Transcript Chapter 23 The Student Handbook to THE APPRAISAL OF REAL ESTATE Yield Capitalization — Theory and Basic Applications    Modern computers allow appraisers to easily discount future.

Chapter 23
The Student Handbook to
THE APPRAISAL OF REAL ESTATE
Yield Capitalization —
Theory and Basic Applications
1



Modern computers allow appraisers to easily discount
future cash flows to present value. In the past this
process was difficult.
Any investment can be considered the present worth of
future benefits.
A dollar today will grow to $X over a period of time, and
$X to be received in the future is worth a dollar today if
discounted at the same rate.
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
2



Discounting is the process in which future cash flows are
converted into present value.
Discounting requires many calculations that are tedious
for any human, but easy for many modern computers.
The sum of the present values of the future cash flows is
the present value of the investment. This includes
periodic cash flows and the reversion.
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
3

The time value of money is represented in the “six
functions of a dollar” tables.
 These tables show how the value of a dollar can be
impacted with compound interest.
 They reflect the impact on the dollar from interest on
interest.
 There are six tables to follow. Each one shows a
different impact of compound interest.
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
4

What will $1 today grow to with compound interest?
Interest rate = 10%
Amount of original deposit = $1.00
1 + in te re st
End of year
1
1.10
End of year
2
1.10
End of year
3
1.10
End of year
4
1.10
End of year
5
1.10
End of year
6
1.10
End of year
7
1.10
End of year
8
1.10
End of year
9
1.10
End of year
10
1.10
x
x
x
x
x
x
x
x
x
x
x
Pre viou s Balan ce
$1.0000
$1.1000
$1.2100
$1.3310
$1.4641
$1.6105
$1.7716
$1.9487
$2.1436
$2.3579
=
=
=
=
=
=
=
=
=
=
=
Ne w
Balan
$1.10ce
$1.21
$1.33
$1.46
$1.61
$1.77
$1.95
$2.14
$2.36
$2.59
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
5
Table 23.2 Present Value of $1

What is $1 in the future worth today?
Year
10%
Present worth
1
$1.00
/
110.00%
=
$0.9091
2
$0.91
/
110.00%
=
$0.8273
3
$0.83
/
110.00%
=
$0.7545
4
$0.75
/
110.00%
=
$0.6818
5
$0.68
/
110.00%
=
$0.6182
6
$0.62
/
110.00%
=
$0.5636
7
$0.56
/
110.00%
=
$0.5091
8
$0.51
/
110.00%
=
$0.4636
9
$0.47
/
110.00%
=
$0.4273
10
$0.42
/
110.00%
=
$0.3818
$1 that is paid in one year is only worth $0.9091 today
$1 that is paid in three years is only worth $0.754545 today
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
6
Table 23.3 Discounted Cash Flow—Level Annuity

