Professor J. Sa-Aadu. Real Estate Finance and Investments by William Brueggeman and Jeffrey Fisher.

Key Assumptions:

• PFMC is faced with only two options: liquidate or keep mortgages but hedge against risk. There are no hybrid options available.

• In considering alternatives to the current mortgage portfolio, we use the prevalent market rate even though technically PFMC may get more or less than the market rate.

• All calculations are done in the accompanying spreadsheet titled вЂ?Analytical Model Calculations - Team 12.xls’ and appropriately referenced in the beginning of each model.

III. Analytical Models

MODEL A: Fair Pricing of Mortgage

(Please refer to Analytical Model Calculations вЂ" Exhibit #1 for all calculations)

Premise: The initial situation holds true: Four balloon mortgages of $500,000 amortized over 25 years and term of 11 years. Pricing scheme was done a year ago and used a combination of 7% contract rate and 5 points. Market rate at the time of issuance was 8%.

Questions: Will the combination of 7% contract rate and 5 points allow PMFC to earn a competitive rate of return on these mortgages?

Solution: The contract rate of 7% is used to determine the monthly payment of the borrower. To find the cost of the mortgage to the borrower, the Annual Percentage Rate (APR) is calculated. The APR reflects any discount points and is treated as additional income for PMFC. For the current mortgage portfolio, the APR is calculated to be 7.7428%. However, the prevalent market rate at the time was 8%.

Determination: The combination of 7% contract rate and 5 points did not allow PMFC to earn a competitive rate of return on these mortgages since the 7.7428% return is below the market rate of 8%.

MODEL B: APR and Yield Analysis (points deducted paid upfront)

(Please refer to Analytical Model Calculations вЂ" Exhibit #2 for all calculations)

Premise: The goal is to find the expected yield on the mortgages if they are held in their portfolio until maturity.

Questions: What are the Annual Percent Rate (APR), the Effective Annual Yield (EAY), and the Bond Equivalent Yield (BEY) to be earned by PMFC?

Solution: The APR is the effective rate the borrower will pay on the loan. It is the internal rate of return on a mortgage based on its coupon rate, discount points, amortization and term. For the PMFC mortgages, it is calculated to be 7.7428%.

The EAY is the effective cost of the mortgage and comes from six factors: the coupon rate, discount points (upfront cash paid by borrower to lower the coupon rate), fees, prepayment penalties, the effective life of the mortgage (how long the borrower actually holds the mortgage before refinancing or selling the house), and frequency of amortization. For the current portfolio, it is calculated to be 8.0236%.

The BEY makes the yield on a mortgage comparable to a corporate bond or treasury bond of similar maturity and was found to be 7.8688%.

Determination: The APR assumes that borrowers never refinance, and makes no provision for fees, such as prepayment penalties, other than discount points. Thus the APR does not give an accurate picture of actual cost or effective yield of mortgages.

The EAY may include a calculation assumption. If the EAY includes a pre-payment penalty, the lender must estimate the effective life

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