Question

Shrieves Hospital Ltd. is considering adding a new line to its diagnostic product mix, and the capital
budgeting analysis is being conducted by Sidney Johnson, a recently graduated MHA. A new bone density
scanner would be set up in unused space in Shrieves's main clinic. The machinery’s invoice price would be
approximately $200,000; another $10,000 in shipping charges would be required; and it would cost an
additional $30,000 to install the equipment. The machinery has an economic life of four years, and Shrieves
has obtained a special tax ruling which places the equipment in the MACRS three-year class. The machinery
is expected to have a salvage value of $25,000 after four years of use. The new line would generate
incremental sales of 1,250 scans per year for four years at an incremental cost of $100 per scan in the
first year, excluding depreciation. Each scan would generate revenue of $200 in the first year. The price
and cost of each scan are expected to increase by 3 percent per year due to inflation. Further, to handle
the new line, the hospital's net operating working capital would have to increase by an amount equal to 12
percent of sales revenues*. The hospital's tax rate is 40 percent, and its corporate cost of capital is 10
percent.
a. Perform a sensitivity analysis on the corporate cost of capital, number of scans, and salvage value.
Assume that each of these variables can vary from its base case by plus and minus 15 and 30 percent.
Include a sensitivity diagram.
b. Perform a scenario analysis using the worst-, most likely, and best-case probabilities in the table below:
			Number of	Price
	Scenario	Probability	scans	per scan
	Best	25%	1,600	$240
	Most likely	50%	1,250	$200
	Worst	25%	900	$160
c. Assume that Shrieves's average project has a coefficient of variation of NPV in the range of 0.2–0.4.
The hospital typically adds or subtracts 3 percentage points to its corporate cost of capital to adjust for
risk. Should the new line be accepted?
*
In the section entitled "Changes in Net Working Capital" in Chapter 11, Gapenski states that expansion
projects require additional inventories and accounts receivable which must be financed, just as an increase
in fixed assets must be financed. In this situation, the hospital's net working capital would have to increase
by an amount equal to 12 percent of sales. Sales in Year 1 are estimated at $250,000, so Shrieves must
have (.12 * $250,000 =) $30,000 in net working capital at Year 0. If sales increase to $257,500 in Year 2,
Shrieves must have (.12 * $257,500 =) $30,900 at Year 1. Because it already has $30,000 of net working
capital on hand, its net investment in working capital at Year 1 is just ($30,900 - $30,000 =) $900. If sales
increase to $265,225 in Year 3, its net investment in working capital in Year 2 is (.12 * 265,225 =)
$31, 827 - $30,900 = $927. If sales increase to $273,182 in Year 4, its net investment in working capital
in Year 3 is (.12 * 273,182 =) $32,782 - $31,827 = $955. Shrieves will have no sales after Year 4, so it will
require no working capital at Year 4. Thus, it would have a positive cash flow of $32,782 at Year 4 as
working capital is sold but not replaced.

Answer 1

Cost of Machine	200,000		Tax rate		40%
Shipping Cost	10,000		Cost of Capital		10%
installation cost	30,000
Total Book value of Machinery	240,000
Life of machine	4	MACRS three-year class
Salvage Value	25,000

	0	1	2	3	4
Purchase of machine	(240,000)
Salvage Value					25,000	Assuming no capital gain tax
Incremental Sale		1,250	1,250	1,250	1,250
Price per scan		200.00	206.00	212.18	218.55	Price increasing per year as per inflation
increase in price per Scan			3%	3%	3%
Cost per scan		100.00	103.00	106.09	109.27	Cost increasing per year as per inflation
increase in cost per Scan			3%	3%	3%
Sales Revenue		250,000.00	257,500.00	265,225.00	273,181.75	Price per scan*Sales Units
Cost of Sales		(125,000.00)	(128,750.00)	(132,612.50)	(136,590.88)	Cost per scan*Sales Units
Gross Profit		125,000.00	128,750.00	132,612.50	136,590.88	Sales - Cost
MACRS three-year class rate		33.33%	44.45%	14.81%	7.41%
Depreciation		(79,992.00)	(106,680.00)	(35,544.00)	(17,784.00)	book value * MACRS rate for the year
Pre tax Profit		45,008.00	22,070.00	97,068.50	118,806.88	Gross Profit less Depreciation
Taxes		(18,003.20)	(8,828.00)	(38,827.40)	(47,522.75)	Pre tax profit * 40%
Post Tax Profit		27,004.80	13,242.00	58,241.10	71,284.13	Pre tax profit less tax
Working Capital as % of Sales		12%	12%	12%	12%
Working Capital		30,000.00	30,900.00	31,827.00	32,781.81	12% of sales revenue
(Increase)/Decrease in Working Capital		(30,000.00)	(900.00)	(927.00)	32,781.81	Previous year WC less current year WC. Working Capital is released in final year
Depreciation added back		79,992.00	106,680.00	35,544.00	17,784.00	Being non cash expense
Free Cash Flow	(240,000)	76,997	119,022	92,858	146,850	Post tax profit + Change in WC + Depreciation
Discount rate	1	0.91	0.83	0.75	0.68	1/(1+r)^n, r = discount rate, n = year
Discounted cash flow	(240,000)	69,997	98,365	69,766	100,300	Free cash flow * discount rate
PV of Discounted Cash flow	98,429					Sum of all discounted cash flows

Answer b	Scenario Analysis
			Price per Scan
	# of Scans	98,429	240	200	160
		1600	291,282	166,037	40,792
		1250	196,276	98,429	581
		900	101,271	30,820	(39,630)
	So Expected value base on scenario probability     =   25%*291282 + 50%*98429 + 25%*(39630) =					112,127.23
Answer c	At given levels of risk, project is still NPV positive as we can see from the sensitivity analysis from above. So Project is acceptable