Question

Owners of an economy motel chain are considering building a new 200-unit motel. The present worth cost of building the motel is $8,000,000 and the firm estimates furnishings for the motel will cost an additional $800,000 and will require replacement every 5 years. Annual operating and maintenance costs for the facility are estimated to be $750,000 and the average rate for a unit is anticipated to be $50/day. A 15 year planning horizon is used by the firm for ventures of this type; a terminal salvage value of 15% of the original building cost is anticipated, and furnishings have no salvage value at the end of each replacement cycle. Assuming average daily occupancy percentages of 50%, 60%, 70%, 80% for years 1 through 4, respectively, and 90% for years 5-15, MARR of 12%, 365 operating days per year and ignoring the cost of the land, should the motel be built? Make your decision using each of the following measures of worth:

a. Present Worth

b. IRR

Answer 1

Working notes:

(A) If occupancy (in percent) is P%, annual revenue = 200 x P x $50 x 365 = $3,650,000 x P

(B) Market value in (terminal) year 15 (Added to revenue of year 15) = $8,000,000 x 0.15 = $1,200,000

(C) In years 5 and 10, total annual costs will be higher $800,000 (cost of additional furnishing). It is assumed that the motel will not replace furnishing in the last year of operation (year 15), when it will sell the motel.

(D) Annual net benefit (NB) = Annual revenue - Annual cost

(E) Cash flow of the operations is charted below.

Year	Occupancy (%)	Cost ($)	Revenue ($)	NB ($)
	(1)	(2)	(3)=$3,650,000x(1)	(4)=(3)-(2)
0		80,00,000		-80,00,000
1	50	7,50,000	18,25,000	10,75,000
2	60	7,50,000	21,90,000	14,40,000
3	70	7,50,000	25,55,000	18,05,000
4	80	7,50,000	29,20,000	21,70,000
5	90	15,50,000	32,85,000	17,35,000
6	90	7,50,000	32,85,000	25,35,000
7	90	7,50,000	32,85,000	25,35,000
8	90	7,50,000	32,85,000	25,35,000
9	90	7,50,000	32,85,000	25,35,000
10	90	15,50,000	32,85,000	17,35,000
11	90	7,50,000	32,85,000	25,35,000
12	90	7,50,000	32,85,000	25,35,000
13	90	7,50,000	32,85,000	25,35,000
14	90	7,50,000	32,85,000	25,35,000
15	90	7,50,000	44,85,000	37,35,000

Therefore,

(a) Present worth (PW) of NAB is computed as follows [PV factor in year N = 1 / (1.12)^N]

Year	NB ($)	PV factor @12%	Discounted NB ($)
	(4)	(5)	(4)x(5)
0	-80,00,000	1.0000	-80,00,000
1	10,75,000	0.8929	9,59,821
2	14,40,000	0.7972	11,47,959
3	18,05,000	0.7118	12,84,763
4	21,70,000	0.6355	13,79,074
5	17,35,000	0.5674	9,84,486
6	25,35,000	0.5066	12,84,310
7	25,35,000	0.4523	11,46,705
8	25,35,000	0.4039	10,23,844
9	25,35,000	0.3606	9,14,146
10	17,35,000	0.3220	5,58,624
11	25,35,000	0.2875	7,28,752
12	25,35,000	0.2567	6,50,671
13	25,35,000	0.2292	5,80,957
14	25,35,000	0.2046	5,18,711
15	37,35,000	0.1827	6,82,371
		PW of NB ($) =	58,45,195

Since PW > 0, motel should be built.

(b IRR of annual net benefits is computed using Excel IRR function, as follows.

Year	Occupancy (%)	Cost ($)	Revenue ($)	NB ($)
	(1)	(2)	(3)=$3,650,000x(1)	(4)=(3)-(2)
0		80,00,000		-80,00,000
1	50	7,50,000	18,25,000	10,75,000
2	60	7,50,000	21,90,000	14,40,000
3	70	7,50,000	25,55,000	18,05,000
4	80	7,50,000	29,20,000	21,70,000
5	90	15,50,000	32,85,000	17,35,000
6	90	7,50,000	32,85,000	25,35,000
7	90	7,50,000	32,85,000	25,35,000
8	90	7,50,000	32,85,000	25,35,000
9	90	7,50,000	32,85,000	25,35,000
10	90	15,50,000	32,85,000	17,35,000
11	90	7,50,000	32,85,000	25,35,000
12	90	7,50,000	32,85,000	25,35,000
13	90	7,50,000	32,85,000	25,35,000
14	90	7,50,000	32,85,000	25,35,000
15	90	7,50,000	44,85,000	37,35,000
			IRR of NB (%) =	22.26%

Since IRR > MARR, motel should be built.