14-1
Solutions to Questions – Chapter 14
Disposition and Renovation of Income Properties
Question 14-1
What factors should an investor consider when trying to decide whether to dispose of a property that he has
owned for several years?
Question 14-2
Why might the actual holding period for a property be different from the holding period that was anticipated when
the property was purchased?
Question 14-3
What is the marginal rate of return? How is it calculated?
Question 14-4
What causes the marginal rate of return to change over time? How can the marginal rate of return be used to
decide when to sell a property?
Question 14-5
Why might the after-tax internal rate of return on equity (ATIRRe) differ for a new investor versus an existing
investor who keeps the property?
Question 14-6
What factors should be considered when deciding whether to renovate a property?
Question 14-7
Why is refinancing often done in conjunction with renovation?
Question 14-8
Why would refinancing be an alternative to sale of the property?
Question 14-9
How can tax law changes create incentives for investors to sell their properties to other investors?
Question 14-10
How important are taxes in the decision to sell a property?
Question 14-11
Are tax considerations important in renovation decisions?
Question 14-12
What are the benefits and costs of renovation?
Question 14-13
Do you think renovation is more or less risky than a new investment?
14-3
Question 14-14
What is meant by the “incremental cost of refinancing?”
Question 14-15
In general, what kinds of tax incentives are available for rehabilitation of real estate income property?
Question 14-16
Why would an investor consider doing an exchange or an installment sale?
Solutions to Problems – Chapter 14
Disposition and Renovation of Income Properties
INTRODUCTION
The four problems in this chapter deal with disposition and renovation decisions. Students are also expected to recognize that
refinancing is also an alternative to disposition (part g of problem 3), and refinancing is often a part of renovation (part b of
problem 4).
Problem 14-1
(a) If sold today If sold next year
Problem 14-2
14-5
Problem 14-3
(REFER TO TEMPLATE 14_3.XLS)
ASSUMPTIONS:
EGI Year After Sale
350,000
Purchase Price
2,000,000
Projected Increase in EGI
3.00%
per year
Building Value
1,800,000
Operating Expenses
40.00%
of EGI
Land Value
200,000
Loan:
Years since Purchased
2
Loan-to-value ratio
70.00%
Resale Value Today
2,200,000
Interest
10.00%
Selling Expenses
6.00%
Term
25
years
Appreciation Rate
3.00%
Payments per year
12
Depreciable Life
27.5
Tax Rate
36.00%
Equity
600,000
Loan Amount
1,400,000
Loan Information:
Year
2
3
4
5
6
7
8
9
10
11
12
Interest
124,756
136,481
134,787
132,915
130,847
128,563
126,040
123,252
120,173
116,770
113,012
EOY Loan Balance
1,372,095
1,355,914
1,338,039
1,318,293
1,296,478
1,272,380
1,245,758
1,216,348
1,183,859
1,147,968
1,108,318
(a) Cash flow if sold today:
Cash Flows from Sale in Year
2
Sales Price
2,200,000
Sales Costs
132,000
Mortgage Balance
1,372,095
Before-tax Cash Flow
695,905
Sales Price
2,200,000
Sales Costs
132,000
Original Cost Basis
2,000,000
Accumulated Depreciation
130,909
Adjusted Basis
1,869,091
Capital Gain
198,909
Tax
71,607
After-Tax Cash Flow from Reversion
624,298
14-6
(b) Cash flow if not sold:
Year
3
4
5
6
7
Effective Gross Income
350,000
360,500
371,315
382,454
393,928
Operating Expenses
140,000
144,200
148,526
152,982
157,571
Net Operating Income
210,000
216,300
222,789
229,473
236,357
Debt Service
152,662
152,662
152,662
152,662
152,662
Before-tax Cash Flow
57,338
63,638
70,127
76,811
83,695
Taxable Income:
NOI
210,000
216,300
222,789
229,473
236,357
Less: Interest
136,481
