HP12C/MAth

Question 1

How do you do weighted average on HP12C?

Answer 1

$1000 [ENTER] 50 [Σ+] (aka 50%)
$900 [Enter] 40 [Σ+] (aka 40%)
$1200 [Enter] 10 [Σ+] (aka 10%)

[g blue] - [6] (xw - average weighted)

Result $980

Question 2

How to do linear regression on HP12C?

Example:

Estimate a projected sales price of a 1,550-square-foot property where comparable sales provide the following information:

Sale Price Square Feet
#1 $58,000 1,300
#2 $65,000 1,475
#3 $72,000 1,600

Answer 2

58,000 [ENTER] 1,300 [Σ+]
65,000 [ENTER] 1,475 [Σ+]
72,000 [ENTER] 1,600 [Σ+]

1,550 blue [g] [2] y,r

Indicated value of subject is: $69,238.53

Question 3

How many days are between June 3, 2005 and October 16, 2006?

Answer 3

Be sure that your HP12C is set to the correct sequence of data entry blue [g] [5]

6.032005 [ENTER]
10.162006 [ g ] [ DYS] (that one’s in the middle, in blue under [EEX])

Answer on the Display is: 500

Question 4

What date would be 150 days from June 15, 2007?

Answer 4

Be sure that your HP12C is set to the correct sequence of data entry blue [g] [5]

6.152007 [ENTER]
150 [ g ] [DATE] (that one is on the bottom of [CHS] in blue)

The answer on the display is: 11,12,2007 1

That is November (11th month), 12th day of 2007, and 1 means it’s the first day of the week and/or a Monday.

Question 5

If income from a property rises 6% per annum, what will the income be next year if it was $45,000 this year?

Answer 5

45,000 [ENTER]

6 [%] [ + ]

47,700 = 6% more than 45,000

Note: for % less press the [ - ] instead of the [ + ].

Question 6

What is the percentage of increase from $220,000 to $242,000?

Answer 6

220,000 [ENTER]

242,000 [∆%]

10.00 = the percentage of increase is 10%

Note: for % of decrease, enter the higher number followed by the lower.

Question 7

The number 8,000 is what percentage of 32,000?

Answer 7

32,000 [ENTER]

8,000 [%T]

25.00 means that 8,000 is 25% of 32,000.

Question 8

Using the numbers 100, 103, 105, 106, and 108, calculate the standard deviation and mean

Answer 8

100 [Σ+]
103 [Σ+]
105 [Σ+]
106 [Σ+]
108 [Σ+]

blue [g] [.] (s) - standard deviation
blue [g] [0] (x) - mean

Question 9

The Six Functions of a Dollar on HP
- 5 top left buttons

Answer 9

n is the number of periods. This is the time factor.
i is the interest rate
PV stands for Present Value
PMT is the payment
FV is Future Value

Question 10

Create the amortization schedule for the first three payments on the $100,000 loan for 30 years. 10% interes

Answer 10

Payment——-Balance——-Interest——–Principal
—1————–$100,000—–$10,000.00—–$607.92
—2————–$99,392.08—-$9,939.21—–$668.71
—3————–$99,872.34—-$9,872.34—–$735.58

Question 11

How much will we pay in interest the first year for a 30-year (monthly payments) mortgage of $182,000 at a 6.2% interest rate.

Answer 11

First, we need to find the monthly payment:
f CLEAR FIN
30 [g] [n]
6.2 [g] [i]
182000 [PV]
[PMT]

You should have gotten - $1,114.69

12 [f ] [AMORT] = -11,223.50 (Interest for year 1)

[x><y] = - 2,152.78 (Principal for year 1)

[RCL] [PV] = 179,847.22 (Remaining Balance)

[RCL] [n] = 12.00 (Number of payments)

If you want to continue you can just go ahead with the next year.

12 [f ] [AMORT] = -11,086.18 (Interest for 2nd year)

[x><y] = - 2,290.10 (Principal for 2nd year)

[RCL] [PV] = 177,557.12 (Remaining Balance)

[RCL] [n] = 24.00 (Number of payments)

Question 12

You have a mortgage of $112,500 written for 25 years at 7.2% annually (monthly payments). However, there will be a balloon payment due at the end of year five. How much will that be (the amount of the remaining balance of the loan at that point)?

Answer 12

[f] [CLEAR] [FIN]
25 [g] [n]
7.2 [g] [i]
112500 [CHS] [PV]
[PMT] = 809.54

Then we leave all the information in the rest of the registers, but change the entry in the n register to five years and ask for the future value after five years.

5 [g] [n]
[FV] = 102,818.06

Therefore, the remaining balance at the end of five years of the 25-year scheduled payout, to be paid off as a lump sum balloon payment, would be $102,818.06.

Question 13

An office is leased for a three year period at $3,000 per month, payable at the beginning of each month. Market rent is $4,000 per month. The estimated market interest rate is 5%. Calculate the present value.

Answer 13

[ g ] [BEG] (remember the problem said rents paid in advance, so you need to change from END to BEG)

3 [ g ] [ n ] (monthly rent, so just like the monthly mortgage payments = [ g ] needed)
5 [ g ] [ i ]
1,000 [CHS] [PMT]
[PV]
Display reads: $33,504.73

Question 14

A small, single-tenant, freestanding office building rents for $2,500 per month, payable in advance each month. Your research concludes that the Market Rent for this unit would be $3,500 for the full three-year term of the lease. Additional research indicates that the market rate for leasehold investments is 9%. What is the present value of the leasehold interest?

Answer 14

Market Rent: $3,500

Contract Rent: $2,500

It is easy to see that the leasehold interest is $1,000 better off each month. This raises the question:

What is the present value of $1,000 per month for three years at a rate of 9%?

Remember, there are two special things we have to do in this problem:

Put “BEGIN” in the Display; and
Remember to use the blue [ g ] key to change payments to “monthly” as we did when calculating monthly mortgage payments.
First, clear the calculator: [ f ] [REG]. Now press the blue [ g ] key and then the [BEG], (the word “Begin” should be in the Display). Then key in 3 (for the number of years) and then the blue [ g ] key (for monthly intervals). Next press the [ 9 ] key, followed by the blue [ g ] key again (to make it monthly) and then press [ i ]. The calculator is now ready for the money to be entered.

Key in $1,000 (the monthly advantage of the lessee), then the [CHS] and the [PMT]. Since that is the cash flow, it is viewed a payment. To solve for the present value, press [PV].

Let’s look at just the keystrokes:

[ g ] [BEG]
3 [ g ] [ n ]
9 [ g ] [ i ]
1,000 [CHS] [PMT]
[PV]
Display reads: 31,682.66

The value of the Leasehold is $31,682.66

If you did not get the same answer, go back and try it again until you do.

What if the contract rent is greater than market rent? In such cases the Leasehold has no advantage, so it could actually have a negative value.

Question 15

What is the present value of $1,500 per year for 12 years at 15%, with the rent payable at the end of each period?

Answer 15

This time we have to start with the calculator in the “END” mode, so press the blue [ g ] key and then the [END].

As always, clear the calculator: [ f ] [REG]

Now you’re ready!

12 [ n ]
15 [ i ]
1,500 [CHS] [PMT]
[PV]
Display reads: $8,130.93

Question 16

A property is leased at a rent of $20,000 per year (payable at the end of each period) for five years. At the termination of the lease, the property is anticipated to be sold for $300,000. What is the value of the leased fee interest if the market derived rate is 10%?

Answer 16

-Clear the calculator.
-Make sure “Begin” is not in the Display.

5 [ n ]
10 [ i ]
20,000 [CHS] [PMT]
300,000 [CHS] [FV]
[PV]
Display reads: 262,092.13

Question 17

A property is leased for five years. The annual rent starts at $20,000 (payable at the end of each rental period) and increases $1,000 per year. This is the forecasted rent for the entire lease period. The market derived rate for this property is 10%. The value of the reversion at the end of the lease is $250,000. What is the value of the leased fee?

Answer 17

This one looks scarier than it really is. There are just more keystrokes involved because you have to key in each year’s new rent to account for the changes in that category. We have two new keys involved, but they really aren’t totally new. [CFj] or cash flow “j” and the [NPV] or net present value keys are alternative functions of the [PMT] key and the [PV] key.

-Clear the calculator.
-Make sure “Begin” is not in the Display.

20,000 [ g ] [CFj] (Don’t get excited…[CFj] is on the bottom of the [PMT] key.)
21,000 [ g ] [CFj]
22,000 [ g ] [CFj]
23,000 [ g ] [CFj]
274,000[ g ] [CFj] (This is the 5th year’s rent plus the reversion or resale.)
10 [ i ]
[ f ] [NPV] ([NPV] is above the [PV]…that’s why we pressed the [ f ].)
Display reads: 237,907.87

The value of the leased fee interest (present value of the cash flows plus the present value of the reversion) is $237,907.87.

Question 18

The first tenant is a convenience store that pays $2,000 per month. The second is a coin laundry that pays $1,500 per month. The third tenant is a shoe repair shop that pays $500 per month for a small alcove. The fourth tenant is a real estate broker’s office paying $1,000 per month. For the purposes of this case study, assume that all leases are true Net Leases (NNN) where the tenants pay all operating expenses including property management fees so these rents represent the true “Net Income” on each lease.

The investor contacts you to perform an appraisal to estimate the value of a potential leased fee interest in the property. You have experience in performing this type of assignment in this market area, and agree to do it. An engagement letter is signed by both parties, and your task begins.

Through extensive research you find, after weighing capital investment, risk, liquidity, and other factors, the market rate for such investments is 9%. You also perform a prospective value estimate on the real property, based on research with investors and experts in the field, and believe the value of this property at the end of the five years will be $650,000.

Calculated the value of the leased fee interest. Remember, when using income capitalization methodology you use annual income and expenses not monthly in your calculation.

Answer 18

The keystrokes on the HP12C calculator to reach this solution are:

First clear the financial memory by these keystrokes: f [FIN]

Enter the number of periods: 5 [n]

Enter the rate of return: 9 [i]

Enter the annual cash flow by multiplying the monthly net income by 12 then entering it: 5000 ENTER 12 X [CHS] [PMT]

Enter the sale reversion at the end of five years: 650,000 [CHS] [FV]

Request the unknown Present Value: [PV]

The answer to the Chapter 10 case study is $655,834.48.