What is $1 per period worth today ($100,000 per period
and $1,000,000 at the end @10%)?
Ye ar
1
2
3
4
5
6
7
8
9
10
T otal
C ash flow
100,000
100,000
100,000
100,000
100,000
100,000
100,000
100,000
100,000
1,100,000
10%
Discou nt. rate
0.9091
0.8264
0.7513
0.6830
0.6209
0.5645
0.5132
0.4665
0.4241
0.3855
Pre se nt Valu e
90,909
82,645
75,131
68,301
62,092
56,447
51,316
46,651
42,410
424,098
1,000,000
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
7
Table 23.4 Investment Analysis of Drugstore
Discount rate for the periodic cash flows = 8%
Year
Cash f low
x
1
$190,674
x
2
$190,674
x
3
$190,674
x
4
$190,674
x
5
$190,674
x
6
$190,674
x
7
$190,674
x
8
$190,674
x
9
$190,674
x
10
$190,674
x
P resent value of the periodic cash flows only
Discount rate for the reversion @ 14%
10
$2,060,000
Total
Discount Factor
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
0.54027
0.50025
0.46319
=
=
=
=
=
=
=
=
=
=
=
Present Value
$
176,550
$
163,472
$
151,363
$
140,151
$
129,770
$
120,157
$
111,256
$
103,015
$
95,384
$
88,319
$ 1,279,438
0.26974
=
$
555,672
$ 1,835,110
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
8
Table 23.5 Straight-Line Change
$0.05 change in income each year
Discount rate of 9%
1
$1.00
2
$1.05
3
$1.10
4
$1.15
5
$1.20
6
$1.25
7
$1.30
8
$1.35
9
$1.40
10
$1.45
11
$1.50
12
$1.55
13
$1.60
14
$1.65
15
$1.70
16
$1.75
17
$1.80
18
$1.85
19
$1.90
20
$1.95
21
$2.00
22
$2.05
23
$2.10
24
$2.15
25
$2.20
26
$2.25
27
$2.30
T otal
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0.9174
0.8417
0.7722
0.7084
0.6499
0.5963
0.5470
0.5019
0.4604
0.4224
0.3875
0.3555
0.3262
0.2992
0.2745
0.2519
0.2311
0.2120
0.1945
0.1784
0.1637
0.1502
0.1378
0.1264
0.1160
0.1064
0.0976
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
$
$ 0.91743
$ 0.88376
$ 0.84940
$ 0.81469
$ 0.77992
$ 0.74533
$ 0.71114
$ 0.67752
$ 0.64460
$ 0.61250
$ 0.58130
$ 0.55108
$ 0.52189
$ 0.49376
$ 0.46671
$ 0.44077
$ 0.41593
$ 0.39219
$ 0.36953
$ 0.34794
$ 0.32740
$ 0.30787
$ 0.28934
$ 0.27177
$ 0.25513
$ 0.23938
$ 0.22450
$ 14.13278
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
9
Table 23.6 Exponential-Curve Change
$0.04 change in income each year
Discount rate of 9%
Year
Cash Flow
1
$1.00
x
2
$1.04
x
3
$1.08
x
4
$1.12
x
5
$1.17
x
6
$1.22
x
7
$1.27
x
8
$1.32
x
9
$1.37
x
10
$1.42
x
11
$1.48
x
12
$1.54
x
13
$1.60
x
14
$1.67
x
15
$1.73
x
16
$1.80
x
17
$1.87
x
18
$1.95
x
19
$2.03
x
20
$2.11
x
21
$2.19
x
22
$2.28
x
23
$2.37
x
24
$2.46
x
25
$2.56
x
26
$2.67
x
27
$2.77
x
Total
Discount Factor
0.9174
0.8417
0.7722
0.7084
0.6499
0.5963
0.5470
0.5019
0.4604
0.4224
0.3875
0.3555
0.3262
0.2992
0.2745
0.2519
0.2311
0.2120
0.1945
0.1784
0.1637
0.1502
0.1378
0.1264
0.1160
0.1064
0.0976
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Present Value
$0.91743
$0.87535
$0.83519
$0.79688
$0.76033
$0.72545
$0.69217
$0.66042
$0.63013
$0.60122
$0.57364
$0.54733
$0.52222
$0.49827
$0.47541
$0.45360
$0.43280
$0.41294
$0.39400
$0.37593
$0.35868
$0.34223
$0.32653
$0.31155
$0.29726
$0.28363
$0.27061
$14.37121
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
10
Table 23.7 Level Income in Perpetuity
Analysis of property with level income and no change in value at 8%
Direct Capitalization = $25,000 / 0.08 =$312,500
Year
Income
Discount Rate
1
$25,000
x
0.925926
=
2
$25,000
x
0.857339
=
3
$25,000
x
0.793832
=
4
$25,000
x
0.735030
=
5
$25,000
x
0.680583
=
6
$25,000
x
0.630170
=
7
$25,000
x
0.583490
=
8
$25,000
x
0.540269
=
9
$25,000
x
0.500249
=
10
$25,000
x
0.463193
=
11
$25,000
x
0.428883
=
12
$25,000
x
0.397114
=
13
$25,000
x
0.367698
=
13
$312,500
x
0.367698
=
Net present value
Value
$23,148
$21,433
$19,846
$18,376
$17,015
$15,754
$14,587
$13,507
$12,506
$11,580
$10,722
$9,928
$9,192
$114,906
$312,500
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
11
Table 23.8 Analysis of Property with Level Income
and Change in Value
 = 10%
