You are considering a luxury apartment building project that requires an investm
ID: 1191422 • Letter: Y
Question
You are considering a luxury apartment building project that requires an investment of $12,500,000. The building has 50 unites. You expect that the maintenance cost for the apartment building will be $250,000 in the first year, and to rise to $300,000 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 $80,000 per year. After five years of operation, the apartment building can be sold for $14,000,000. 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.
Explanation / Answer
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 is $13,894,968 as per calculations below. Note that, a return on investment of 15% means that, if all the cash inflows & outflows are discounted at 15%, NPV will become 0.
Year
Cash Outflow ($)
Maintenance cost ($)
Supervisor cost ($)
Total Cash outflow ($)
Discount factor @15%
Discounted cash outflow ($)
0
125,00,000
125,00,000
1.0000
125,00,000
1
2,50,000
80,000
3,30,000
0.8696
2,86,957
2
3,00,000
80,000
3,80,000
0.7561
2,87,335
3
3,50,000
80,000
4,30,000
0.6575
2,82,732
4
4,00,000
80,000
4,80,000
0.5718
2,74,442
5
4,50,000
80,000
5,30,000
0.4972
2,63,504
PV of Cash outflow =
138,94,968
PV of cash inflow = PV of rent collected + PV of seilling price after 5 years
$13,894,968 = PV of rent collected + [$14,000,000 / (1.15)5]
PV of rent collected = $(13,894,968 - 6,960,474) = $6,934,494
If rent per year be Y, then:
YEAR
Annual Rent ($)
Discount factor @15%
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 = $6,934,494
Y = $6,934,494 / 3.3522 = $2,068,640
This is the annual rent for total 50 units in the apartment building.
Annual Rent per apartment = $2,078,640 / 50 = $41,373
Year
Cash Outflow ($)
Maintenance cost ($)
Supervisor cost ($)
Total Cash outflow ($)
Discount factor @15%
Discounted cash outflow ($)
0
125,00,000
125,00,000
1.0000
125,00,000
1
2,50,000
80,000
3,30,000
0.8696
2,86,957
2
3,00,000
80,000
3,80,000
0.7561
2,87,335
3
3,50,000
80,000
4,30,000
0.6575
2,82,732
4
4,00,000
80,000
4,80,000
0.5718
2,74,442
5
4,50,000
80,000
5,30,000
0.4972
2,63,504
PV of Cash outflow =
138,94,968
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.