Question 19

If the market rents show the convenience store rental should be $3,000 per month rather than the $2,000 contracted for the full 5 year term of the lease, and you use the same 9% rate, what is the value of the convenience store’s leasehold calculated on the monthly difference (assuming payments at the end of the month)?

Answer 19

If the market rents show the convenience store rental should be $3,000 per month rather than the $2,000 contracted for the full 5 year term of the lease, and you use the same 9% rate, what is the value of the convenience store’s leasehold calculated on the monthly difference (assuming payments at the end of the month)?
$48,173.37
Leasehold Interest. f [FIN] 5 g [n] 9 [i] 1,000 [CHS] [PMT] [PV]

Question 20

A property can be purchased with a 70 percent loan. The loan would have a 20-year term with monthly payments at 8 percent interest. The indicated mortgage capitalization rate is 0.1004. This particular lender is requiring a 1.3 debt coverage ratio. What is the indicated overall rate (RO) based on this information?

Answer 20

9.14%

1.3 ENTER .1004 [X] .70 [X]

Question 21

A property is purchased for $100,000 and produces cash flows of $10,000 for five years, at which time it is sold for $110,000. Calculate the internal rate of return.

Answer 21

For example, a property is purchased for $100,000 and produces cash flows of $10,000 for five years, at which time it is sold for $110,000. The internal rate of return can be calculated as follows using your HP12C financial calculator:

100000 [CHS] [CFo] (you need a negative number to begin with to express the outflow of cash in the purchase - the CFo is under the PV key)

10000 [g] [CFj] (the income is express as positive - the CFj key is under the PMT key)

4 [g] [Nj] (this is the number of cash flows in years BEFORE the final year)

10000 [ENTER] 110000 + (This adds the final year cash flow to the sale proceeds also received at the end of that final year)

[g] [CFj] (This enters both the final year cash flow and the sale proceeds into the series of cash flows, since it happens only once you do not need the Nj entry)

[f] [IRR] (The IRR key is in gold over the FV key)

After flashing for a while your display should show 11.59 which is the Internal Rate of Return

Question 22

You want to know the Internal Rate of Return on an investment in an income producing property that was originally purchased for $500,000. Assume an annual cash flow of $35,000 during the entire five-year holding period. The property is sold at the end of the holding period for $650,000.

Answer 22

You want to know the Internal Rate of Return on an investment in an income producing property that was originally purchased for $500,000. Assume an annual cash flow of $35,000 during the entire five-year holding period. The property is sold at the end of the holding period for $650,000.

Here are your keystrokes:

5 [ n ]
500,000 [CHS] [PV]
35,000 [PMT]
650,000 [FV]
[ i ]
Display reads: 11.75

The Internal Rate of Return is 11.75%

Question 23

Calculate the Internal Rate of Return on an investment property with an original purchase price of $400,000. Assume the first year’s cash flow is $30,000, but in this case it will increase by 3% annually for a five-year holding period. The property will be sold at the end of the holding period for a price of $500,000.

Answer 23

11.86%

Keystrokes are as follows:

400,000 [CHS] [g][CFo]
(Note: CFo is a new key for us on bottom of PV)

30,000 [ g ] [CFj] (Note: CFj is a new key for us on bottom of PMT)
30,900 [ g ] [CFj] (Note: second year is 3% more than first year)
31,827 [ g ] [CFj] (Note: + 3%)
32,782 [ g ] [CFj] (Note: + 3%)
533,765 [ g ] [CFj] (Note: + 3% last year’s cash flow plus reversion)
[ f ] [IRR] (Note: IRR is a new key for us above the FV)

Display reads: 11.86

The internal rate of return is 11.86%

Question 24

Estimate the value of a life interest in a property with a present market value of $300,000. The life tenant’s life expectancy is 12 years, based on a life expectancy actuarial table. The market interest rate for this property is estimated to be 10%. The estimated value of the property at the end of the life tenancy (12 years) is estimated to be $500,000.

Answer 24

12 [ n ]
10 [ i ]
500,000 [CHS] [FV]
[PV]
Display reads: 159,315.41 (present value of the future value)

Then subtract:300,000.00
-159,315.41
140,684.59 Value of the Life Interest

Question 25

Sandwich Lease
When a property is subleased, a sublease receives the rights and obligations of the lease from the prior lessee. We should look at a definition of this “sandwich leasehold estate.”

The Language of Real Estate Appraisal…Second Edition defines it as:

“Sandwich leasehold estate: An estate that arises from a sandwich lease. The value of the sandwich leasehold can be estimated as the present value of the difference between the income from the sublease and the income from the lease. See also fee simple estate, leased fee estate, leasehold estate, subleasehold estate.

For example, suppose a property is currently leased at a below-market rate of $400,000 per year. The lessee then subleases the property for the next five years at $500,000 (flat rental with a net lease). Assume a discount rate of 15 percent. The value of the sandwich leasehold can be estimated as follows:

Answer 25

Discounting at 15%, $100,000 x an (15%, 5 yrs.) = $335,215…”

[SIDE NOTE]

With your HP-12C you could do the following keystrokes:

5 [ n]
15 [ i ]
100,000 [CHS] [PMT]
[PV]
Display reads: 335,215.51

Question 26

Sandwich Lease
When a property is subleased, a sublease receives the rights and obligations of the lease from the prior lessee. We should look at a definition of this “sandwich leasehold estate.”

The Language of Real Estate Appraisal…Second Edition defines it as:

“Sandwich leasehold estate: An estate that arises from a sandwich lease. The value of the sandwich leasehold can be estimated as the present value of the difference between the income from the sublease and the income from the lease. See also fee simple estate, leased fee estate, leasehold estate, subleasehold estate.

For example, suppose a property is currently leased at a below-market rate of $400,000 per year. The lessee then subleases the property for the next five years at $500,000 (flat rental with a net lease). Assume a discount rate of 15 percent. The value of the sandwich leasehold can be estimated as follows:

Answer 26

Discounting at 15%, $100,000 x an (15%, 5 yrs.) = $335,215…”

[SIDE NOTE]

With your HP-12C you could do the following keystrokes:

5 [ n]
15 [ i ]
100,000 [CHS] [PMT]
[PV]
Display reads: 335,215.51

Question 27

Continuing with the Sandwich Lease Definition
“.Assume that the market rate is $500,000 in year 1 and increases by 3 percent per year. Discount rate 18%

Sandwich lease is flat $500,000. For 5 years

Answer 27

Year 1 2 3 4 5
500,000 515,000 530,450 546,364 562,754
500,000 500,000 500,000 500,000 500,000
0 15,000 30,450 46,364 62,754

Discounting at 18 percent (a higher discount rate is used to adjust for risk; the subleasehold estate is riskier than the sandwich leasehold), the value of the leasehold estate equals

V = (15,000 ÷ 1.18)2 + (30,450 ÷ 1.18)3 + (46,364 ÷ 1.18)4 + (62,754 ÷ 1.18)5
V = 80,650

If we assume that it is reasonable to sum the values of the sandwich leasehold and the subleasehold to find the value of the leasehold, the value of the leasehold can now be calculated as $335,215 + 80,650 = $415,865. The leasehold value may not be equal to the subleasehold value plus the sandwich leasehold, depending on the relationship between the discount rates applicable for each interest.”

[SIDE NOTE]
On your HP-12C, do the following keystrokes:
Step One: 0 [ g ] [CFj]
15,000 [ g ] [CFj]
30,450 [ g ] [CFj]
46,364 [ g ] [CFj]
62,754 [ g ] [CFj]
18 [ i ]
[ f ] [NPV]

Display reads: 80,649.96 or 80,650 (rounded)

Question 28

Calculate the floor area ratio on a 150,000 square foot warehouse situated on 10 acres of land.

Answer 28

.34

Question 29

An anchor tenant moves out of a shopping center. Because that vacancy results in lower sales volume in the retail center, one of the remaining stores in the center is now producing rent (overage and minimum rent combined) of $15,000. Comparable nearby fully leased spaces in a center without a similar anchor vacancy indicate that it should produce overage and minimum rent of $20,000 if the center had a new anchor tenant. Assume a cap rate of 11% and assume that the external obsolescence attributable to the building is 60%. What is the dollar amount of external obsolescence attributable to the building?

Answer 29

HP12C keystrokes – 5000 [ENTER] .11 [÷] .6 [x]
$27,273

Question 30

In comparing an investment opportunity to the return from an annuity, an appraiser calculates the return on the annuity. The initial deposit into the annuity is $5,000, and there will be annual deposits of the same amount for 8 years on the anniversary of the first deposit. If the interest rate is 5% compounded annually, what would be the balance at the end of the eight years?

Answer 30

Don’t forget to set the HP12C to the “BEG” function (blue key under the “7” key) then set it back to “END” when you are finished.

 [g] [BEG]
 8[n]
 5[i]
 5,000 [CHS] [PMT]
 [FV]
 display reads: 50,132.81

Question 31

An appraiser is attempting to project Replacement Reserves for a retail center. Research indicates that it will cost $90,000 to paint the exterior and that it will need to be done in 6 years. If the funds can be deposited into an account paying 5% interest, how much would have to be deposited each month to have sufficient funds to paint the building at the end of the time allotted?

Answer 31

Don’t forget to set the HP12C to the “BEG” function (blue key under the “7” key) then set it back to “END” when you are finished.

Deposit:

   [g] [BEG]
   6 [ g ] [ n ]
   5 [ g ] [ i ]
   90,000 [CHS] [FV]
   [PMT]
   Display reads: 1,069.99

Question 32

What is the present value of a cash flow of $45,000 per year at 8% for 7 years?

Answer 32

7 [ n ]
8 [ i ]
45,000 [CHS] [PMT]
[PV]
Display reads: 234,286.65

Question 33

An appraiser completes all three approaches to value on an office building. The indicated value in the Sales Comparison Approach is $850,000, but the comparables used were not strongly compatible with the subject property, and were in different market areas. As a result, the appraiser decides that the Sales Comparison Approach should only be given 20% weight in the final reconciliation.

