Time Value of Money: Buy versus Rent by Sean Cleary and Stephen Foerster, Ivey Publications, August 11, 2014
Question
Purchase Price
Legal fees
Deed transfer tax (@3%)
Down Payment (20%)
Total Due at Closing
Amortization Period (Years)
Payment Frequency
Number of Payments remaining
(1)
Mortgage Amount
$480,000 Princ OS
Quoted Rate
Eff. Monthly rate
4%
0.0033059
MonthlyMortgage Payments
Monthly Condo Fees
Monthly Taxes
Monthly Repairs etc.
Total Monthly Payments if Buy
Monthly Rent
Net Additional Payments
(2)
(3)
(4) Principal Outstanding
Initially
After 2 years
After 5 Years After 10 Years
$600,000
2000
18000
120000
140000 Enter as +C7+C8+C9
25
23
20
15
12
12
12
12
300
276
240
180
Monthly Opportunity Costs of
(Closing Costs + Down Pmt)
TOTAL Additional Monthly CF “costs”
$456,609.29
$417,858.79
$342,109.01
Selling Price
Realtor Fees (@5%)
Other Selling fees
Princ OS
Net Proceeds
Funds at Closing
Opportunity Cost of Extra Payments Incl. Funds Used at Initial Closing
$140,000
$34,727
$140,000
$92,259
$140,000
$204,722
Net FV
63336.72
82117.83
118831.30
(58,513.34)
(67,365.22)
(79,970.06)
PV of Future Net (NPV)
$2,524.90
1055
300
50 Make sure this amount is monthly
(5a) NPV – No Change in Price
2 years
5 years
10 years
$600,000
$600,000
$600,000
$30,000
$30,000
$30,000
$2,000
$2,000
$2,000
$456,609
$417,859
$342,109
$111,391
$150,141
$225,891
Selling Price
Realtor Fees (@5%)
Other Selling fees
Princ OS
Net Proceeds
(5b) 10% down, back to 600k, then up 10%
2 years
5 years
10 years
540000.00
600,000.00
660,000.00
27,000.00
30,000.00
33,000.00
2,000.00
2,000.00
2,000.00
456,609.29
417,858.79
342,109.01
54,390.71
150,141.21
282,890.99
$3,929.90
3000
$929.90 [Note: This is a formula which results in a number]
Funds at Closing
Opportunity Cost of Extra Payments Incl. Funds Used at Initial Closing
140,000.00
34,727.42
140,000.00
92,259.04
140,000.00
204,722.29
Net FV
120,336.72
82,117.83
61,831.30
PV of Future Net (NPV)
111,172.53
67,365.22
41,610.69
462.82
$1,392.72
Note: Any tax benefit or expense has been ignored in this analysis.
Selling Price
Realtor Fees (@5%)
Other Selling fees
Princ OS
Net Proceeds
(5c) Condo price increases 2% annually
2 years
5 years
10 years
624,240.00
662,448.48
731,396.65
31,212.00
33,122.42
36,569.83
2,000.00
2,000.00
2,000.00
456,609.29
417,858.79
342,109.01
134,418.71
209,467.26
350,717.81
Funds at Closing
Opportunity Cost of Extra Payments Incl. Funds Used at Initial Closing
140,000.00
34,727.42
140,000.00
92,259.04
140,000.00
204,722.29
Net FV
40,308.72
22,791.77
5,995.52
37,239.02
18,697.19
4,034.81
PV of Future Net (NPV)
Selling Price
Realtor Fees (@5%)
Other Selling fees
Princ OS
Net Proceeds
Funds at Closing
Opportunity Cost of Extra Payments Incl. Funds Used at Initial Closing
(5d) Condo price increases 5% annually
2 years
5 years
10 years
661,500.00
765,768.94
977,336.78
33,075.00
38,288.45
48,866.84
2,000.00
2,000.00
2,000.00
456,609.29
417,858.79
342,109.01
169,815.71
307,621.70
584,360.93
140,000.00
34,727.42
140,000.00
92,259.04
140,000.00
204,722.29
Net FV
4,911.72
75,362.66
239,638.63
PV of Future Net (NPV)
4,537.67
61,823.63
161,269.93
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