Question

Owners of a motel chain are considering a new investment. The cost of the 125-unit motel (excluding furnishings) is $10 million and the furnishings, which cost $2 million must be replaced every five years (with no salvage value). The annual O&M costs are $200,000 per year, the average daily room rate is $110/day (increasing by 3% per year), and the buildings will be sold in 15 years for 20% of the original building cost. Ignoring taxes, if the motel operates 365 days/year, what is the required occupancy rate if the motel chain needs to make a return of 10% per year on its investment (use end-of-year convention)?

please show all the steps

Answer 1

The required occupancy is 34%

Time	Capital	Salvage Value	O&M (goes up 3% every year)	Annual Revenue at 100% occupancy = 110 x 125 x 365 x 1.03^(t-1)	Required occupancy	Annual Revenue at required occupancy = 110 x 125 x 365 x 1.03^(t-1)	Net cash flow	PV @10% = Net CF / (1.1^t)
0	-12000000						-12000000	-12000000
1			-200000	5018750	34%	1710905.149	1510905.149	1373550
2			-206000	5169312.5	34%	1762232.303	1556232.303	1286142
3			-212180	5324391.875	34%	1815099.272	1602919.272	1204297
4			-218545	5484123.631	34%	1869552.25	1651006.85	1127660
5	-2000000		-225102	5648647.34	34%	1925638.818	-299462.944	-185942.9
6			-231855	5818106.76	34%	1983407.983	1751553.168	988706.1
7			-238810	5992649.963	34%	2042910.222	1804099.763	925788.4
8			-245975	6172429.462	34%	2104197.529	1858222.756	866874.6
9			-253354	6357602.346	34%	2167323.455	1913969.438	811709.9
10	-2000000		-260955	6548330.416	34%	2232343.158	-28611.47862	-11030.96
11			-268783	6744780.329	34%	2299313.453	2030530.177	711688.4
12			-276847	6947123.739	34%	2368292.856	2091446.082	666399.2
13			-285152	7155537.451	34%	2439341.642	2154189.465	623992
14			-293707	7370203.574	34%	2512521.891	2218815.149	584283.4
15		2000000	-302518	7591309.682	34%	2587897.548	4285379.603	1025886
Total								3.312777