In contrast, the Income Approach data was deemed to be current and reflective of the current market. Interviews with market participants provided consistent indicators, and the appraiser determines that this approach should be given the greatest weight, and allocates 70% to the Income Approach, which came in at $890,000.

The Cost Approach of $835,000, although supportive of the Sales Comparison Approach, is only given the remaining weight (10%). This is due to the building being located in a dense urban area with little prospect for building an alternative without tearing down improvements to an already improved site (which adds greatly to the development costs), and also due to the fact that the market is just not doing such at this time, in this area.

Utilizing the weighted mean technique on your HP-12C financial calculator, what is the indicated reconciled value of the office building?

Answer 33

850,000 [ENTER]

.20 [Sum+ ]

890,000 [ENTER]

.70 [Sum+ ]

835,000 [ENTER]

.10 [Sum+ ]

[ g ] [ xw ]

Display reads: 876,500

Question 34

An office space in a large office building is leased for a four-year period at $4,000 per month (payable in advance). Market rent would be $5,000 per month. The estimated market interest rate is 6%. Calculate the present value of the leasehold interest.

Answer 34

Market Rent $5,000
Contract Rent -$4,000
Advantage $1,000

Compute the present value of $1,000 per month for 48 months at 6%.

[ g ] [BEG] (Remember, the problem said rents paid in advance)
4 [ g ] [ n ] (Monthly rent, so just like the monthly mortgage payments = [ g ] needed)
6 [ g ] [ i ]
1,000 [CHS] [PMT]
[PV]
Display reads: 42,793.22

Note: Don’t forget to remove “Begin” from the window…[ g ] [END]

Question 35

A single-tenant investment property is leased for five years. The annual rent starts at $20,000 and increases by $1,000 each year. (Due to economic times, the owner has agreed to the lease payments being payable at the end of each rental period rather than in advance.) This is the forecasted rent schedule for the entire lease period. The market derived rate for this property is 10%. The value of the reversion at the end of the lease is $250,000. What is the value of the leased fee?

Answer 35

20,000 [ g ] [CFj] (Remember, [CFj] is on the bottom of the [PMT] key.)
21,000 [ g ] [CFj]
22,000 [ g ] [CFj]
23,000 [ g ] [CFj]
274,000 [ g ] [CFj] (This is the 5th year’s rent plus the reversion or resale.)
10 [ i ]
[ f ] [NPV] ([NPV] is above the [PV]…that’s why you press the [ f ].)
Display reads: 257,907.87

The value of the leased fee interest (present value of the cash flows plus the present value of the reversion) is $257,907.87.

Question 36

An investor is exploring several investment opportunities. There is a new construction strip center with four tenants who have already signed leases and who will take occupancy next month. All four leases call for the rent to be paid at the end of each month, and all four run for five years, expiring on the same date.

The first tenant is a convenience store that pays $2,000 per month. The second is a coin laundry that pays $1,500 per month. The third tenant is a shoe repair shop that pays $500 for a small alcove. The fourth tenant is a real estate broker’s office paying $1,000 per month. The leases are all true NNN Leases where the tenant’s reimburse the landlord for all operating expenses on the property except the owner’s internal bookkeeping expense. Thus these rents reflect the effective Net Operating Income.

The investor contacts an appraiser to perform an appraisal to estimate the value of a potential leased fee interest in the property. An engagement letter is signed by both parties.

Through extensive research, the appraiser finds that after weighing capital investment, risk, liquidity, and other factors, the market rate for such investments would be 9%. The appraiser also performs a prospective value estimate on the real property, based on research with investors and experts in the field, and believes the resale of this property at the end of the five years will be $650,000.

Calculated on an annual income basis, what is the value of the leased fee interest?

Answer 36

5 [ n ]
9 [ i ]
60,000 [CHS] [PMT]
650,000 [CHS] [FV]
[PV]
Display reads: 655,834.48

Question 37

A property sold for $760,000 and has the following reconstructed operating income statement summary:

PGI $240,000
V&C/L (4%) -9,600
EGI 230,400
OE -138,200
NOI 92,200

What is the Operating Expense Ratio? ________________________

What is the Net Income Ratio? ______________________

Answer 37

Operating Expense Ratio:
138,200 ÷ 230,400 = .60

Net Income Ratio:
92,200 ÷ 230,400 = .40

Question 38

A property sold for $760,000 and has the following reconstructed operating income statement summary:

PGI $240,000
V&C/L (4%) -9,600
EGI 230,400
OE -138,200
NOI 92,200

What is the Potential Gross Income Multiplier? ________________________

What is the Effective Gross Income Multiplier? ________________________

Answer 38

Potential Gross Income Multiplier:
760,000 ÷ 240,000 = 3.167

Effective Gross Income Multiplier:
760,000 ÷ 230,400 = 3.299

Question 39

A property sold for $760,000 and has the following reconstructed operating income statement summary:

PGI $240,000
V&C/L (4%) -9,600
EGI 230,400
OE -138,200
NOI 92,200

(Assuming the monthly rents are equal throughout the year)

What is the Potential Gross Rent Multiplier? ________________________

What is the Effective Gross Rent Multiplier? ________________________

Answer 39

Potential Gross Rent Multiplier:
760,000 ÷ 20,000 = 38.000

Effective Gross Rent Multiplier:
760,000 ÷ 19,200 = 39.583

Question 40

The property you are asked to appraise has a mortgage of $400,000 with annual mortgage payments of $44,000. You complete a reconstructed operating statement that indicates a Net Operating Income of $50,000. Comparable properties in the area indicate an equity capitalization rate of 0.08. Based on this data, what is the value of this property utilizing the Equity Residual Technique?

Answer 40

Net Operating Income $50,000

Deduct Annual Debt Service -44,000

Income to Equity 6,000

Capitalize Equity Income (6,000 / 0.08) 75,000

Add Mortgage Value to Equity Value (75,000 + 400,000) $475,000

End of

Question 41

A new assignment involves a property with an available equity of $25,000. As in many prior case studies, the appraiser prepares a reconstructed operating statement, and the indicated Net Operating Income is calculated to be $10,000.

Research determines that an appropriate equity capitalization rate for the subject property would be 10%. Additional research yields an indicated mortgage capitalization rate as being 8%.

What is the indicated value of the mortgage? _________________________

Answer 41

Equity $25,000

Net Operating Income 10,000

Subtract the Equity x Equity Rate (25,000 x 0.10) -2,500

Income to Mortgage 7,500

Divide Mortgage Income by Mortgage Rate (7,500 / .08) $93,750

Question 42

There is a new assignment in which the appraiser will be utilizing an overall rate to capitalize the Net Operating Income. This case study also utilizes techniques learned in Chapter 22.

The data that is available indicates that financing is readily available at 70% of the total property value. Loan term on such financing is 20 years, and payments are at 8% interest. Research indicates a mortgage capitalization rate of .1004, and through comparable sales, the equity capitalization rate is estimated at 7%.

Based on the data included here, what is the indicated overall capitalization rate using the Band of Investment (Mortgage Equity) methodology?

Overall capitalization rate: ________________________

Answer 42

Mortgage: 0.70 x 0.1004 = .0703

Equity: 0.30 x 0.0700 = +.0210

Overall Capitalization Rate: .0913

Question 43

In yet another assignment, an appraiser elects to utilize the Debt Coverage Ratio methodology to determine an overall rate.

Properties similar to the subject can be purchased with a 70% mortgage, and would have a 20-year amortization at 8% interest.

Research indicates that the mortgage capitalization rate is 0.1004, and this particular lender is requiring a 1.2 Debt Coverage Ratio.

What is the indicated overall capitalization rate? _____________________

Answer 43

.7*0.1004 *1.2 = .0843

Question 44

Using linear regression, with a single variable being the living area square footage of the properties, calculate an indicated value for your subject property that has 7,200 square feet.

Sale Price Square Foot
$26,000 6,800
$29,000 7,000
$34,000 7.900
$35,000 8,100
$37,000 8,800
$38,000 9,900

Indicated value: ______________________

Answer 44

26,000 [ENTER] 6,800 [ Sum+ ]
29,000 [ENTER] 7,000 [ Sum+ ]
34,000 [ENTER] 7.900 [ Sum+ ]
35,000 [ENTER] 8,100 [ Sum+ ]
37,000 [ENTER] 8,800 [ Sum+ ]
38,000 [ENTER] 9,900 [ Sum+ ]

7,200 [ g ] [ 2 ]

Display reads: 29,839.54

Question 45

A property produces a Net Operating Income of $10,000 per year. The holding period is five years.

It is estimated that the value will increase by 20% over the holding period.

If the discount rate is 10%, and the multiplier from the financial tables is 0.163797, what is the value?

Value: _______________________

Answer 45

Overall Rate
0.10 – (0.20 x 0.163797) = 0.067241

10,000 / 0.067241 = 148,720

Question 46

An appraiser desires to calculate the Net Present Value of a property that was originally purchased for $600,000.

The income for the first year is $45,000, $50,000 for the second, $55,000 in the third year, $60,000 in the fourth, and finally $65,000 in the fifth year.

The anticipated sale price at the end of the holding period is estimated to be $700,000.

The yield rate is 11%.

What is the Net Present Value? _____________________

Answer 46

600,000 [CHS] [ g ] [CFo]
45,000 [ g ] [CFj]
50,000 [ g ] [CFj]
55,000 [ g ] [CFj]
60,000 [ g ] [CFj]
765,000 [ g ] [CFj]
11 [ i ]
[ f ] [NPV]
Display reads: 14,851.31

Net Present Value: $14,851.31

Question 47

An investor client is trying to determine the total value of all assets held. You are contacted to estimate the value of a life interest that is held on an industrial warehouse property.

The present market value of the property is determined to be $300,000. The life expectancy of the life tenant is estimated to be 15 years. The market rate for this type of property is 10%. The estimated value of the property at the end of the 15 years is $450,000.

What is the value of the life interest? ______________________

Answer 47

Keystrokes for Life Interests:

15 [ n ]
10 [ i ]
450,000 [CHS] [FV]
[PV]
Display reads: 107,726

300,000
-107,726
192,274 (Value of the life interest)

Question 48

A property is leased at a below-market rent of $300,000 annually.