Y = 0.10
N = 5 years
R = Y – ( x 1/ S n )
R = 0.10 – (0.10 x 0.16380)
R = 0.083620
Direct capitalization: $25,000/0.083620 = $298,972
Year
Cash Flow
1
2
3
4
5
5
Net present value
$25,000
$25,000
$25,000
$25,000
$25,000
$328,869
x
x
x
x
x
x
Discount Factor
0.1000
0.9090909
0.8264463
0.7513148
0.6830135
0.6209213
0.6209213
Present Value
=
=
=
=
=
=
$22,727
$20,661
$18,783
$17,075
$15,523
$204,202
$298,972
* The reversion was calculated as 125% of the present value, or $298,972 x 1.10 = $328,869
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
12
Table 23.9 Constant Change in Income and Value
Increase in income and value = 35.00%
Income = $35,000
Holding period = 10 years
Y = 0.08
R = Y - ( 1/n)
R = 0.08 - (0.35 * 0.10)
R = 0.08 - 0.035
R = 0.045
Direct Capitalization: $35,000 / 0.045 = $777,778
To calculate the amount of cash flow change each period, the following formula applies:
V x ( 1/n) x Y = the increase in cash flows
777,778 x (0.35 x 0.10) x 0.08 = the increase in cash flows
777,778 x 0.035 x 0.08 = 2,177.78
Year
Initial Income
1
$35,000
2
$35,000
3
$35,000
4
$35,000
5
$35,000
6
$35,000
7
$35,000
8
$35,000
9
$35,000
10
$35,000
10
$1,050,000
Net present value
+
+
+
+
+
+
+
+
+
Income Change
$2,178
$4,356
$6,533
$8,711
$10,889
$13,067
$15,244
$17,422
$19,600
Adj Income
=
=
=
=
=
=
=
=
=
$35,000
$37,178
$39,356
$41,533
$43,711
$45,889
$48,067
$50,244
$52,422
$54,600
x
x
x
x
x
x
x
x
x
x
Disc. Rate
0.08
0.925926
0.857339
0.793832
0.735030
0.680583
0.630170
0.583490
0.540269
0.500249
0.463193
0.463193
=
=
=
=
=
=
=
=
=
=
=
=
=
Present Value
$32,407
$31,874
$31,242
$30,528
$29,749
$28,918
$28,046
$27,146
$26,224
$25,290
$486,353
$777,778
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
13
Table 23.10 Constant-Ratio Change in Income and
Value
Assume the property is in an area where 8% yields are required. P roperties are appreciating 3% per year.
Income is $35,000/year and it is increasing at 3% per year also.
R=
Y - CR
R=
0.08-0.03
R=
0.05
Direct Capitalization:
$35,000
/0.05 =
$700,000
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Income
Reversion
3.00%
$35,000.00
$36,050.00
$37,131.50
$38,245.45
$39,392.81
$40,574.59
$41,791.83
$43,045.59
$44,336.95
$45,667.06
$47,037.07
$48,448.19
$49,901.63
$51,398.68
$52,940.64
$54,528.86
$1,123,295
Cash Flows
$35,000
$36,050
$37,132
$38,245
$39,393
$40,575
$41,792
$43,046
$44,337
$45,667
$47,037
$48,448
$49,902
$51,399
$52,941
$1,177,823
Total =
Discount Factor
0.925925926
0.85733882
0.793832241
0.735029853
0.680583197
0.630169627
0.583490395
0.540268885
0.500248967
0.463193488
0.428882859
0.397113759
0.367697925
0.340461041
0.315241705
0.291890468
Net Present Value
$32,407.41
$30,907.06
$29,476.18
$28,111.54
$26,810.08
$25,568.88
$24,385.13
$23,256.19
$22,179.51
$21,152.69
$20,173.39
$19,239.44
$18,348.73
$17,499.25
$16,689.10
$343,795.41
$700,000.00
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
14
Table 23.11 Constant-Ratio Change in Income and
Value
Assume the property is in an area where 8% yields are required. P roperties are appreciating 3% per year.
Income is $35,000/year and it is increasing at 3% per year also.
R=
Y - CR
R=
0.08-0.03
R=
0.05
Direct Capitalization:
$35,000
/0.05 =
$700,000
Year
1
2
3
4
5
6
7
8
9
10
10
Income
3.00%
$35,000.00
$36,050.00
$37,131.50
$38,245.45
$39,392.81
$40,574.59
$41,791.83
$43,045.59
$44,336.95
$45,667.06
Reversion
Cash Flows
$35,000
$36,050
$37,132
$38,245
$39,393
$40,575
$41,792
$43,046
$44,337
$45,667
* $904,741
Total =
Discount Factor
0.925926
0.857339
0.793832
0.735030
0.680583
0.630170
0.583490
0.540269
0.500249
0.463193
0.463193
Net Present Value
$32,407.41
$30,907.06
$29,476.18
$28,111.54
$26,810.08
$25,568.88
$24,385.13
$23,256.19
$22,179.51
$21,152.69
$435,745.32
$700,000.00
* $700,000 x 1.03 10 = $940,744.47
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
15
Problems

