HW2 You consider developing a rental apartment complex. It will cost you $1000,000 per year for two years (time 0 and time 1). Starting two
years from now and forever (time 2 and later), you will be paying $20,000 per year for maintenance and making revenue $152,000 per year. What
is the NPV of this project if the interest rate is 6%? Hint: it is a sum of a regular NPV and an infinite annuity.
-1,000,000-1,000,000/1.06 +(152,000-20,000)/.06/1.06 = 132,075.47
Note:the last term has 1.06, because the annuity formula accounts for one year wait, so we need to add one more year.
How large was the decline in house prices during the housing bust of 2007-12? Pick thFe closest number: (1) 10%, (2) 30%, (3) 50%, (4) 75%.
HW1What will happen to house prices if banks stop giving mortgages?
(A) go up; (B) go down; (C) stay unchanged; (D) any of A-C may happen
What is the definition of homeownership rate?Fraction of households living in units that they own
Which of the following numbers is closest to the current homeownership rate in the US? (D) 65%
As compared to households, firms Are less likely to own real estate
Which of the following years is closest to the one when house prices in the US started falling during the most recent housing crisis (C) 2007
What is the second-largest debt of the US households? Student loans
HW3Ann obtains a fully amortizing 30-year Fixed Rate Mortgage for $1,250,000 at 4.38% with monthly payments. What fraction of Ann’s 40th
payment goes to interest? Write your answer in percent, without the % sign.
First compute the monthly payment: I=0.365 N=360 PV=1250000 FV=0 CPT PV= 6244.75
Then compute the balance after 39 months of payments. 360-39=321months
I=0.365 N=321 PMT=-6244.75 FV=0 CPT PV= 1179630.52
Then (1179630.52*4.38%)/12 = 4305.65 % of interest= (4305.65/6244.75) = 68.95%
Ann is looking for a fully amortizing 30-year Fixed Rate Mortgage for $1,250,000 with monthly payments.
Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.
Assuming Ann makes payments for 30 years, what is Ann’s IRR for mortgage A?
Note: IRR is always annualized. If you’ve found a monthly rate, multiply by 12
What I do first --> 1250000-(0.015*1,250,000)=1,231,250 then find the PMT
Then --> N=360, PMT= -6244.75 , PV=1231250, FV=0, CPT I/Y 0.38
NOTE that this is for one month BUT we need it for the whole year so: 0.38*12= 4.56 (4.51)
Ann is looking for a fully amortizing 30-year Fixed Rate Mortgage for $1,250,000 with monthly payments.
Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.
Assuming Ann makes payments for 2 years, then immediately pays the remaining balance, what is Ann’s IRR for mortgage A?
At time 0, Ann receives the mortgage: 1,250,000 – (.015*1,250,000) = 1,231,250
From time 1 to time 24 she makes monthly payment: 6,244.75 PMT
Additionally, at time 24 she repays the remaining mortgage balance = PV of all future payments using the mortgage interest rate (not the IRR we
are looking for) = 6,244.75 / .0438 * 12 * (1 - 1 / (1 + .0438 / 12)^(360-24)) = 1,207,884.48
You can find the mortgage balance (1207884.48 above) this way: 360-24,=, N, 4.38/12, =, I/Y, 6244.75, PMT, CPT, PV Then enter 24, N, -6244.75,
PMT, 1231250, PV, -1207884.48, FV, CPT, I/Y, *, 12, =5.18%
Ann is looking for a fully amortizing 30-year Fixed Rate Mortgage for $1,250,000 with monthly payments. Mortgage A has a 4.38% interest rate
and requires Ann to pay 1.5 points upfront. Mortgage B does not require to pay any fees upfront.
Assuming Ann plans to make payments for 2 years and then immediately pay the remaining balance, what should be the interest rate on mortgage
B to make Ann indifferent between these two mortgages? Hint: Ann only cares about IRR, so she is indifferent if IRRs are the same.
5.18% - must be the same as mortgage A if repaid in 2 years, .
Why? Ann is indifferent if IRRs of the two mortgages are the same. So, we need to find the interest rate on B such that it has the same IRR as A
repaid in 2 years, i.e. IRR of B must be 5.18%. But B has no fees, so its IRR always equals its interest rate, so its interest rate must me 5.18%.
Ann obtains a 30-year Interest Only Fixed Rate Mortgage for $1,250,000 at 4.38% with monthly payments. What will Ann’s monthly payments
be? Hint: you don’t need to know the mortgage term.
.0438/12*1,250,000 = 4,562.5, because it is an interest only mortgage
Ann gets a fully amortizing 30 year fixed rate mortgage with monthly payments. The initial balance is $1,000,000. The annual interest rate is 3.50%,
compounded monthly. What fraction of the 241th payment will go to principal?