The lessee elects to sublease the property for the next 5 years at a flat rent of $400,000.

If the discount rate is 12%, using your financial calculator, what is the value of this sandwich lease?

Value of sandwich lease: _______________________

Answer 48

Keystrokes are:

5 [ n ]
12 [ i ]
100,000 [CHS] [PMT]
[PV]
Display reads: 360,477.62

Value of the Sandwich Lease is $360,477.62

Question 49

Mortgage financing is available for marina purchases. Typical terms require a 30% down payment, with a 20-year term and an interest rate of 8%. The annual mortgage constant is 0.10185. Investors in marinas and other similar properties demand a return to equity of 13%. What is the idicated Cap Rate?

Answer 49

Band of Investment, Mortgage/Equity: (0.7 x 0.10185) + (0.3 x 0.13) = indicated cap rate 0.071295 + 0.039 = 0.110295 or 11.03% indicated cap rate (rounded)

Question 50

A $102,500 mortgage has monthly payments for 25 years, at 6.25% interest. How much are the monthly payments?

Answer 50

$676.16
25 gn, 6.25 gi, 102,500 CHS PV, PMT

Question 51

A $112,000 mortgage, with 6.4% interest, has a monthly payment of $727.09 How many years was the original term of the loan?
- 20
- 22
- 27
- 29

Answer 51

27
Use your 12C: 6.4 g i, 112,000 PV, 727.090 CHS PMT, n, 12 ÷ Answer is 27 years.

Question 52

A $222,500 mortgage, with 6.75% interest, has a monthly payment of $1,691.81. How many years was the original term of the loan?
- 20
- 22
- 25
- 30

Answer 52

20
Use your 12C: 6.75 gi, 222,500 PV, 1,691.81 CHS PMT, n, 12 ÷ Answer is 20 years

Question 53

A $264,000 mortgage has monthly payments for 20 years, at 5.95% interest. How much are the monthly payments?
- $1,508.12
- $1,574.34
- $1,737.99
- $1,883.77

Answer 53

$1,883.77

Question 54

A $264,000 mortgage has monthly payments for 30 years, at 5.95% interest. How much are the monthly payments?
- 1488.12
- 1574.34
- 1737.99
- 2046.47

Answer 54

1574.34

Question 55

A $92,000 mortgage, with 7.2% interest, has a monthly payment of $695.32. How many years was the original term of the loan?
- 20
- 22
- 25
- 29

Answer 55

22
Use your 12C: 7.2 gi, 92,000 PV, 695.32 CHS PMT, n, 12 ÷ Answer is 22 years.

Question 56

A 30-year mortgage has an interest rate of 5.9% and monthly payments of $1,156.62. What was the original mortgage amount?
- 165000
- 184500
- 188000
- 195000

Answer 56

195000
Use your 12C: 30 gn, 5.9 gi, 1,156.72 CHS PMT, PV Answer is $195,000.

Question 57

A condo homeowner’s association needs to build up $60,000 to replace the roofs in 5 years. They can expect 3.75% interest. How much is needed each payment if they make quarterly payments?
- 1873.45
- 2238.4
- 2511.55
- 2716.07

Answer 57

2716.07
Use your 12C: [g] BEG 5 ENTER 4 X n, 3.75 ENTER 4 ÷ i, 60,000 CHS FV, PMT Answer is $2,716.07.

Question 58

A homeowner’s association needs to build up $50,000 to replace the roofs in eight years. They can expect 3.75% interest. How much will be needed if they make quarterly payments?
- 873.45
- 1038.4
- 1211.55
- 1334.57

Answer 58

1334.57
Use your 12C: [g] [BEG] 8 ENTER 4 X n, 3.75 ENTER 4 ÷ I, 50,000 CHS FV, PMT Answer is $1,334.57

Question 59

A homeowner’s association needs to build up $60,000 to replace the roofs in 5 years. They can expect 3.75% interest. How much is needed each payment if they made annual payments?
- 9773.45
- 10138.4
- 10997.55
- 10730.71

Answer 59

10730.71

Question 60

A property sold for $240,000 and the buyer put $50,000 down and got a mortgage for the balance of the purchase price. The seller paid two points. How much was that?
- 1900
- 3200
- 3800
- 4800

Answer 60

3800

Question 61

An apartment owner needs to build up $30,000 to replace the boilers in 7 years. He decides to make semi-annual payments to an interest-bearing account paying 4.0%. How much are the semi-annual payments?
- 1645.89
- 1841.23
- 2251.04
- 2325.78

Answer 61

1841.23
Use your 12C: [g] [BEG] 7 ENTER 2 X n, 4 ENTER 2 ÷ I, 30,000 CHS FV, PMT Answer is $1,841.23.

Question 62

At the end of last month, your bank balance was $2,754.40. During the month you deposited $250.00, $543.25, $1,100, and $47.95. You made withdrawals of $500.00, $17.32, $914.50, and $51.00. What is your current balance?
- 2912.45
- 3212.78
- 3368.3
- 4187.23

Answer 62

3212.78
Use your 12C: 2,754.4 ENTER 250 + 543.25 + 1,100 + 47.95 + 500 – 17.32 – 914.50 – 51 - Answer is $3,212.78

Question 63

Here are 10 gross income multipliers. 5.9 6.2 5.7 6.3 6.4 6.0 5.5 5.8 6.3 6.9 What is the mean?
- 5.9
- 6
- 6.1
- 6.2

Answer 63

6.1

Question 64

Here are 10 gross income multipliers. 5.9 6.2 5.7 6.3 6.4 6.0 5.5 5.8 6.3 6.9 What is the range of the GIMs?
- 5.5-6.9
- 5.7-6.3
- 1.2
- 1.4

Answer 64

1.4

Question 65

Here are 10 gross income multipliers. 5.9 6.2 5.7 6.3 6.4 6.0 5.5 5.8 6.3 6.9 What is the sum of the differences between the mean and the variants (X – X)?
- 2.8
- 3.2
- 3.4
- 3.8

Answer 65

3.2

Find mean, then calculate difference between each multiplier

Question 66

Here are 12 numbers. 41 56 38 61.5 49 59 32 67.5 60 52 47 44 What is the standard deviation?
- 8.77
- 9.02
- 10.66
- 11.94

Answer 66

10.66
Use your 12C: f CLEAR S 41 S+ 56 S+ 38 S+ 61.5 S+ 49 S+ 59 S+ 32 S+ 67.5 S+ 60 S+ 52 S+ 47 S+ 44 S+ g g s Answer is 10.66.

Question 67

Here are eight land sales. $45,000 $37,000 $34,500 $48,000 $41,000 $47,500 $39,500 $51,000 What is the average absolute deviation?
- 4337.5
- 4500.75
- 4725
- 4937.5

Answer 67

4937.5

Find mean
For each point, subtract the mean and take absolute value
Do average of these differences

Question 68

Here are eight land sales. $65,000 $77,000 $62,500 $75,000 $80,000 $77,500 $72,500 $82,000 What is the average deviation?
- 4518.09
- 5453.13
- 5625.79
- 5983.33

Answer 68

5453.13
First you have to find the mean of these numbers. Add them up and divide by 8. The answer is $73,937.50. Then, you have to take each of the GIMs and determine how much each one differs from the mean we just found (73,937.50). For example: the first number is 65,000. 73,937.50 – 65,000 = 8,937.50. The second number is 77,000. 77,000 – 73,937.50 = 3,062.50. We are looking for absolute numbers – how far is each GIM away from the mean – regardless of whether it is a positive or negative number. Calculate each of these 8 differences and then add them up. The answer is 43,625. 43,625 ÷ 8 = 5,453.13.

Question 69

Here is a table showing 10 GRMs. GRMs 98.5 93.6 112.8 122.0 104.2 91.7 98.8 114.2 117.9 123.5 What is the modal GRM?
- 98.8
- 104.2
- 112.8
- None

Answer 69

None

Question 70

Here is a table showing 15 rents. Monthly rents $775 $800 $750 $825 $875 $850 $850 $750 $775 $850 $800 $800 $750 $900 $875 What is the modal rent?
- 800
- $750 and 800
- $800 and 810
- $750, $800, and $850

Answer 70

$750, $800, and $850

Question 71

How much do I have to put aside each year, at 4.5% interest, to accumulate $25,000 to repave a parking lot in seven years?
- 2944.88
- 2983.29
- 3339.48
- 3896.02

Answer 71

2983.29

Question 72

How much should I pay today for a contract that will pay me $250,000 in 5 years, discounted at 8%?
- 168026.47
- 170145.80
- 173093.21
- 182840.62

Answer 72

170145.80
Use your 12C: 5n, 8i, 250,000 CHS FV, PV

Question 73

If a 20-year mortgage, with an interest rate of 6.15%, has monthly payments of $1,305.20; what was the original mortgage amount?
- 180000
- 184500
- 195000
- 203000

Answer 73

180000
Use your 12C: 20 g n, 6.15 g i, 1,305.20 CHS PMT, PV Answer is $180,000.

Question 74

If I deposit $22,000 in a bank account at 2.75% interest, how much will I have at the end of 9 years?
- 24567.3
- 26073.45
- 27135.94
- 28084.01

Answer 74

28084.01
Use your 12C: 9n, 2.75i, 22,000 CHS PV, FV Answer is 28,084.01

Question 75

We have a $146,500 mortgage, for 25 years and the monthly payment is $989.28. What is the interest rate?
- 5.4%
- 5.9%
- 6.5%
- 6.7%

Answer 75

6.5%
Use your 12C: 25 gn, 146,500 PV, 989.28 CHS PMT, i, 12 X Answer is 6.5%.

