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Questions for Slide Deck 2: Learn Your Calculator
7.
A lender offers you a $100,000 30-year, fully amortizing, fixed rate mortgage with monthly payments at
an annual interest rate of 6%. What is the monthly payment? After making 3 years of payments of the
mortgage above, what is the mortgage balance?
Make sure P/Y = 12
N = 30*12 = 360
I/YR = 6
PV = -$100,000
FV = 0
 PMT = 599.5505
Then set N = 36 and compute FV = 96,084.0701
(or set N = 324 and compute PV = -96,084.0701)
8.
A borrower has offered to pay you a constant $2,500 per month at the end of each month for 20 years.
You discount these cash flows at a mortgage rate of 6%. What is this worth to you?
Make sure P/Y = 12
N = 20*12 = 240
I/YR = 6
PMT = 2,500
FV = 0
 PV = -348,951.9292
9.
A borrower has offered to pay you (the lender) a constant $1,000 per month at the end of each month for
the next 30 years. You discount these cash flows at the nominal mortgage equivalent rate of 5%. What is
this worth to you?
Make sure P/Y = 12
N = 360
I/YR = 5
PMT = 1,000
FV = 0
 PV = -186,281.617
10. Your bank is thinking of selling the loan issued in the previous question to secondary markets. At the time
of the sale, there is a 50% chance the contractual cash flows will be discounted at a 6 percent rate and a
50% chance the cash flows will be discounted at a 4 percent rate. What is the expected value of the loan
to be sold to secondary markets?
Set N = 360, PMT = 1,000, FV = 0
PV at 6%: Set I/YR = 6, PV = -166,791.6144
PV at 4%: Set I/YR = 4, PV = -209,461.2405
Expected value = 0.5*166,791.6144 + 0.5*209,461.2405 = 188,126.4274
11. A borrower approaches a lender and offers to pay $1,000 each year for 5 years (end of year) for a loan
issued today. Assume the lender discount cash flows using an annual interest rate of 5%. What size loan
can the lender offer?
Set P/YR = 1
N = 5, I/YR = 5, PMT = 1,000, FV = 0, PV = -4,329.4767
12. The borrower comes back to the lender and asks if he can borrow more money today if he offers $1,000
at the end of the first year and then “steps up” subsequent payments over time at the rate of 3 percent
per year for rest of the life the loan. The lender continues to discount the loan at an annual interest rate
of 5%. What size loan can the lender offer? (compute with calculator)
Set P/YR = 1
CF0 = 0
CF1 = 1,000
CF2 = 1,030
CF3 = 1,060.90
CF4 = 1,092.727
CF5 = 1,125.5088
Set I/YR = 5, compute NPV = 4,583.9214
13. The lender comes back to the borrower and offers the following deal: Pay me $900 at the end of the 1st
year, and then step up payments each year at 15% per year. Your discount rate will be 6.2 percent. How
much money does the lender offer to the borrower?
Set P/YR = 1
CF0 = 0
CF1 = 900
CF2 = 1,035
CF3 = 1,190.25
CF4 = 1,368.7875
CF5 = 1,574.1056
Set I/YR = 6.2, compute NPV = 5,000
14. You own a property that pays $1,500 in net rent at the end of years 1 and 2. You expect to sell the
property at a cap rate of 5% at the end of year 2. Assume you discount net rents at a 3% rate and you
discount the proceeds from the sale of the building at a 5.16% annual rate. How much do you expect to
sell the property for? What is the building worth to you today?
The rent payments are worth
$1,500/(1.03) + $1,500/(1.03)2 = $1,456.311 + $1,413.894 = $2,870.205
The sale price of the building is $1,500/0.05 = $30,000 which is worth
$30,000/(1.0516)2 = $27,128.145
The total amount you would pay is $29,998.35
15. Suppose you purchase the building for the answer the previous question and then experienced the cash
flows as expected including the sale price. What was the IRR of the building’s cash flows? (Hint: use cash
flow buttons on your calculator)
Make sure P/YR = 1. Then compute this as
CF0 = -$29,998.35
CF1 = $1,500
CF2 = $31,500
Compute IRR/YR = 5.003
16. Assume in the previous 2 questions that you discount the proceeds from the sale of the building at a 5.5%
annual rate. Compute (a) how much you would pay for the property and (b) the IRR.
