Question

14.7 California Health Center, a for-profit hospital, is evaluating the purchase of new diagnostic equipment. The equipment, which costs $600,000, has an expected life of five years and an estimated pretax salvage value of $200,000 at that time. The equipment is expected to be used 15 times a day for 250 days a year for each year of the project’s life. On average, each procedure is expected to generate $80 in collections, which is net of bad debt losses and contractual allowances, in its first year of use. Thus, net revenues for Year 1 are estimated at 15 × 250 × $80 = $300,000.

Labor and maintenance costs are expected to be $100,000 during the first year of operation, while utilities will cost another $10,000 and cash overhead will increase by $5,000 in Year 1. The cost for expendable supplies is expected to average $5 per proce- dure during the first year. All costs and revenues, except deprecia- tion, are expected to increase at a 5 percent inflation rate after the first year.

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e equipment falls into the MACRS five-year class for tax depreciation and is subject to the following depreciation allowances:

Year    Allowance

1    0.20 2    0.32 3    0.19 4    0.12 5    0.11 6    0.06

1.00

The hospital’s tax rate is 40 percent, and its corporate cost of capi- tal is 10 percent.

a. Estimate the project’s net cash flows over its five-year estimated life. (Hint: Use the following format as a guide.)

Year

012345

Equipment cost Net revenues Less: Labor/maintenance costs

Utilities costs Supplies Incremental overhead Depreciation

Operating income Taxes

Net operating income Plus: Depreciation Plus: Equipment salvage value

Net cash flow

b. What are the project’s NPV and IRR? (Assume for now that the project has average risk.)

Answer 1

a]		0	1	2	3	4	5
	Net revenues		$       3,00,000	$       3,15,000	$          3,30,750	$       3,47,288	$        3,64,652
	- Expendable supplies [15*250*5]		$           18,750	$           19,688	$             20,672	$           21,705	$            22,791
	- Labor/Maintenance costs		$       1,00,000	$       1,05,000	$          1,10,250	$       1,15,763	$        1,21,551
	- Utilities		$           10,000	$           10,500	$             11,025	$           11,576	$            12,155
	- Incremental cash overhead		$             5,000	$             5,250	$                5,513	$             5,788	$              6,078
	Depreciation rate [MACRS 5 Year]		20.00%	32.00%	19.00%	12.00%	11.00%	6.00%
	- Depreciation		$       1,20,000	$       1,92,000	$          1,14,000	$           72,000	$            66,000	$      36,000
	NOI		$           46,250	$         -17,438	$             69,291	$       1,20,455	$        1,36,078
	- Tax at 40%		$           18,500	$            -6,975	$             27,716	$           48,182	$            54,431
	NOPAT		$           27,750	$         -10,463	$             41,574	$           72,273	$            81,647
	+ Depreciation		$       1,20,000	$       1,92,000	$          1,14,000	$           72,000	$            66,000
	OCF		$       1,47,750	$       1,81,538	$          1,55,574	$       1,44,273	$        1,47,647
	- Capital expenditure	$       6,00,000
	+ Salvage value						$        2,00,000
	- Tax on salvage value:
	Book value						$            36,000
	Gain on sale						$        1,64,000
	-Tax on gain = 164000*40% =						$            65,600
	Project's Net cash flows	$      -6,00,000	$       1,47,750	$       1,81,538	$          1,55,574	$       1,44,273	$        2,82,047
b]	PVIF at 10%	1	0.90909	0.82645	0.75131	0.68301	0.62092
	PV at 10%	$      -6,00,000	$       1,34,318	$       1,50,031	$          1,16,885	`	$        1,75,129
	NPV	#VALUE!
	IRR is that discount rate for which NPV is 0. It has to be found out by trial and error. The cash
	flows are discounted using varying discount rates by trial and error till 0 NPV is obtained.
	Discounting with 15%:			`				NPV
	PVIF at 15%	1	0.86957	0.75614	0.65752	0.57175	0.49718
	PV at 15%	$      -6,00,000	$       1,28,478	$       1,37,268	$          1,02,293	$           82,489	$        1,40,227	$       -9,245
	Discounting with 14%:
	PVIF at 14%	1	0.87719	0.76947	0.67497	0.59208	0.51937
	PV at 14%	$      -6,00,000	$       1,29,605	$       1,39,687	$          1,05,008	$           85,421	$        1,46,486	$         6,208
	The IRR [discount rate for 0 NPV] lies between 14% and 15%.
	By simple interpolation, IRR = 14%+1%*6208/(6208+9245) =	14.40%