Question 76

What are the monthly payments on a $234,000 mortgage at 5.8% annual interest for 20 years?
- 1649.56
- 1415.78
- 2083.21
- 1974.56

Answer 76

1649.56
Use your 12C: 20 gn, 5.8 gi, 234,000 CHS PV, PMT Answer is $1,649.56.

Question 77

You bought a house for $256,000 and sold it for $295,000, minus a 5% commission. What was the net percentage of your gain?
- 6.3
- 7.7
- 8.1
- 9.5

Answer 77

9.5%
Use your 12C: 295,000 Enter 95% Answer is $280,250. 256,000 ENTER 280,250 [delta]% Answer is 9.5%

Question 78

Your stock went from $125 to $97.25 in 3 years. What is the average percent change per year?
- 7.4%
- -7.4%
- 9.5%
- -9.5%

Answer 78

-7.4%

Question 79

*A property sold for $240,000 and the buyer put $50,000 down. The seller paid 2 points. How much was that?**
- 1900
- 3200
- 3800
- 4800

Answer 79

3800

Question 80

How much is (145.78 + 216.82) X (590.50 – 188.25) ÷ 46.12?
- 1518.78
- 2939.2
- 3162.53
- 4452.95

Answer 80

3162.53

Question 81

An investor sells his apartment house for $3,450,000. The sales commission is 8.5%. What is the net amount received by the owner?
- 3156750
- 3245000
- 3298750
- 3310000

Answer 81

3156750

Question 82

The subject real estate is a one-acre site that the appraiser thinks has a market value of $75,000. In this market, the typical land-to-property value ratio is 1/5. What is the appropriate building cost of this site?

Answer 82

$300,000

The correct calculation is:
Land value: 1 / 5 = 20%
Therefore, property value x 20% = the land value or
VO x 0.2 = $75,000
Therefore, 75,000 / 0.2 = $375,000
Therefore, the building value is calculated as:
$375,000 x 0.8 = 300,000
(0.8 is the complement of 0.2)

Question 83

The subject real estate is a 25-acre parcel in the path of development. However, there is an old farmhouse located in the middle of the property on a five-acre site. The house and five acres are leased to a tenant on a two-year lease with 20 months remaining at $500 per month. The real estate can now be sold at $50,000 per acre, but it is not available for sale until the lease expires because the house is in the way. What is the value of the property today if the discount rate is 12% and no change in land value is anticipated for the next 20 months? Note that the real estate taxes are the only holding cost at $6,000 per year. The location of the house precludes all development and should have a market value of less than $100,000 with five acres.

Answer 83

$1,024,431

The following calculations were made on a Hewlett Packard 12C (HP-12C) financial calculator:
25 x 50,000 = $1,250,000 FV
$1,250,000 FV
0 PMT
20 n
12 g i
Solve for PV = 1,024,431
n = 20 because it is already monthly
i needs to be divided by 12 to make it monthly

Question 84

A parcel of real estate is zoned commercial but is improved with a residence. The sales data shows the following current values and trends:

Residential Site Value - $45,000 +1%/yr (+$450)
Commercial Site Value - $250,000 + 5%/yr ($12,500)
Residential Improved Property - $500,000 +1%yr ($3,000)

Assuming that it is Year 0 now, when will the highest and best use shift to commercial land? Use straight-line calculations. The demolition cost is $1,000.

Answer 84

At the end of Year 6

Assuming that it is now Year 4, the site value equals $46,800, the commercial site value equals $300,000, and the residential improved property value equals $312,000 (option a). In Year 5, the site value equals $47,250, the commercial site value equals $312,500, and the residential improved property value equals $315,000 (option b). In Year 7, the site value equals $48,150, the commercial site value equals $337,500, and the residential improved property value equals $321,000 (option d). In Year 6, the residential site value equals $47,700, the commercial site value equals $325,000, and the residential improved value equals $318,000.

Question 85

An office building sold for $1.25 million with the seller holding a $1 million conditional sale contract for five years with monthly payments at 6% in a market where the interest rate was 8%. The buyer indicated that she thought the financing package available for this property, which was not available for any others, added $25,000 to the price. The seller confirmed that this was a realistic estimate of the cost of financing. What was the cash-equivalent sale price?

Answer 85

The correct calculation is:
$1,250,000 - $25,000 = $1,225,000
No complicated calculation is needed in this case because the contributory value of the financing stated by the buyer is a better indicator of that increment than making a calculation in an attempt to replicate what a buyer would think.

Question 86

What is the yield on an investment that was purchased for $49,700 five years ago and then resold now for $100,000? There were no income or expenses each year. Round your answer to the near full percentage.

Answer 86

15%

The correct keystrokes for the HP-12C are:
49,700 CHS PV
100,000 FV
5 n
0 PMT
Solve for i = 15.0082%

Question 87

What is the annual yield rate on a mortgage that was made with a term of 30 years with monthly payments and a stated interest rate of 8.0% but with four points charged by the lender if the loan runs full term?

Answer 87

8.44%

First, solve for the payment based on 100% (-1).
The correct keystrokes for the HP-12C are:
30 g n
8 g i
1 CHS PV
0 FV
Solve for PMT = 0.00733765
0.96 CHS PV (96% is 100% less the points)
Solve for i = 0.7029
This is the monthly number, but the answer needs to be annual:
ENTER 12 X = 8.435

Question 88

A property recently sold for $587,000, and the buyer indicated that he anticipated a 10-year holding period and used a 7% discount rate and a level net income of $64,000. What should have been the expected reversion at the time of resale?

Answer 88

$270,465

The correct keystrokes for the HP-12C are:
10 n
7 i
587,000 CHS PV
64,000 MT
Solve for FV = 270,465

Question 89

A mortgage loan was made with the intention for it to be sold on the secondary market. The loan was made with a 30-year term but only has 27 years left. The loan payments are $1,255 per month. The current market rate for 25- to 30-year mortgages like this is 5.5%. What should this mortgage loan sell for with no other points, concessions, or incentives?

Answer 89

$211,587

The correct keystrokes for the HP-12C are:
27 g n
5.5 g i
1,255 PMT
0 FV
Solve for PV = -$211,587
The present value of only three years of these cash flows is $41,562 (option a). As with any other investment, the value is the present value of the future cash flows. If the calculation is made with 30 years instead of 27, the result is $211,033 (option c). Pressing FV instead of PV on the HP-12C results in $930,985 (option d).

Question 90

A property sold in January of 2011 for $456,000 and then sold again in April of 2012 for $435,000. The sale in 2011 included $5,000 in seller concessions with the price. What is the annualized straight-line rate of change implied by this sale and resale?

Answer 90

-2.84%

The correct calculation is:
$435,000 - $451,000 = -16,000 / 451,000 = -0.355 / 15
= -0.0024 x 12 = 0.0284 = -2.84%

Question 91

What is the mortgage constant for a loan with a 6.75% interest rate and a 20-year amortization period with monthly payments?

Answer 91

9.12%

The correct keystrokes for the HP-12C are:
20 g n
6.75 g i
1 CHS PV
0 FV
Solve for PMT
12 x = 0.091244

Question 92

The subject real estate is a vacant parcel of land in an area of development. This corner site is rectangular and measures 1,320 feet by 2,640 feet, of which 15 feet is in the county road right-of–way and therefore unusable. There is a zoning requirement that 10% of the gross acreage must be set aside for buffers, retention ponds, and landscape features. The area required for streets is 12% of the net area after the existing right-of-way area (15 feet of the perimeter) has been deducted. The highest and best use is for development of a residential platted development with an average lot size of 1/3 acre. How many lots will this land support? Use square feet calculations.

Answer 92

183 lots

1,320 x 2,640 = 3,484,800 (gross area) minus the right of way, which is (15 x 3,960) - (15 x 15) = 59,175
There is an overlap of 15 feet in the corner that needs to be removed from the right-of-way calculation.
The net area is 3,484,800 - 59,175 = 3,425,625
The buffer area required by zoning is 10% of the gross area, or 3,484,800 x 0.1 x 348,480
The streets will require 12% of the net area, or 0.12 x 3,425,625 = 411,075
The 1/3-acre lot will be 43,560 / 3 = 14,520
The calculation is
3,484,800 - 59,175 = 3,425,625 (net area) - 348,480 - 411,075 = 2,666,070 (usable area)
Finally, 2,666,070 / 14,520 = 183.61, which is rounded down to 183 lots. (It has to be rounded down to meet the requirements.)

Question 93

What is the annual debt service on a $100,000 mortgage loan for a mortgage with an 8.75% interest rate and a 15-year amortization with biweekly payments (made every two weeks)? The biweekly payments are in arrears.

Answer 93

$11,982.04

The correct keystrokes for the HP-12C are:
100,000 CHS PV
26 × 15 n
8.75 / 26 i
0 FV
Solve for PMT = 460.84 × 26 = 11,982.04
This question is asking for the annual debt service. The biweekly payment amount is $460.85 (option a). The monthly debt service for monthly payments is $999.45 (option b). The annual debt service for monthly payments is $11,993.38 (option d).

Question 94

A property sold for $145,000 with $30,000 down and the balance in the form of a purchase money mortgage at 9.0% interest for 20 years with monthly payments.
Shortly after the sale, the seller sold the mortgage for $105,000. What yield will the buyer of the mortgage realize if the mortgage is paid off after 10 years? Round your answer to the nearest 1/2 percent.

Answer 94

10.5%

The correct keystrokes for the HP-12C are:
20 g n
9 g i
115,000 CHS PV
0 FV
Solve for PMT = 1,034.69
10 g n
Solve for FV = 81,679.77
105,000 CHS PV
Solve for i = 0.8805 x 12 = 10.56%

Question 95

The subject was purchased for $333,000 on June 1, 2009, and resold for $444,000 on February 1, 2012. What is the compound rate of change on an annual basis?

Answer 95

11.34% per year

The correct keystrokes for the HP-12C are:
32 / 12 = 2.6667 n
333,000 CHS PV
0 PMT
444,000 FV
Solve for i = 11.3386
The compound rate of change on a monthly basis is 0.90% per year (option a). The rate for straight-line calculations is 12.50% per year (option c). The overall amount of change (not annual and not compounded) is 33.33% per year (option d).

Question 96

The subject is a life estate on a property that would be worth $350,000 today and would grow at a rate of 2% per year compounded if it were fee simple. The remainderman is estimated to get the property in fee simple in 35 years. If the discount rate for the holding period is 8%, what is the value of the life estate? Round your answer to the nearest $5,000.