134,787
132,915
130,847
128,563
Depreciation
65,455
65,455
65,455
65,455
65,455
Taxable Income
8,064
16,059
24,419
33,171
42,339
Tax
2,903
5,781
8,791
11,941
15,242
After-tax Cash Flow:
Before-Tax Cash Flow
57,338
63,638
70,127
76,811
83,695
Tax
2,903
5,781
8,791
11,941
15,242
After-Tax Cash Flow
54,435
57,857
61,336
64,869
68,453
(c) Cash flow if sold after 5 years:
Cash Flows from Sale in Year
7
Sales Price
2,550,403
Sales Costs
153,024
Mortgage Balance
1,272,380
Before-tax Cash Flow
1,124,999
Sales Price
2,550,403
Sales Costs
153,024
Original Cost Basis
2,000,000
Accumulated Depreciation
458,182
Adjusted Basis
1,541,818
Capital Gain
855,561
Tax
308,002
After-Tax Cash Flow from Reversion
816,997
ATIRR on holding property 5 additional years:
Year
2
3
4
5
6
7
ATCF
(624,298)
54,435
57,857
61,336
64,869
885,450
ATIRR
14.32%
(e)
(f)
(g)
(h)
The answer depends on the rate of return available for investing in Royal Palms (assuming Royal Oaks must be sold). If the
(i)
Marginal Rate of Return
Year
3
4
5
6
7
8
9
10
11
12
Effective Gross Income
350,000
360,500
371,315
382,454
393,928
405,746
417,918
430,456
443,370
456,671
Operating Expenses
140,000
144,200
148,526
152,982
157,571
162,298
167,167
172,182
177,348
182,668
Net Operating Income
210,000
216,300
222,789
229,473
236,357
243,448
250,751
258,274
266,022
274,002
Debt Service
152,662
152,662
152,662
152,662
152,662
152,662
152,662
152,662
152,662
152,662
Before-tax Cash Flow
57,338
63,638
70,127
76,811
83,695
90,786
98,089
105,612
113,360
121,341
NOI
210,000
216,300
222,789
229,473
236,357
243,448
250,751
258,274
266,022
274,002
Less Interest
136,481
134,787
132,915
130,847
128,563
126,040
123,252
120,173
116,770
113,012
Depreciation
65,455
65,455
65,455
65,455
65,455
65,455
65,455
65,455
65,455
65,455
Taxable Income
8,064
16,059
24,419
33,171
42,339
51,953
62,044
72,646
83,797
95,536
Tax
2,903
5,781
8,791
11,941
15,242
18,703
22,336
26,153
30,167
34,393
Before-Tax Cash Flow
57,338
63,638
70,127
76,811
83,695
90,786
98,089
105,612
113,360
121,341
Tax
2,903
5,781
8,791
11,941
15,242
18,703
22,336
26,153
30,167
34,393
After-Tax Cash Flow
54,435
57,857
61,336
64,869
68,453
72,083
75,753
79,459
83,193
86,948
ATCF From Sale
3
4
5
6
7
8
9
10
11
12
Sales Price
2,266,000
2,333,980
2,403,999
2,476,119
2,550,403
2,626,915
2,705,723
2,786,894
2,870,501
2,956,616
Sales Costs
135,960
140,039
144,240
148,567
153,024
157,615
162,343
167,214
172,230
177,397
Mortgage Balance
1,355,914
1,338,039
1,318,293
1,296,478
1,272,380
1,245,758
1,216,348
1,183,859
1,147,968
1,108,318
Before-tax Cash Flow
774,126
855,902
941,467
1,031,074
1,124,999
1,223,542
1,327,031
1,435,821
1,550,303
1,670,901
Sales Price
2,266,000
2,333,980
2,403,999
2,476,119
2,550,403
2,626,915
2,705,723
2,786,894
2,870,501
2,956,616
Sales Costs
135,960
140,039
144,240
148,567
153,024
157,615
162,343
167,214
172,230
177,397
Original Cost Basis
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
2,000,000
Accumulated Depreciation
196,364
261,818
327,273
392,727
458,182
523,636
589,091
654,545
720,000
785,455
Adjusted Basis
1,803,636
1,738,182
1,672,727
1,607,273
1,541,818
1,476,364
1,410,909
1,345,455
1,280,000
1,214,545
Capital Gain
326,404
455,759
587,032
720,279
855,561
992,937
1,132,470
1,274,226
1,418,271
1,564,674
Tax
117,505
164,073
211,332
259,301
308,002
357,457
407,689
458,721
510,578
563,283
ATCF From Sale
656,621
691,828
730,135
771,773
816,997
866,085
919,342
977,100
1,039,726
1,107,618
Marginal Rate of Return
Holding Period
CF0
CF1
MRR
1
(624,298)
711,056
13.90%
2
(656,621)
749,686
14.17%
3
(691,828)
791,471
14.40%
4
(730,135)
836,643
14.59%
5
(771,773)
885,450
14.73%
6
(816,997)
938,168
14.83%
7
(866,085)
995,095
