Question

Suppose that an investor is considering the purchase of an multifamily housing. The potential gross income of the first year of operations has been estimated at $550,000. To value the property, the investor assume the following factors:

Rents are estimated to increase by 2.5% per year. 5.5% vacancy loss rate and no other income. The vacancy loss rate will remain constant. Fixed and variable expenses were estimated at $97,000 and $155,000, respectively. These expenses will continue to represent the same fraction of effective gross income. Maintain the property for ten years and the net sale proceeds in year 10 have been estimated at $2,730,000.

What is the value of the property with an appropriate cap rate of 8.5%?

A) $2,900,345

B) $3,068,809

C) $3,800,441

Answer 1

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8	Year 9	Year 10
Previous Annual rent	550000	550000	532744	516029	499839	484157	468967	454253	440000	426195
Occupancy rate (1 - vacancy loss rate)	nil	94.50%	94.50%	94.50%	94.50%	94.50%	94.50%	94.50%	94.50%	94.50%
Increase rate	nil	2.50%	2.50%	2.50%	2.50%	2.50%	2.50%	2.50%	2.50%	2.50%
Gross Annual Income	550000	532744	516029	499839	484157	468967	454253	440000	426195	412823
Less: Variable Expenses(28%)	(155000)	(149168)	(144488)	(139955)	(135564)	(131311)	(127191)	(123200)	(119335)	(115590)
Less: Fixed Expense	(97000)	(97000)	(97000)	(97000)	(97000)	(97000)	(97000)	(97000)	(97000)	(97000)
Net income	298000	286576	274541	262884	251593	240656	230062	219800	209860	200233
Sale value										2730000
Total	298000	286576	274541	262884	251593	240656	230062	219800	209860	2930233
PVIF @ 8.50%	0.922	0.850	0.783	0.721	0.665	0.613	0.565	0.521	0.480	0.442
PV of cashflows	274756	243590	214966	189539	167309	147522	129985	114516	100733	1295163

Value of property = $2,900,345(Approx)

note: the little difference in answer is due to rounding off, since in the question nothing is given we have solved it rounding off to nearest one.