Answer 96

First, calculate the future value with 2% growth:
35 n
2 i
350,000 CHS PV
0 PMT
Solve for FV = $699,961
Next, discount that at 8%:
35 n
8 i
0 PMT
699,961 FV
Solve for PV = 47,342
This is the present value of the remainderman’s interest.
Subtract this from the fee value to get the value of the life estate:
350,000 − 47,342 = 302,658, rounded to 305,000

Question 97

The subject real estate is a gravel extraction operation. The property has historically sold $200,000 in gravel each year. The royalties paid to the underlying fee owner are 20% of the gross sales (net of all expenses). The geologist stated that there were six more years of gravel left at that rate. The resale value at the end of the mining operation is $50,000 (recreation land). What is the value of the underlying fee position today if the discount rate is 10%?

Answer 97

The correct keystrokes for the HP-12C are:
200,000 × 0.20 = 40,000
6 n
10 i
40,000 PMT
50,000 FV
Solve for PV = 202,434

Question 98

The subject real estate is improved with a two-story residence. The second floor has a rectangular extension that is shaped like a pyramid. The area of the residence that has this “cap” on it is a rectangle that measures 12 feet by 12 feet, and the pyramid is 8 feet from base to peak. The local contractor stated that the roof for this type of structure would cost $15 per cubic foot over the cost of a standard roof. What is the total cost of the roof for this pyramid extension over the cost of a standard roof?

Answer 98

$5,760

The formula that should be used here is:
base area × height / 3 = volume

Question 99

value of π

Answer 99

3.1416

Question 100

1 cubic foot = ? gallons

Answer 100

7.48052

Question 101

The buyer of a small farm (125 acres) reportedly paid $700,000 for the property. The seller took back a purchase-money mortgage for $600,000 at 5% in a market where local banks were quoting 8%. The amortization was based on a loan term of 20 years, but there was a Year 5 balloon payment of $500,729. The seller and buyer are not revealing the details of the sale and would not estimate the contribution of the financing. There have been no sales in this area of properties that are similar in size, features, and location, so the appraiser needs to use this as a comparable sale. What is the mathematical contribution of the financing?

Answer 101

$68,600

The correct keystrokes for the HP-12C are:
20 g n = 240
5 g i = 0.41666
600,000 CHS PV
0 FV
Solve for PMT = 3,959.73
Change n to 5 g n
Solve for FV = $500,729.18
Change i to 8 g i
Solve for PV = -$531,382.55 (value of the mortgage loan)
$600,000 +
Read $68,617.45

Question 102

A development has 28 lots that have been in inventory for four years. The market will limit sales to five lots per year. Lot prices will be stable for three years but then increase by 5% per year. There are various values on the lots, but the average value today is $50,000. The lots are priced at $100,000 each, and this is the reason why none have sold. The real estate taxes are $200 per lot for the inventory of the previous year. Sales commissions are 5% of gross sales. Since the lots are already built, the market appears to be recovering; the entrepreneurial incentive is only 15% of the gross sale price. There is $25,000 of deferred maintenance and about $1,000 per year in ongoing maintenance. What is the value of all 28 lots today if the discount rate is 10% and there is annual accounting?

Answer 102

$812,000

Discounting can also be done on the HP-12C calculator using the CFj key.
The correct keystrokes are:
f CLx
193,400 g CFj
194,400 g CFj
195,400 g CFj
206,400 g CFj
217,900 g CFj
137,315 g CFj
10 i
f NPV
Read 837,070
ENTER 25,000
Read 812,069.72
If you forget the deferred maintenance, you will get $837,000 (option b). If you
don’t discount the cash flows, you will get $1,145,000 (answer c). If you don’t
deduct expenses or discount the value, you will get $1,461,769 (answer d).

Question 103

A comparable sale sold for $345,000 with $5,000 in financing concessions. The land value of this property is $55,000. What is the land-to-building value percentage?

Answer 103

19.29%

The correct calculation is:
$55,000 / ($345,000 − 5,000 − 55,000) = 0.1929
Remember that the land-to-building ratio is the value of the land divided by the building value, which is the sale price less the land value.

Question 104

An appraiser found that an apartment with a detached garage generated $75 more per month in gross rent than an apartment without a detached garage. If the gross rent multiplier is 85, what is the adjustment for a garage in that market? The overall capitalization rate (RO) for this market is 12%.

Answer 104

$6,375

The correct calculation is:
$75 × 85 = $6,375

Question 105

The published sale price of a small apartment building comparable sale was $245,000. The buyer and seller agreed to the purchase of the property for $245,000, with the seller taking back a purchase money mortgage of $175,000 at 7% interest for 30 years with a balloon payment in six years. The payments were monthly. The market interest rate for a property like this at the time of sale was at 9% with no points. Determine the cash-equivalent sale price using the calculator yield-to-market technique and assuming that the buyer would keep the financing in place for six years. Round your answer to the nearest increment of $25,000.

Answer 105

$225,000

The correct keystrokes for the HP-12C are:
30 g n
7 g i
175,000 CHS PV
0 FV
Solve for PMT = 1,164.28
Change the number of periods to the balloon term: - 6 g n
Solve for FV = $162,210
Change the interest rate (9 g i) to the market rate
Solve for PV = - $159,309
Add the down payment of $70,000 back in = 229,309

Question 106

Laura the appraiser researched comparable sales in a new home market and found that a new 2,000-sq.-ft. home with a two-car attached garage on a standard lot would sell for $250,000. She also found that each additional square foot of GLA up to about 500 square feet would add about $75 per square foot to the sale price, each additional square foot of GLA above 2,500 square feet but below 3,000 square feet would add about $65 per square foot to the sale price, and each additional square foot above 3,000 square feet and below 3,500 square feet would add about $55 per square foot to the sale price. Assuming that these ratios are correct, how much GLA does a house that sold for $335,000 have if it is located on a standard lot with a two-car attached garage?

Answer 106

3,250 square feet

The correct calculation is:
250,000 + (500 × 75) + (500 × 65) + (X × 55) = 335,000
(500 × 75) + (500 × 65) + (X × 55) = 85,000
37,500 + 32,500 + (X × 55) = 85,000
X × 55 = 15,000
X = 272.73 (This is not the GLA total but the increment above 3,000 sq. ft.)
GLA = 2,000 + 500 + 500 + 272.73 = 3,273 sq. ft.
This can also be calculated by adding the values until the correct amount is
reached:
C4-Q102 Solution.PNG
This means the answer is more than 3,000 but less than 3,500 sq. ft.
The area above 3,000 sq. ft.: 15,000 / 55 = 272.73 sq. ft.
Therefore, the GLA is 3,273 sq. ft.

Question 107

A residential property just sold for $500,000. It is located on a $100,000 lot. The structure included GLA, a finished basement, an enclosed porch, and an attached garage. The total area of all these components is 7,500 square feet, of which 60% is GLA, 25% is basement area, 5% is porch area, and 10% is garage area. The basement is worth 75% of the GLA value per square foot, the porch is worth 50% of the GLA value per square foot, and the garage is worth 65% of the GLA value per square foot. What is the value per square foot of the garage space?

Answer 107

$40 per square foot

The correct calculation is:
500,000 − 100,000 = $400,000 (value of the improvement)
Next, calculate the value of the GLA:
(7,500 × 0.60 × X) + (7,500 × 0.25 × 0.75 X) +
(7,500 × 0.05 × 0.50 X) + (7,500 × 0.10 × 0.65 X) = 400,000
(4,500 X) + (1,875 × 0.75 X) + (375 × 0.50 X) + (750 × 0.65 X) = 400,000
(4,500 X) + (1,406 X) + (187.5 X) + (487.5 X) = 400,000
6,581.25 X = 400,000
X = 60.78
The last calculation is done to get the value of the garage.
The garage is 65% of that amount, which equals $39.51.

Question 108

Use linear regression and consider only the following comparable sales to determine what a 111-acre property would be worth if these properties are very comparable and the sales are very recent.

01 - 070 - $5,714
02 - 090 - $5,556
03 - 150 - $5,167
04 - 155 - $5,195
05 - 195 - $5,055
06 - 200 - $5,000
07 - 230 - $5,463
08 - 285 - $4,417
09 - 310 - $4,381
10 - 366 - $4,317

Answer 108

$5,479 per acre

Question 109

A property has an overhead garage door that is 13 years old. It costs $1,900, including installation. In this market, the inclement weather comes from the west. These overhead doors typically last 15 years if they face west and 25 years if they face east. This door faces east. What is the amount of value left in this item?
$253
$912
$988
$1,647

Answer 109

$912

Question 110

The subject residence is 10 years old, and its short-lived items are listed in the following table. What is the amount of depreciation shown for the exterior doors?

Answer 110

$1,760

The correct calculation is:
$4,400 × (10 / 25 = 40%) = $1,760

Question 111

A comparable sale has a sale price of $500,000 (VO) and a lot value of $80,000 (VL). The site improvements (VSI) have a contributory value of $15,000, and the cost of construction of the house is $500,000. What is the implied economic life if the house is 18 years old?

Answer 111

95

The correct calculation is:
500,000 (VO) − 80,000 (VL) − 15,000 (VSI)
= 405,000
500,000 − 405,000 = 95,000
95,000 / 500,000 (depreciation) = 0.1900
0.1900 / 18 = 0.0106, then 1 / 0.0106 = 94.7368

Question 112

An appraiser indicated that the subject has 2.35% depreciation per year overall. If the subject is six years old, what is the indicated economic life?

Answer 112

The correct calculation is:
1 / 0.0235 = 42.55
In this case, the age of the building is not needed. Because the building is depreciating at a rate of 2.35% per year, we need to figure out how many years it will be before the building is 100% gone. Therefore, 100% / 2.35% = 42.55

Question 113

A property sold for $743,000. The sale was arm’s-length and had no concessions, and there were no expenditures immediately after the sale. The appraiser’s opinion of the site value (VL) was $94,000, and the site improvements (VSI) have a contributory value of $10,000. If the building cost is $700,000 and the building is six years old, what is the implied economic life?