14.90%
8
(919,342)
1,056,559
14.93%
9
(977,100)
1,122,919
14.92%
10
(1,039,726)
1,194,566
14.89%
Problem 14-4
(REFER TO TEMPLATE 14_4a.XLS)
ASSUMPTIONS:
Year
Net Operating Income
Debt Service
Before-tax Cash Flow
Taxable Income:
NOI
Less: Interest
Taxable Income
After-Tax Cash Flow:
Before-Tax Cash Flow
After-Tax Cash Flow
CURRENT
IF RENOVATED
Purchase Price
800,000
Renovation Cost
200,000
Building Value
600,000
Initial Increase in NOI
20.00%
Land Value
200,000
Annual Increase in NOI
3.00%
Loan-to-value ratio
75.00%
Terminal Cap Rate
10.00%
Interest
10.00%
Selling Expenses
6.00%
of sale price
Term
20
years
New Loan:
Payments per year
12
% of Renovation Costs
75.00%
Years since Purchased
2
Interest Rate
11.00%
Current NOI
90,000
Term
20
Projected Increase in NOI
2.00%
per year
Payments per year
12
Resale Value Today
820,000
Appreciation Rate
2.00%
per year
Depreciable Life
39
years
Tax Rate
28.00%
Equity
200,000
Loan Amount
600,000
14-9
Cash Flows from Sale in Year
7
Sales Price
905,346
Sales Costs
54,321
Mortgage Balance
504,433
Before-tax Cash Flow
346,592
Sales Price
905,346
Sales Costs
54,321
Original Cost Basis
800,000
Accumulated Depreciation
107,692
Adjusted Basis
692,308
Capital Gain
158,718
Tax
44,441
After-Tax Cash Flow from Reversion
302,151
CASH FLOWS WITH RENOVATION
Loan Information:
Additional Equity Investment
50,000
Loan Value
729,104
Year
2
3
4
5
6
7
8
9
10
11
12
Interest
0
79,676
78,446
77,073
75,541
73,832
71,926
69,798
67,425
64,777
61,822
EOY Loan Bal.
729,104
718,471
706,608
693,372
678,604
662,128
643,744
623,234
600,350
574,818
546,332
Year
3
4
5
6
7
8
Net Operating Income
108,000
111,240
114,577
118,015
121,555
125,202
Debt Service
90,309
90,309
90,309
90,309
90,309
90,309
Before-tax Cash Flow
17,691
20,931
24,269
27,706
31,246
34,893
Taxable Income:
NOI
108,000
111,240
114,577
118,015
121,555
125,202
Less: Interest
79,676
78,446
77,073
75,541
73,832
71,926
Depreciation
20,513
20,513
20,513
20,513
20,513
20,513
Taxable Income
7,811
12,282
16,992
21,961
27,210
32,763
Tax
2,187
3,439
4,758
6,149
7,619
9,174
After-Tax Cash Flow:
Before-Tax Cash Flow
17,691
20,931
24,269
27,706
31,246
34,893
Tax
2,187
3,439
4,758
6,149
7,619
9,174
After-Tax Cash Flow
15,504
17,492
19,511
21,557
23,628
25,719
14–10
Cash Flows from Sale in Year
7
Sales Price
1,252,016
Sales Costs
75,121
Mortgage Balance
662,128
Before-tax Cash Flow
514,767
Sales Price
1,252,016
Sales Costs
75,121
Original Cost Basis
1,000,000
Accumulated Depreciation
133,333
Adjusted Basis
866,667
Capital Gain
310,228
Tax
86,864
After-Tax Cash Flow from Reversion
427,904
(a) Incremental Analysis – Renovation Vs. No Renovation
INCREMENTAL ANALYSIS – RENOVATION VS. NO RENOVATION
Year
2
3
4
5
6
7
ATCF with renovation
(250,000)
15,504
17,492
19,511
21,557
451,531
ATCF no renovation
(200,000)
15,688
16,629
17,559
18,473
321,521
Incremental CF
(50,000)
(184)
863
1,952
3,084
130,010
ATIRR on Equity
22.49%
(b)
(REFER TO TEMPLATE 14_4b.XLS)
ASSUMPTIONS:
CURRENT
IF RENOVATED
Purchase Price
800,000
Renovation Cost
200,000
Building Value
600,000
Initial Increase in NOI
20.00%
Land Value
200,000
Annual Increase in NOI
3.00%
Loan-to-value ratio
75.00%
Terminal Cap Rate
10.00%
Interest
10.00%
Selling Expenses
6.00%
of sale price
Term
20
years
New Loan:
Payments per year
12
% of Renovation Costs
75.00%
Years since Purchased
2
Interest Rate
11.00%
Current NOI
90,000
Term
20
Projected Increase in NOI
2.00%
per year
Payments per year
12
Resale Value Today
820,000
Appreciation Rate
2.00%
per year
Depreciable Life
39
years
Tax Rate
28.00%
Equity
200,000
Loan Amount
600,000
2
3
4
5
6
7
8
9
10
11
12
Interest
83,599
80,867
79,260
77,467
75,467
70,744
67,966
64,866
EOY Loan Bal.
