Question

Suppose that you are considering an investment in an apartment building. The specifics are:                                                            
- The building is four years old, has a 85 percent occupancy rate, and has an expected useful life of 25 years. Assume that this occupancy rate is expected to continue for the life of the building.
- There are 130 2-bedroom units, 100 1-bedroom units, and 70 studios.
- The 2-bedroom units rent for $2800 per month, the 1-bedroom units for $2000 per month, and the studios for $1200 per month.
- Current rent control laws will prevent the rents from ever being raised.
- The estimated annual maintenance cost for the building is $1500000 per year (this is independent of the number of apartments rented).
- There is an additional estimated maintenance cost at $200 per unit per month, when each unit is rented.
- There will be no salvage value to the building in 25 years, but it is estimated that it will cost 6 million dollars at that time to demolish the building as will be required in the purchase contract. (You are not purchasing the land. You will have a 25-year lease of the land, which is paid for in the purchase of the building.)      
- The asking price of the building is $30 million.
- The tax-rate is 30%, and assume the building will be fully depreciated over its useful life.
- The WACC is 9%.                                                                   
Develop the pro-forma income statement, compute the Operating Cash-Flows and NPV. Assume that your bossy boss wants you to do a sensitivity analysis regarding the project. He is concerned that the vacancy rate may increase by as much as 5% (occupancy will go down to 80%). Compute the NPV for this scenario (round to nearest $10,000).

Answer 1

Proforma Income statement

Revenue 2-bedroom (130*85%) * 2800 * 12 = 3712800 1- bedroom ( 100*85%)* 2000 * 12 = 2040000 studio ( 70*85% ) * 1200 *12 = 856800	$ 6609600
Variable maintanance cost 2-bedroom 110.5 * 200 * 12 = 265200 1- bedroom 85 * 200 *12 = 204000 studio 59.5 * 200 * 12 = 142800	$ 612000
fixed maintanance cost	$ 1500000
Gross profit	$ 4497600
Depreciation 30 millio / 25	$ 1200000
operating profit	$ 3297600
Tax @ rate 30%	$ 989280
Earning after tax (net income)	$ 2308320

Operating cash flow

	Initial investment 0th year	year 1 to year 25 operating cash flow	Terminal year cash flow (end of 25th year)
	30 million	Earning after tax (net income)	$ 2308320	salvage value	0
		add back depreciation	$ 1200000	book value(fuuly depreciated)	0
		Net operating cash flow	$ 3508320	Disposal of asset expenses (outflow)	($ 6000000)
				Tax benefit from this expenses @ 30% * 6million	$ 1800000
				Net cash outflow	$ 4200000
total cash flows	(30million) outflow		$ 3508320 inflow each 1 to 25 years		($ 4200000) outflow
*PV factor @ $ 1 WACC= 9%	1		(1/1.09)25GT = 9.823		(1/1.09)25 =0.116
PV of Cashflow	(30 million)		= 34462227 another way (a/r)(1 - 1 / (1+r)n) (3508320 / 9% ) * (1-1 / 1 +9%)25 = 38981333 * (1-1/ 8.623) = 38981333 * ( 1 - 0.116) = 34462227		= (487200)

NPV = Pv of cash inflow - PV of cash outflow

NPV = 34462227 - (30 million + 487200 ) = $ 3975027

Assume that your bossy boss wants you to do a sensitivity analysis regarding the project. He is concerned that the vacancy rate may increase by as much as 5% (occupancy will go down to 80%). Compute the NPV for this scenario (round to nearest $10,000).

Sensitivity analysis

If the occupancy rate are chamged from 85% to 80% will affect the revenue and operating cash flow, so we need to recalculate operating cash flow agian with this change ( everything remain same )

it reduce the cashflow

Revenue = 2 -bedroom (130*80%) * 2800 * 12 = 3494400 1- bedroom ( 100*80%)* 2000 * 12 = 1920000 studio ( 70*80% ) * 1200 *12 = 806400	$ 6220800
-VC= ((130*80%) + ( 100*80%)+ ( 70*80% ) ) * 200 * 12	$ 576000
-FC maintance (no change)	$ 1500000
-Depreciation (no change)	$ 1200000
=Earnig Befor Tax	$ 2944800
-tax	$883440
= earning after tax	$ 2061360
add back depreciation	$ 1200000
operating cash flow (from 1 to 25 year are same)	$ 3261360
PV factor $ 1 rate 9%	(1/1+9%)25gt = 9.823
PV of cashflow	= 32036339

PV of initial investment = 30 million (no change) (outflow)

PV of terminal cash flow (non operating ) = 487200 (no change ) (outflow)

New NPV = 32036339 - (30 million + 487200 ) = $ 1549139

**If the occupancy rate are changed, it will affect the NPV by reducing $ 2425888 from old NPV