Answer 113

69

The correct calculation is:
743,000 (VO or sale price) − 94,000 − 10,000 (VL + VSI) = 639,000 (VB)
700,000 (cost) − 639,000 (VB) = 61,000 (depreciation)
61,000 / 700,000 = 0.087143 (% depreciation overall)
0.087143 / 6 = 0.014524 (% depreciation/year)
1 / 0.014524 = 68.8524 years (% depreciation/year divided into 100%)

Question 114

An office building has four 16-ton air conditioning units costing $22,000 each. However, the AC contractors all say that four 12-ton units that cost only $14,000 each would suffice. The units were designed to cool a now-bankrupt company that was heavily reliant on large computers, which caused excess heat. The units are eight years old and have a 14-year economic life. What is the functional obsolescence if there are no excess operating costs?

Answer 114

$13,714

The correct calculation is:
(4 × 22,000 × (6 / 14)) − (4 × 14,000 × (6 / 14)) = 13,714
This compares the depreciated value of what is in place versus what should be in place for market requirements—in other words, what is there versus what should be there. The difference between the cost of the two units is $8,000 (option a). If the depreciation is compared, the answer is $13,714 (option b). If the total cost new for all four units is compared, the result is $32,000 (option d).

Question 115

A comparable property sold for $329,000 with no concessions. The site value (VL) was estimated at $35,000, and the site improvements (VSI) have a contributory value of $7,000. The cost to construct the building was $340,000. What is the percentage of depreciation for the building?

Answer 115

15.58%

The correct calculation is:
329,000 (VO) − 42,000 (VL and VSI) = 287,000 (VB)
340,000 (cost) − 287,000 (VB) = 53,000 (depreciation)
53,000 / 340,000 = 0.1559

Question 116

Using the following comparable sales only, what is the range of indicated total economic life? depreciation per year ranges from 0.0111 to 0.0123.

Answer 116

81 to 90 years

Question 117

The subject real estate is improved with a 3,100-sq.-ft. residence. It has four central forced air conditioner units in place. The market standard for this size building is only one air conditioner unit. The cost of the four units is $42,000, but one unit would only cost $12,000. These units are 10 years old and have 4% depreciation per year. What is the functional obsolescence from this overimprovement?

Answer 117

18,000

The owners of this property have wasted a lot of money on excess cooling equipment, but some of the extra (wasted) cost would already be compensated for in the physical depreciation. (The superadequate units are not new). The calculation is (42,000 × 0.60) − (12,000 × 0.60) = $18,000.

Question 118

The subject real estate is a 0.65-acre site improved with a 15-year-old, single-unit residence built on a slab located in a warm climate. There is no basement or garage. The subject rents for $600 per month, and the gross rent multiplier is 50. There are four houses in the immediate area that are all rented for $650 per month with similar expenses and features. They are almost identical except that they have one-car attached garages, which the subject lacks. The cost of a one-car garage is $5,000, and the depreciation from all sources is 25%. Which of the following statements is correct?

The subject has no functional depreciation for the lack of a garage.

The subject has $2,500 in functional obsolescence for the lack of a garage.

The subject has $5,000 in functional obsolescence because that is what it cost to build it.

There is a loss for the lack of a garage, but it is best labeled as external obsolescence.

Answer 118

The subject has no functional depreciation for the lack of a garage.

The value of the garage is $2,500 (50 (rent) × 50 (GRM) = 2,500). If the subject had a garage, it would normally be worth $3,750 (5,000 × 0.75 = 3,750). This means the garage should be worth $3,750, but it isn’t; it is worth $2,500. Therefore, the house without the garage is correct in this market.

Question 119

Using the following sales data only, calculate the overall percentage of depreciation assuming that the subject is 10 years old. Use a linear regression model rather than averaging.

Answer 119

11.73%

The average of the total depreciation gives no weight to the variable.
The correct keystrokes for the HP-12C are:
CLx
0.1309 ENTER
11 ∑+ 0.1111 ENTER
9 ∑+ 0.1250 ENTER
11 ∑+ 0.0779 ENTER
7 ∑+ 10 g y^, r = 0.1173

Question 120

If a property has a PGI of $54,000, vacancy and collection losses of 5% (total), and total expenses of $23,000, what is the OER?

Answer 120

44.83%

Question 121

In a soft market, a landlord accepted a new tenant with a 60-month lease at $5,000 per month but gave the new tenant six months of free rent before the lease started. Use the average (straight-line) rent method to calculate the effective monthly rent.

Answer 121

The correct calculation is:
60 × 5,000 = 300,000
300,000 / 66 = 4,545.45

Question 122

A property has a net income of $36,000 per year. The operating expense ratio is 36%. The vacancy and collection loss is estimated to be 4%. What is the EGI?

Answer 122

$56,250

The correct calculation is:
36,000 / 0.64 = 56,250

OER - Operating Expense Ratio
EGI - Effective Gross Income

OER = Expenses / EGI =>
Expenses = OER * EGI
Expenses = 0.36*EGI

NOI - Net Operating Income
NOI = EGI - Expenses =>

36,000 = EGI - 0.36*EGI = 0.64 EGI
EGI = 36000/0.64 = 56,250

Question 123

If a property has an OER of 42% and the net operating income (IO) is $49,500, what is the EGI?

Answer 123

$85,345

OER - Operating Expense Ratio
EGI - Effective Gross Income

OER = Expenses / EGI =>
Expenses = OEREGI
Expenses = 0.42EGI

NOI - Net Operating Income
NOI = EGI - Expenses =>
49,500 = EGI - 0.42*EGI = 0.58 EGI
EGI = 49,500 /0.58 = 85,345

Question 124

A sale of a net leased property was verified at $150,000 cash. The lease calls for seven annual rental payments (in arrears) of $18,000. What discount rate is reflected for the leased fee interest if the property is expected to be worth $150,000 at the end of the lease? Round your answer to the nearest even percent.

Answer 124

12%

The correct keystrokes for the HP-12C are:
7 n
150,000 CHS PV
18,000 PMT
150,000 FV
Solve for i = 12%
Since this investment has no change in value from the purchase to the resale, the capitalization and yield rates are the same because R = Y − Δn

Question 125

What is the overall capitalization rate (RO) for a property that has a PGI of $45,000, an EGI of $41,500, and an OER of 33%? The net income multiplier is 16.55.

Answer 125

6.04%

The reciprocal of the net income multiplier is the capitalization rate:
1 / 16.55 = 0.0604

Question 126

What is the internal rate of return on a real estate investment paying $10,000 per year for the next 20 years with payments at the end of the period if the purchase price is $71,306? There is no reversion on this investment.

Answer 126

12.75%

The correct keystrokes for the HP-12C are:
10,000 PMT
20 n
71,306 CHS PV
0 FV
Solve for i = 12.7525

Question 127

If the expected yield in a market is 9% and the income and value are increasing at 2% per year, what is the value of a property with $100,000 net income?

Answer 127

$1,428,571

The math is based on R = Y − Δa, which in this scenario is
R = Y − CR
The correct calculation is:
R = 0.09 − 0.02 = 0 .07
100,000 / 0.07 = 1,428,571

Question 128

What is the net income ratio for a property that has an expense ratio of 35%, a vacancy and collection loss of 5.5%, and an annual debt service of 19%?

Answer 128

The net income ratio is the complement of the OER, so the correct calculation is:
1.0 − 0.35 = 0.65, or 65%

Question 129

The subject property is a four-acre site that was leased 22 years ago for $1,000 per month, absolute net for 99 years. There were no improvements at that time, but there is a 35,000-sq.-ft. office building on it now that was built by the tenant. This area is quite popular now and probably will be in the future. The typical holding period for a leased property like this is 20 years. The value of the property would be based on a terminal capitalization rate of 8%. What is the value of the leased fee using a 6% discount rate? Assume that there are no sales costs on the reversion.

Answer 129

$184,000

The correct keystrokes for the HP-12C are:
12,000 / 0.08 = 150,000 (resale value)
20 n
6 i
12,000 PMT
150,000 FV
Solve for PV = 184,410

Question 130

The subject is the fee simple interest less the subsurface mineral (water) rights to a five-acre parcel. Ten years ago, the Resnick family signed a contract with the city of Drysville to extract water from the property via a well. This contract was for 25 years, and the payment was $0.06 per 1,000 gallons of water. In the last 10 years, the city has extracted about 40,000,000 gallons per year from this well. What would be the adjustment for this water extraction contract if the capitalization rate is 0.11?

Answer 130

$22,000

The correct calculation is:
40,000,000 / 1,000 × 0.06 = $2,400
2,400 / 0.11 = 21,818

Question 131

A local investor recently purchased a small strip center for $1,235,000. He obtained a 75% mortgage at 7% interest with a 25-year amortization. The payments are $6,546.54 per month. The buyer expected the first year’s NOI to be $96,000. What is the equity dividend rate (RE)?

Answer 131

0.0565

EquityDividendRate(RE)= AnnualCashFlowAfterDebtService /
InitialEquityInvestment

Annual Cash Flow After Debt Service = NOI - Annual Debt Service

Initial Equity Investment = Purchase Price - Mortgage Amount

The correct calculation is:
Mortgage payment = $6,546.54
Annual debt service = $78,558.51
1,235,000 (VO) × 0.25 = 308,750 (VE)
96,000 (IO) − (6,546.54 × 12) = 17,441.52 (IE)
17,441.52 / 308,750 = 0.056491

Question 132

What is the value of a property that generates $10,000 per year in NOI? It is located in a market where net income and property values are increasing by 2% per year. The yield rate in this market is 8%. Round your answer to the nearest $5,000.

Answer 132

$165,000

The correct calculation is:
R = Y − CR
R = 0.08 − 0.02
R = 0.06
10,000 / 0.06 = 166,666

Question 133

If a property would sell based on an equity dividend rate of 9% and qualifies for a 75% mortgage with 30 years of monthly payments at 11.0% interest, what is the indicated overall capitalization rate? Round your answer to the nearest 1/10 of a percent. Use the band-of-investment technique.

Answer 133

10.8%

Overall capitalization rate (RO) using the band-of-investment technique, we combine the required returns from both the mortgage (debt) and the equity (investor’s capital). This technique considers the weighted average of the mortgage capitalization rate and the equity dividend rate based on their respective proportions in the financing structure.

