(Practice Problems) FRM and ARM
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Finance
Date
Apr 3, 2024
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docx
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1)
What are the major differences between the CAM, and CPM loans? What are the advantages to
borrowers and risks to lenders for each? What elements do each of the loans have in common?
CAM - Constant Amortization Mortgage
- Payments on constant amortization mortgages are determined first by computing a constant amount of each monthly payment to be applied to principal. Interest is then computed on the monthly loan balance and added to the monthly amount of amortization to determine the total monthly payment. CPM - Constant Payment Mortgage
- This payment pattern simply means that a level, or constant, monthly payment is calculated on an original loan amount at a fixed rate of interest for a given term. At the end of the term of the mortgage loan, the original loan amount or principal is completely repaid and the lender has earned a fixed rate of interest on the monthly loan balance. However the amount of amortization varies each month.
2)
What are the advantages and disadvantages (for both the borrower and lender) of a GPM, as compared to an otherwise similar CPM? Under what circumstances (economic and property specific) will a GPM be most useful?
The GPM is useful not only in inflationary environments in which high interest rates make CPM mortgage payments hard to afford, but also for dealing with loans on income properties that are
in turnaround, development, or workout situations, in which their ability to generate net rent is expected to increase over time. GPMs may also be useful for first-time homebuyers, whose incomes can be expected to grow.
3)
What are loan closing costs? How do they affect borrowing costs and why?
Closing costs are incurred in many types of real estate financing, including residential property, income property, construction, and land development loans. Closing costs that do affect the cost of borrowing are additional finance charges levied by the lender. These charges constitute additional income to the lender and as a result must be included as a part of the cost of borrowing. Lenders refer to these additional charges as loan fees.
4)
Does repaying a loan early ever affect the actual or true interest cost to the borrower?
It depends. If no additional fees are charged (and no PPP), the true interest rate always equals the contract rate of interest. If additional fees are charged, earlier prepayment increases the effective borrowing cost.
5)
A. What are some of the reasons up-front points and fees are so common in the mortgage business? B. What is the major reason for the existence of prepayment penalties?
a. Up-front fees are a way for the loan originator to make some profit while providing some disincentive against early prepayment of the loan by the borrower. These fees can also be used as a trade-off against the level of the regular loan payment: Greater origination fees and discount points allow lower regular loan payments for the same yield (other answers exist as well). b. The main reason for prepayment penalties is that the investors want a certain yield locked in and therefore want to mitigate prepayment risk.
6)
What is negative amortization? Negative amortization means that the loan balance owed increases
over time because payments
are less than interest due.
7)
A fully amortizing mortgage loan is made for $80,000 at 6 percent interest for 25 years. Payments are to be made monthly. Calculate:
a.
Monthly payments
b.
Interest and principal payments during month 1
c.
Total principal and total interest paid over 25 years
d.
The OLB (RMB) if the loan is repaid at the end of year 10.
e.
Total monthly interest and principal payments through year 10.
f.
What would the breakdown of interest and principal be during month 50?
(a) Monthly payment (PMT (n,i,PV, FV) = $515.44
Solution:
n = 25x12 or 300
i = 6%/12 or .50
PV =
$80,000
FV
=
0
Solve for payment:
PMT
=
-$515.44
(b) Month 1:
interest payment:
$80,000 x (6%/12) = $400
principal payment:
$515.44 - $400 = $115.44
(c) Entire 25 Year Period:
total payments:
$515.44 x 300
= $154,632
total principal payment:
$80,000
total interest payments:
$154,632 - $80,000
=
$74,632
(d) Outstanding loan balance if repaid at end of ten years = $61,081.77, as presented below for FV.
Solution:
n
=
120 (pay off period)
i
=
6%/12 or 0.50
PMT =
$515.44
PV
=
$80,000
Solve for FV:
FV
=
$61,081.77
(e) Trough ten years:
total payments:
$515.44 x 120 = $61,852.80
total principal payment (principal reduction):
$80,000 – 61,081.77* = $18,918.23
*PV of loan at the end of year 10
total interest payment:
$61,852.80 - $18,918.23 = $42,934.57
(f) Step 1, Solve for loan balance at the end of month 49:
n
= 49
i
=
6%/12 or 0.50
PMT =
$515.44
PV
=
- $80,000
Solve for loan balance:
PV
=
$73,608.28 Step 2, Solve for the interest payment at month 50:
interest payment:
$73,608.28 x (.06/12)=
$368.04
principal payment:
$515.44 - $368.04
=
$147.40
8)
A fully amortizing mortgage is made for $80,000 for a term of 25 years. Total monthly payments
will be $899.86 per month. What is the interest rate on the loan?
The interest rate on the loan is 12.96%.
Solution:
n
=
25x12 or 300
PMT
=
-$899.86
PV
=
$80,000
FV
=
0
Solve for the annual
interest rate:
i
=
1.08 (x12) or 12.96%
9)
What is the effective borrowing cost of the loan from the previous question if the borrower pays
two points up front to get the loan?
n
=
25x12 or 300
PMT
=
-$899.86
PV
=
$78,400
FV
=
0
Solve for the annual
interest rate:
i
=
1.11 (x12) or 13.26% *
* “I” is actually a little lower than 1.11 (calculator reports 1.11 even though the number it stores is lower)
10) What is the effective borrowing from the previous problem if the borrower pays two points up front to get the loan, and holds the loan for 5 years?
RMB at end of 5 years?
n = 60
PMT = -899.86
PV = 80,000
I = 12.96 / 12 = 1.08
CPT FV = -$76,994.79
Solve for EBC using cash flows
n = 60
PMT = -899.86
PV = 78,400
FV = -76994.79
CPT I = 1.13 (x 12) = 13.52*
* “I” is actually a little higher than 1.13 (calculator reports 1.13 even though the number it stores is lower)
11) A lender is considering what terms to allow on a loan. Current market terms are 8 percent interest for 25 years for a fully amortizing loan. The borrower, Rich, has requested a loan of $100,000. The lender believes that extra credit analysis and careful loan control will have to be exercised because Rich has never borrowed such a large sum before. In addition, the lender
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