B240= N= 120 PMT=4,480.67 I=0.2917 CPT PV=454,117.97
Interest= 454,117.97 * 0.035 /12= 1,324.51
Principal= 4,480.67-1,324.51=3,166.16
3,166.16/4,480.67= 70.51%
A bank makes a 30 year Fully Amortizing FRM for $1,000,000 at an annual interest rate of 4.25% compounded monthly, with monthly payments.
What is the market value of this loan after 7 years of payments if the annual interest rate for this loan is 7% compounded monthly?
Ν=360 Ι=0.354166667 PV=1000000 FV=0 CPT PMT= 4919.39891 THEN
30-7=23, N=23*12=276 I=0.5833 PMT=4919.3989 FV=0 CPTPMT=673964.8382
A borrower takes out a 30-year mortgage loan for $250,000 with an interest rate of 5% and monthly payments. What portion of the first month’s
payment would be applied to interest? 250000*0.05=12500 then 12500/12=1042
A borrower obtains a $150,000 reverse annuity mortgage with monthly payments over 10 years. If the interest rate of the mortgage loan is 8%,
what is the monthly payment received by the borrower? $820
If a borrower lives in a recourse state and defaults on a mortgage note that does not contain an exculpatory clause and the lender receives less
than the amount owed on the mortgage when the property is sold, the lender will take legal action against the borrower to recover the difference
If a lender is to repossess or bring about the sale of a property if the borrower defaults on the mortgage loan, the lender is said to have a ___ in the
real estate. Secured interest
A(n) ___ estate represents the most complete form of ownership of real estate; the owner is free to divide it up into lesser estates and sell, lease,
or borrow against them as he or she wishes. (A) Fee simple
Mr. Smith has allowed Mrs. Jones to run a sewer line through Mr. Smith’s backyard so that Mrs. Jones has access to the city sewer system. This
is an example of a(n): (A) Easement
Which type of deed offers the grantee the MOST protection? (C) General warranty deed
What term BEST describes a person that owns a property and is conveying title to the property to another person? (B) Grantor
What type of estate lasts for an indefinite period of time? (A) Freehold estate
Which of the following is NOT a good method of title assurance? (D) Seller provides a quitclaim deed
Which of the following documents conveys title to a property at the time the purchaser completes the performance of the obligation called for in
the document? (D) Land contract
What legal document conveys title from one person to another? C) Deed
A historical summary of the publicly-recorded documents that affect the ownership of a property is know as a(n): (C) Abstract of title
Which of the following is FALSE regarding a tax sale? (A) An accurate and complete description of the property is required to be posted
for possible purchasers before the sale
A reversion and a remainder are similar in that: (A) Both can be sold or mortgaged
Which of the following is FALSE concerning Mechanic’s Liens? (C) Lasts even after the bill for labor and materials has been paid
IRR=(Payoff/Investment)^(1/T)-1
NPV = -initial investment – or +(Cash flows)/( 1+r)^i
A “short sale” of real estate is A sale in which the proceeds from the sale are less than the balance owed on the loan secured by the property sold
Which of the following situations is NOT a common cause for the use of a purchase-money mortgage? (D) The seller desires to artificially
raise the price of the property by receiving a higher-than-market interest rate
Which of the following is NOT a minimum mortgage requirement? C) Prepayment clause
A mortgage is BEST defined as a legal document that: (B) Names real estate as the security or collateral for the repayment of a loan
In jurisdiction where a deed of trust is used to finance real estate, there are three parties to the loan secured by the deed of trust. Which of the
following is NOT one of those three parties? (D)Grantor
Which of the following is NOT a determinant of interest rates for single family residential mortgages?(D)The demand and supply of apartments
Mortgage: Loan and pledge of real estate collateral against a promissory note that conveys ownership if the borrower fails to fulfill his
contractual obligations.
Promissory Note: document that is evidence that debt exists between borrower & lender. Shows rights and responsibilities of both parties:
Amount of the loan, Rate and frequency of payment, Term (Maturity),Fees, Prepayment penalties, if any Default mechanics Recourse (ie
personal liability of the borrower beyond collateral)
Title: collection of rights in a given property.
Deed: legal document that conveys the Title to the owner. (vehicle title/deed)
Property free from encumbrances: leases, liens & easements unless stated.
Lien: right of a creditor to collateral if contract obligations not met.
Mechanic’s Lien: put on a property by contractor, worker or material supplier
1Yes, 2 65%, 3special warranty deed, 4do nothing…, 5 55000 def lender 1, 6 102,647.83, 7 1,609,346.44, 8 +34.29%, 9 372,563.23, 10 6,059.80,
11 454,117.97, 12 70.51%, 13 4.00%, 14 8.08%, 15NPV= -200000-(300000/(1+r))-(500000/(1+r)^2)+(4000000/(1+r)^3), 16 104.79,
17NPV= -105000+(110400/(1+r)), 18 -105000+(110400/(1+IRR))=0 => IRR=(110400/105000)-1=5.14%