RO=(MortgagePortion×Mortgage capitalization rate (RM)+(EquityPortion×Equity dividend rate (RE)

0.75% × 0.11428 + 0.25% × 0.09 = 10.821%

Equity Dividend Rate is given

Mortgage Capitalization Rate is percentage of the loan paid annually and is calculated as:

Input on HP
- monthly interest (11%/12)
- number of periods (30*12)
- hypothetical loan amount PV=1

Calculate pmt = 0.00943673
Multiply it by 12 (12 months) = 0.11324077

Aka we pay total of $0.1132 on $1 loan, or 11.32% annually, which is the Mortgage Capitalization Rate

This means that, based on the band-of-investment approach, a property financed with 75% debt at an 11% mortgage rate and expecting a 9% equity return would have an overall capitalization rate of 10.8%.

Question 134

A property was purchased for $1,250,000. The NOI is $100,000. Both the NOI and value are expected to increase at a compound rate of 1% per year. What yield will be achieved if the property is held for 10 years?

Answer 134

9%

(After calculation for I, which is cap rate, remember Cap Rate = Yield - change => Yield = Cap Rate plus Change = 0.08+0.01)

Question 135

The owner of a residential property bequeathed a life estate in the property to his wife and gave the remainderman’s interest to his son by a first marriage. The life tenant is currently 69 years old. According to life expectancy tables, the life tenant should live to the age of 79. The value of the fee simple interest today is $325,000. Discount rates in the market are approximately 11.5%. What is the value of the life estate as of today? Assume a 2%-per-year increase in property value in this market.

Answer 135

$192,000

First, calculate the value of reversion in 10 years. The correct keystrokes for the HP-12C are:
10 n
2 i
325,000 CHS PV
0 PMT
Solve for FV = 396,173 (future value of the property at the end of the life estate)
Change the i to 11.5 n
Solve for PV = 133,394 (present value of the remainderman’s interest)
Subtract the remainderman’s interest from the fee simple interest:
325,000 − 133,394 = 191,606 (This is the value of the life estate that has 10 years left.)

Question 136

A property has the following income structure:

The fee simple interest to vacant land was owned by Lance.
Five years ago, Lance leased it to Stephanie for 45 years at $3,000 per month.
Stephanie built a $500,000 building on the leased land and offered it for lease.
Angelino leased the improved property from Stephanie for $100,000 per year net.
The yield rate on the leased fee is 6% because of the low risk. (Land leases in which the tenant builds a new substantial building on the land have a low risk of default unless there is a subordination agreement.)
The yield on the leasehold is 9.5%.
What is the capitalization rate (RLH) for the leasehold interest if the lease terminates in 40 years and there are no renewal options?

Answer 136

0.097587

Capitalization rate (RLH) for the leasehold interest indicates the rate of return an investor would require on the leasehold interest, based on its income and the fact that the leasehold will expire in 40 years with no renewal option.

The correct keystrokes for the HP-12C are:
40 n
9.5 i
1 CHS PV
0 FV
Solve for PMT = 0.097587

Question 137

Ten years ago, a 2.5-acre site was leased from the Green Family Trust to the Burgundy Family Trust for 75 years (65 years remaining) on a net basis for $90,000 per year. The Burgundy Family Trust built a small retail building on the site nine years ago, and they leased the property eight years ago to White and Co. for $350,000 per year on a net basis. However, the Burgundy Family Trust still pays the lease payments to the Green Family Trust. The market rent on this property is $400,000. If the capitalization rate is 11% for the leasehold interest and 15% for the subleasehold, what is the calculated value of White and Co.’s interest?

Answer 137

$50,000 / 0.15 = $333,333

Question 138

The subject property was leased for five years at $5,000 per month, but there is only one year left on the lease. The market rate for this property is $7,000 per month and should remain at that level for at least five years. What is the value of the leased fee estate if the appropriate discount rate (YO) is 9.0% (considering one year on the lease and going to market rent after that) and the terminal capitalization rate (RN) is 11.0%? The holding period is five years and the calculation is annual at the end of the period.

Answer 138

$801,024

Cfj1-60,000
cfj2-84,000
cfj3-84,000
cfj4-84,000
cfj5-847,636
i-9
Solve for NPV = 801,023.60

cfj5=84,000 + reversion value, which is 84,000/0.11 (the terminal cap rate)

Question 139

What is the present value of an investment that produces $34,000 per year in income payable in advance and has a reversion in seven years of $445,000 with a required yield of 6.775% per year? In this market, all cash flows are estimated on an annual basis.

Answer 139

The correct keystrokes for the HP-12C are:
g BEG
34,000 PMT
7 n
445,000 FV
6.775 i
Solve for PV = 478,431.51

Question 140

A property has an NOI of $150,000 per year. The value of the land (VL) is $550,000. The land capitalization rate (RL) is 9.75%, and the building capitalization rate (RB) is 12.25%. What is the property value to the nearest $100,000?

Answer 140

1,336,735 =~$1,300,000

Question 141

The subject property has a projected level income of $30,000 for the next five years. The property value is expected to increase by 10% over the projection period of five years. The yield rate is 8%. What is the market value of the property?

Answer 141

The correct keystrokes for the HP-12C are:
5 n
8 i
1 CHS PV
1.10 FV
Solve for PMT = 0.062954 (RO)
30,000 / 0.062954 = 476,535.74
This problem can also be solved using the formula:
R = Y − Δ 1 / Sn, but it can be solved on the HP-12C alone as shown.

Question 142

Calculate the leased fee value of the real estate investment based on the following data: The property is leased for 10 years at $55,000 per year (net), and the property value is expected to decline by 10% over the 10 years. The required yield rate is 11%.

Answer 142

The correct keystrokes for the HP-12C are:
10 n
11i
1 CHS PV
0.9 FV
Solve for PMT = 0.11598 (capitalization rate)
55,000 / 0.115980 = 474,219

Question 143

What is the value of a property with an NOI of $75,000, an annual debt service of $60,000, a loan-to-value (LTV) ratio of 75%, and a mortgage constant of 0.1281?

Answer 143

The correct calculation is:
60,000 (IM) / 0.1281(RM) = 468,384 (VM)
VO × 0.75 (LTV) = 468,384
468,384 / 0.75 = 624,512 (VO)

Question 144

to remember:

The subject is a 100-acre agricultural site in a market where such sites sell for $10,000 per acre. The subject is next to a busy interstate highway, but there is no potential for commercial use due to the lack of access and population density. There is a large billboard on the site that is leased for $500 per month on a net basis for 15 more years with two 20-year renewal options at the same rate. This is a legal nonconforming use because current zoning in this town and all nearby towns prohibits any “off-site signs.” Therefore, renewal of the billboard lease is almost guaranteed. (This site cannot be replaced.) What is the adjustment for the billboard lease on the subject 100-acre parcel assuming that the comparable sales do not have this feature? The reversion in 15 years is estimated to be equal to the current value because there will still be 40 years left in the options. The discount rate is 7%. Assume end-of-year accounting. The leased premises are about 0.2 acres, but the farmer said the sign causes about 0.5 acres to be non-tillable.

Answer 144

The formula R = Y − Δ1/Sn is applicable here, but in this case it is simply
R = Y because the income is level and there is no change in value. Therefore:
R = Y
R = 0.07
The adjustment is $6,000 / 0.07 = 85,714
Less the loss in land that is used for the sign = $5,000
The adjustment to a sale without a billboard would be $80,714, rounded to $81,000

Question 145

What is the indicated equity dividend rate (RE) of a property with a sale price of $400,000, an NOI of $35,000, and mortgage terms of 9.75% interest for 25 years, fully amortized with monthly payments, and a loan-to-value ratio of 65%?

Answer 145

0.0514

First, calculate the capitalization rate (RO). The correct calculation is:
35,000 / 400,000 = 0.08750 (RO)
Next, calculate the RM using the HP-12C. The correct keystrokes for the HP-12C are:
9.75 g i
25 g n
1 CHS PV
0 FV
Solve for P = 0.008911
ENTER 12x = 0.10694 (RM)
Then multiply the RM (0.10694) by the loan percent (65%) to get the weighted rate for the mortgage:
0.65 × 0.10694 = 0.06951
Subtract the weighted rate for the mortgage from the overall rate of 0.0875 to produce the weighted amount for equity:
0.08750 − 0.06951 = 0.01799
Divide the weighted rate for the equity by the equity ratio (35%) to produce the equity dividend rate (RE):
0.01799 / 0.35 = 0.05140

Question 146

The subject property is the leasehold interest in a parcel of land that was leased eight years ago for 75 years at $1,000 per month on a net basis. It was vacant land at the time of the lease. Susan, the tenant, built an office building on that vacant land. After construction, she leased it out to a tenant for $110,000 per year for 20 years on a net basis. Susan pays the land lease out of the $110,000 per year income. The typical holding period for a leasehold interest like this is 20 years. The terminal capitalization rate for the leasehold interest is 14%. What is the value of the leasehold interest if the discount rate for the leasehold interest is 12%?

Answer 146

$805,000

The correct keystrokes for the HP-12C are:
20 n
12 i
98,000 PMT
(98,000 / 0.14 = 700,000) FV
Solve for PV = $804,572

Question 147

What is the indicated value of a leased property having a level income stream of $36,000 per year over the next 10 years with the expectation to appreciate 25% in value from the current value in 10 years based on a yield rate of 10%? Round your answer to the nearest $25,000.

Answer 147

The correct calculation is:
R = Y − (Δ 1 / Sn)
R = 0.10 - (0.25 × 0.06275) = 0.08431
36,000 / 0.08431 = 426,982
This can also be done on the HP-12C using percentages to get the capitalization rate:
10 n
10 i
1 CHS PV
1.25 FV
Solve for PMT = RO = 0.08431
36,000 / 0.08431 = 426,982

Question 148

What is the market value of a property with an NOI of $25,000, an annual debt service of $20,000, a loan-to-value ratio of 75%, a mortgage constant of 0.1158, and a debt coverage ratio of 1.25? Round your answer to the nearest $25,000. Use the debt service coverage ratio technique.

Answer 148

The correct calculation is:
1.25 × 0.75 × 0.1158 = 0.10856
25,000 / 0.10856 = 230,287

Market Value = NOI / (DSCRLoan-To-Value-RatioMortgage Constant)