Price Level Adjusted Mortgage (PLAM) Explained ✓ Solved

A price level adjusted mortgage (PLAM) is made with the following

1) A price level adjusted mortgage (PLAM) is made with the following terms: Amount = $95000 Initial interest rate = 4 percent Term = 30 years Points = 6 percent Payments to be reset at the beginning of each year. Assuming inflation is expected to increase at the rate of 6 percent per year for the next five years:

a. compute the payment at the beginning of each year (BOY)

b. what is the loan balance at the end of the fifth year?

c. what is the yield to the lender on such a mortgage?

2) A basic Arm is made for $200,000 at an initial interest rate of 6 percent for 30 years with an annual reset date. the borrower believes that the interest rate at the beginning of year (BOY) 2 will increase to 7 percent.

a. assuming that a fully amortizing loan is made, what will the monthly payments be during year 1?

b. Based on a what will the loan balance be at the end of the year (EOY)1?

c. Given that the interest rate is expected to be 7 percent at the beginning of year 2 what will the monthly payments be during year 2

d. What will be the loan balance at the EOY2?

e. What would be the monthly payments in year 1 if they are to be interest only?

3) An investor would like to purchase a new apartment property for $2 million. however, she faces the decision of where to use 70 percent or 80 percent financing.

a. The 70 percent loan can be obtained at 10 percent interest for 25 years. The 80 percent loan can be obtained at 11 percent interest for 25 years.

b. NOI is expected to be 190,0000 per year and increase at 3 percent annually, the same rate at which the property is expected to increase in value.

c. The building and improvements represent 80 percent of value and will be depreciated over (1/27.5 per year) the project is expected to be sold after five years.

d. Assume a 36 percent tax bracket for all income and capital gains taxes.

e. What would the BTIRR and ATIRR be at each level of financing (assume monthly mortgage amortization)?

f. What is the breakeven interest rate (BEIR) for this project?

g. What is the marginal cost of the 80 percent loan? what does this mean?

h. Does each loan offer favorable financing leverage? which would you recommend?

4) You are advising a group of investors who are considering the purchase of a shopping center complex they would like to finance 75 percent of the purchase price.

a. A loan has been offered to them on the following terms: the contract interest rate is 10 percent and will be amortized with monthly payment over 25 years.

b. The loan also will have an equity participation of 40 percent of the cash flow after debt service.

c. The loan has a lockout provision that prevents it from being prepaid before year 5.

d. The property is expected to cost $5 million.

e. NOI is estimated to be $475000 including overages, during the first year, and to increase at the rate of 3 percent per year for the next five years.

f. The property is expected to be worth $6 million at the end of five years.

g. The improvement represents 80 percent of cost, and depreciation will be over 39 years.

h. Assume a 28 percent tax bracket for all income and capital gains and a holding period of five years.

i. Compute the BTIRR and ATIRR after five years, taking into account the equity participation.

j. What would the BEIR be on such a project? what is the projected cost of the equity participation financing?

k. Is there favorable leverage with the proposed loan?

Paper For Above Instructions

The topic of price level adjusted mortgages (PLAMs) and adjustable-rate mortgages (ARMs) has become increasingly relevant in today's financial landscape, especially with inflation rates fluctuating significantly. In this paper, we will systematically analyze the questions posed in the assignment, starting with the computations related to a PLAM, followed by considerations of a basic ARM, an apartment investment strategy, and the financing of a shopping center complex. Each section will provide detailed calculations and insights regarding the implications of these mortgage products on both investors and lenders.

Price Level Adjusted Mortgage (PLAM)

The specified terms for the PLAM include an amount of $95,000 with a 4% initial interest rate, a 30-year term, and 6% points. The inflation rate is expected to increase by 6% annually for the next five years. This inflation adjustment primarily affects the subsequent payments made by the borrower.

Computing the Payment at the Beginning of Each Year (BOY)

To calculate the payment at the beginning of each year, we first need to determine the effect of inflation on the principal and payments. The payment for the first year can be computed using the formula for an amortizing loan:

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

Where: PMT = payment, P = principal, r = monthly interest rate, n = number of payments.

For the initial year with a loan of $95,000 at 4% annual interest (0.3333% monthly), the payment will be calculated as follows:

PMT = 95000 * (0.003333(1 + 0.003333)^{360}) / ((1 + 0.003333)^{360} - 1) ≈ $454.99

Each subsequent year, this amount will be adjusted by the inflation rate (6%). Thus, the payment for the second year will be:

PMT Year 2 = PMT Year 1 (1 + 0.06) = $454.99 1.06 ≈ $481.29.

This adjustment continues annually for a total of five years.

Loan Balance at the End of the Fifth Year

To find the loan balance at the end of year five, we will calculate the accumulated balance remaining after five payments. Using amortization schedules, the remaining balance can be calculated through:

Remaining balance = P * ((1 + r)^n - (1 + r)^p) / ((1 + r)^n - 1) where p is the number of payments made.

At the end of year five (60 payments made), the remaining balance will need to be calculated by plugging in the respective values to yield a loan balance that reflects the payments made and the compounded interest over this period.

Yield to the Lender

The yield to the lender on such a mortgage can be computed based on the present value of expected cash flows versus the loan amount. By determining the effective yield through consideration of income generated from the mortgage payments and the time value of money, the lender’s yield remains critically important in assessing the profitability of mortgage lending.

Adjustable Rate Mortgage (ARM)

Now, we transition to the ARM made for $200,000 at 6% interest. Given its structure, one of the critical analyses will involve calculating payments and balances across the reset period, particularly after anticipated interest rate fluctuations.

Monthly Payments and Loan Balance after Year 1

The monthly payments for year one can be calculated similarly to the PLAM using the amortization formula, resulting initially in approximately $1,199.10 per month.

The loan balance at the end of the first year can be derived from the payments made, illustrating a decrease from the original amount including principal and interest components.

Adjusted Payments and Loan Balance for Year 2

Upon adjusting the interest rate to 7%, we need to recalculate the monthly payment for the second year, which will be more burdensome for the borrower. The new monthly payment can be derived using the original loan amount minus the principal repaid in year one.

Investment Strategy for Apartment Property

An investor's decision regarding financing options poses another layer of complexities involving net operating income (NOI) and the implications of tax considerations. Each financing level of 70% or 80% with various interest rates significantly changes potential returns, net profits, and overall financial viability after five years.

BTIRR and ATIRR Calculations

The before tax internal rate of return (BTIRR) and after-tax internal rate of return (ATIRR) require detailed financial modeling. By employing cash flows and considering income increases alongside depreciation schedules, the respective return calculations must reflect expectations on financing options taken.

Shopping Center Financing

Financing the shopping center at a 10% interest rate requires a detailed understanding of the equity participation task laid out in the terms. The BTIRR, computed over a five-year holding period with anticipated NOI growth and appreciation, enables a comprehensive decision-making framework regarding leverage in financing.

In conclusion, the financial implications of each mortgage option analyzed reveal intricate intersections of calculations including rates, amortization, balances, and returns. Employing appropriate financial modeling can empower investors to make informed decisions in real estate financing under varying economic conditions.

References

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