The rent payments are worth $2,870.205 … this hasn’t changed
The sale price of the building is worth $30,000/(1.055)2 = $26,953.572
The total amount you would pay is $29,823.777
Make sure P/YR = 1. Enter CF0 = -$29,823.777, CF1 = $1,500, CF2 = $31,500
Compute IRR/YR = 5.317
17. You buy a hotel that pays $1,500 in annual year‐end NOI for 5 years and then expect to sell the hotel for
at a cap rate of 4% at the end of year 5. You purchased the hotel at a 5% cap rate. What is the IRR?
Purchase price 1500/0.05 = $30,000. Sale price is $37,500.00
Enter CF0 = -$30,000, CF1 = $1,500, N1 = 4, CF2 = $39,000 Compute IRR/YR = 9.164
18. You pay $10,467 for a building that generates annual net rent of
$1,000 at the end of year 1
$2,000 at the end of years 2, 3, 4, 5, 6
$3,000 at the end of year 7
What is the IRR/YR of the purchase of the building?
Make sure P/YR = 1. Then compute this as
CF0 = -$10,467
CF1 = $1,000
CF2 = $2,000
N2 = 5
CF3 = 3,000
Compute IRR/YR = 6.9994
19. What is the most you would pay in the previous problem if you only require a 5% return on the building?
HINT: clear all, Set I/YR=5 and use NPV to solve when CF0 = 0.
Make sure P/YR = 1. Then compute this as
CF0 = 0, CF1 = $1,000, CF2 = $2,000 , N2 = 5, CF3 = 3,000,
Set I/YR = 5, Compute NPV = 11,331.0472
20. You pay $30,000 for a building that pays net rents of $1,500 in the first year. You expect to sell at the end
of the first year. The going out cap rate is heavily dependent on how the Federal Reserve ends its QE
program. There is a 70% chance the Federal Reserve “softly” tapers, and your going out cap rate will be
4% implying a sale price of $37,500. And, there is a 30% chance the Federal Reserve ends QE abruptly,
implying a going out cap of 6.5% and therefore a sale price of $23,077.
a. What is the IRR in the softly taper scenario?
b. What is the IRR in the abrupt ending scenario?
c. If you were to compute an “expected” sales price of the building, and then compute the IRR
based on the expected sales price, what would it be?
Softly taper sale price is $1,500/0.04 = $37,500
Abrupt landing sale price is $1,500/0.065 = $23,076.923
Expected sale price = 0.7*$37,500 + 0.3*23,076.923 = $33,173.077
Make sure P/YR = 1
a. CF0 = -$30,000, CF1 = $39,000, IRR/YR = 30.000
b. CF0 = -$30,000, CF1 = $24,576.923, IRR/YR = -18.077
c. CF0 = -$30,000, CF1 = $34,673.077, IRR/YR = 15.577
21. You own a property that pays $3,000 in NOI at the end of years 1 and 2. You expect to sell the property at
a cap rate of 6% at the end of year 2. Assume you discount net rents at a 2% annual rate and you
discount the proceeds from the sale of the building at a 7% annual rate.
a. How much do you expect to sell the property for?
b. What is the property worth to you today?
Make sure P/YR = 1
Compute value of rents:
Clear all. CF0 = 0, CF1 = 3,000, CF2 = 3,000. Set I/YR = 2, compute NPV = $5,824.6828
Compute value of sale (sale price = $3,000/0.06 = $50,000)
Clear all. CF0 = 0, CF1 = 0, CF2 = 50,000. Set I/YR = 7, compute NPV = $43,671.9364
Property is worth $5,824.6828 + $43,671.9364 = $49,496.6192
22. You purchase a property on January 1, 2015 that pays a constant $1,500/year in NOI (paid Dec 31 every
year). You intend to sell the building on Dec 31, 2017 at an 8% cap rate. What would you have to pay for
the building on January 1, 2015 to earn a 7% IRR?
Make sure P/YR = 1
CF0 = 0
CF1 = 1,500
CF2 = 1,500 + 1,500/0.08 = 1,500 + 18,750 = 20,250
Set I/YR = 7, compute NPV = 19,089.0034