753,844
727,509
712,014
675,438
629,908
603,119
Loan Information:
Year
2
3
4
5
6
7
8
9
10
11
12
Interest
48,585
57,365
56,096
54,695
53,146
51,436
49,546
47,459
45,152
42,605
39,791
EOY Loan Bal.
579,104
566,987
553,602
538,815
522,479
504,433
484,498
462,475
438,146
411,269
381,578
CASH FLOWS WITHOUT RENOVATION
NOI
108,000
111,240
114,577
118,015
121,555
125,202
Less: Interest
83,599
82,308
80,867
79,260
77,467
20,513
20,513
20,513
20,513
20,513
Taxable Income
After-tax Cash Flow:
Before-Tax Cash Flow
13,245
16,485
19,822
23,260
26,800
Sales Price
Sales Costs
Mortgage Balance
Before-tax Cash Flow
Sales Price
Sales Costs
Original Cost Basis
Accumulated Depreciation
133,333
Adjusted Basis
Capital Gain
Year
2
3
4
5
6
7
ATCF with renovation
415,504
ATCF no renovation
15,688
16,629
17,559
18,473
Incremental CF
Year
3
4
5
6
7
8
Net Operating Income
108,000
111,240
114,577
118,015
121,555
125,202
Debt Service
94,755
94,755
94,755
94,755
94,755
94,755
Before-tax Cash Flow
13,245
16,485
19,822
23,260
26,800
30,447
Problem 14-5
Problem 14-6
The marginal rate of return (MRR) starts off higher and decreases at a faster rate over time as shown below.
Holding Period
Original MRR
New MRR
1
15.43%
20.20%
2
15.56%
19.94%
3
15.65%
19.68%
4
15.69%
19.42%
5
15.71%
19.15%
6
15.69%
18.89%
7
15.65%
18.63%
8
15.58%
18.37%
9
15.49%
18.11%
10
15.38%
17.86%
Problem 14-7 part a
Sale price
$2,000,000
Adjusted basis
$1,500,000
Capital gain
$500,000
Sale price
$2,000,000
Mortgage Balance
$1,750,000
assumed by seller
Equity
$250,000
Profit ratio
200%
Down Payment
$50,000
Seller Financing
$200,000
Interest rate
10.00%
Installment payments
$50,000
Ordinary income tax rate
35%
Capital gain tax rate
20%
Year
0
1
2
3
4
Total
Installment Payment
$50,000
$50,000
$50,000
$50,000
$50,000
$250,000
x Profit Ratio
200%
200%
200%
200%
200%
= Gain to report
$100,000
$100,000
$100,000
$100,000
$100,000
$500,000
x Capital gain tax rate
20%
20%
20%
20%
20%
= Capital gain tax
$20,000
$20,000
$20,000
$20,000
$20,000
$100,000
End yr balance
$200,000
$150,000
$100,000
$50,000
$0
Interest
$20,000
$15,000
$10,000
$5,000
$50,000
x Ordinary income tax
rate
35%
35%
35%
35%
Ord income tax
7000
5250
3500
1750
$17,500
Installment Payment
$50,000
$50,000
$50,000
$50,000
$50,000
$250,000
14–14
Less ordinary income tax
$0
$7,000
$5,250
$3,500
$1,750
Less capital gain tax
$20,000
$20,000
$20,000
$20,000
$20,000
After tax cash flow
$30,000
$43,000
$39,750
$36,500
$33,250
Discount rate
7.00%
PV
$160,067
Cash Sale
Sale price
$2,000,000
Gain to report
$500,000
Tax
$100,000
Mortgage balance
$1,750,000
After Tax Cash Flow
(PV)
$150,000
Part b.
Exchange versus Regular Sale and Purchase New
Prop
Calc of tax savings if exchanged:
Sale Price if sold today
$2,000,000
Adjusted Basis today
1,500,000
Gain if sold today
$500,000
Capital Gain Tax Rate
20%
Tax if sold today
$100,000
Calc of add dep benefits if not exchanged:
Depreciable life
30
Add depreciation if sale & purchase new
$16,667
Ord inc. tax rate
35%
Dep. tax savings if sale & purchase new
$5,833
Calc of additioal tax at end of holding period if exchanged:
Holding period
5
Additional Gain at sale of exchanged prop
Deferred gain
$500,000
Less: difference in accum dep
$83,333
Net
$416,667
Cap gains tax rate at end of holding period
20%
Additional tax at sale of exchanged prop
$83,333
Calc of return on tax savings from exchange:
PV
($100,000)
PMT
$5,833
FV
$83,333
N
5
Rate
2.67%
This means that by paying the taxes today instead of doing the exchange the investor is only earning 2.67% on his or her
money. This is quite low suggesting that it is better to do the exchange.