Suggested solutions begin on page 365.
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
16
Problem 1D
RO = YO - CR
RO = 0.10 - 0.02
RO = 0.08
100,000
/
0.08
=
1,250,000
0.02
$
100,000
$
102,000
$
104,040
$
106,121
$
108,243
$
110,408
$
112,616
$
114,869
$
117,166
$
119,509
Solve for
x
x
x
x
x
x
x
x
x
+
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.02
$
NP V @ 10%
1,523,743
=
=
=
=
=
=
=
=
=
=
=
0
102,000
104,040
106,121
108,243
110,408
112,616
114,869
117,166
119,509
1,643,252
1,249,999
CF
CF1
CF2
CF3
CF4
CF5
CF6
CF7
CF8
CF9
CF10
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
17
Problem 2B
RO =
RO
RO
1/S n
= (Y-R)/1/Sn )
=
=
FV
=
=
=
=
=
=
=
=
=
I/V
$7,000/$150,000
0.04667
0.16057
(0.11 - 0.04667)/0.16057
0.06333/0.16057
0.39441
$150,000 x 1.39441
$209,162
Prove
N
I
PV
P MT
Solve FV
5
11
-150,000
7,000
209,164
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
18
Problem 3B
Clear registers
1
0
5,000
3
6,000
5
9,000
4
1,209,000
9
Solve for NP V
P /yr.
CFO
CFJ
NJ
CFJ
NJ
CFJ
NJ
CFJ
I/yr.
439,660
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
19
Problem 4B
Clear registers
1
5,000
5,000
2
6,000
5
9,000
5
1,200,000
9
Solve for NP V
P /yr.
CFO
CFJ
NJ
CFJ
NJ
CFJ
NJ
CFJ
I/yr
444,003
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
20
Problem 5B
RO =
VO =
YO -  1/S n
Prove
0.08 – (0.10 x 0.170456)
N
5
0.062954
I
8
I/V
PV
-$476,538
30,000/0.062954
PMT
$30,000
476,538
476,538 x 1.10 = 524,192
Solve FV 524,189
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
21
Problem 6C
9
N
-750,000
PV
59,000
PMT
750,000 x 1.25 = 937,500
FV
Solve for I =
9.7288
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
22
Problem 7A
RO =
100,000 /1,250,000
YO =
Ro + CR
YO =
0.08 + 0.01
YO =
0.09
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
23
Problem 8B
-175,300
PV
25,000
PMT
25
N
0
FV
Calculate I
13.68
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
24
Problem 9C
100,000
PMT
11
N
100,000
FV
9
I
Solve for PV
719,272
Student Handbook to THE APPRAISAL OF REAL ESTATE
Chapter 23
25