Question

You are considering a luxury apartment building project that requires an investment of $1,300,000. The building has 50 unites. We expect that the maintenance cost for the apartment building will be $150,000 in the first year, and to rise to $200,000 in the second year, and to continue to increase by $50,000 in subsequent years. The cost to hire a manager for the building is estimate to be $50,000 per year. After five years of operation, the apartment building can be sold for $800,000. What annual rent per apartment unit will provide a return on investment of 15%? Assume that the building will remain fully occupies during the five years.

Answer 1

For this we have to do the NPV analysis, where

NPV = Present value (PV) of all cash inflows - PV of all cash outflows.

PV of cash outflows isas per calculations below. Note that, a return on investment of 15% means that, if all the cash inflows & outflows are discounted at 15%, NPV will become 0.

Year	Cash Outflow	Maintenance Cost	Supervisor cost	Total cash outflow	Discount factor	Discounted cash outflow
0	1300000			1300000	1	1300000
1		200000	50000	250000	0.8696	217400
2		250000	50000	300000	0.7561	226830
3		300000	50000	350000	0.6575	230125
4		350000	50000	400000	0.5718	228720
5		400000	50000	450000	0.4972	223740
					PV of Cash Outflow =	2426815

PV of Cash outflow =  $2,426,815

PV of cash inflow = PV of rent collected + PV of seilling price after 5 years

$2,426,815  = PV of rent collected + [$800,000 / (1.15)5]

PV of rent collected = $(2,426,815 - 397,741) = $2,029,074

If rent per year be Y, then:

Year	Annual Rent($)	Discount factor
1	Y	0.8696
2	Y	0.7561
3	Y	0.6575
4	Y	0.5718
5	Y	0.4972
	Sum of Discount factors	3.3522

Therefore,

Y x 3.3522 = $2,029,074

Y = $2,029,074 / 3.3522 = $605,296.1

This is the annual rent for total 50 units in the apartment building.

Annual Rent per apartment = $605,296 / 50 = $12,105