Question

Dr. Hunter Thompson is considering opening an MRI clinic in Aspen to profit from reckless skiers and snowboarders. The business will operate for three years. For planning​ purposes, all operating cash flows are assumed to occur at​ year-end with the first​ year's flows occurring one year from today. The MRI​ machine, a GE 3.0T Signa Excite​ HD, costs

$ 2.48$2.48

million and will be delivered immediately and installed for

$ 92 comma 000$92,000

​(GE expects cash on​ delivery). Assume that the machine is classified as a​ 5-year property and can be sold for

$ 509 comma 000$509,000

at the end of the three years.​ (MACRS depreciation rates are shown in the table

LOADING...

​.)

The forecasted number of scans each year is

2 comma 5302,530

and the clinic will charge

$ 690$690

per scan. Dr. Thompson will lease office space in a local​ strip-mall. Annual operating expenses are

$ 557 comma 000$557,000

for​ rent, computer equipment​ leases, labor​ (receptionist, nurse and​ technician), maintenance and advertising. Dr. Thompson plans to offer credit to his customers. He expects to have about

4545

days of sales in accounts​ receivable, or about

$ 296 comma 000$296,000.

The famed venture​ capitalist, Oscar​ Acosta, has pledged to provide all of the equity needed for the project with the condition that he receive an annual return of

9.7 %9.7%

on his invested capital. The tax rate is

35 %35%.

a. What are initial cash flows for the MRI​ project?

b. What are the operating cash flows in the first​ year?

c. What are the terminal year cash flows​ (not including the operating cash​ flows)?

d. What is the NPV of the​ project?

Answer 1

Part a)

The value of initial cash flow associated with the project is calculated as below:

Initial Cash Flow = -Purchase Price - Installation Cost - Increase in Working Capital

where, Purchase Price = $2,480,000, Installation Cost = $92,000 and Increase in Working Capital = $296,000

Susbtituting these values in the above formula, we get,

Initial Cash Flow = -2,480,000 - 92,000 - 296,000 = -$2,868,000

_____

Part b)

The value of operating cash flow in Year 1 is derived as below:

	Year 1
Sales Revenue (2,530*690)	1,745,700
Less Annual Operating Expenses	557,000
Annual Depreciation [20%*(2,480,000+92,000)]	514,400
EBT	674,300
Less Taxes	236,005
EAT	438,295
Add Depreciation	514,400
Operating Cash Flow	$952,695

_____

Part c)

The value of terminal year cash flow is arrived as follows:

Book Value of Machine at the End of Year 3 = Total Cost of Machine - Total Cost of Machine*(Sum of Depreciation Rates from Year 1 to Year 3) = 2,572,000 - 2,572,000*(20% + 32% + 19.20%) = $740,736

Loss on Sale of Machine = Book Value of Machine at the End of Year 3 - Sales Value of Machine = 740,736 - 509,000 = $231,736

Tax Savings = Loss on Sale of Machine*Tax Rate = 231,736*35% = $81,107.60

After-Tax Salvage Value = Sales Value of Machine + Tax Savings = 509,000 + 81,107.60 = $590,107.60 or $590,108

Now we can calculate terminal cash flow as below:

Terminal Cash Flow = After-Tax Salvage Value + Recovery of Working Capital = 590,107.60 + 296,000 = $886,107.60 or $886,108

_____

Part d)

Step 1: Calculate Annual Cash Flow for Each Year

The annual cash flow for each year is determined as below:

	Year 1	Year 2	Year 3
Sales Revenue (2,530*690)	1,745,700.00	1,745,700.00	1,745,700.00
Less Annual Operating Expenses	557,000.00	557,000.00	557,000.00
Annual Depreciation	514,400.00 [2,572,000*20%]	823,040.00 [2,572,000*32%]	493,824.00 [2,572,000*19.20%]
EBT	674,300.00	365,660.00	694,876.00
Less Taxes	236,005.00	127,981.00	243,206.60
EAT	438,295.00	237,679.00	451,669.40
Add Depreciation	514,400.00	823,040.00	493,824.00
Operating Cash Flow	952,695.00	1,060,719.00	945,493.40
Add Terminal Cash Flow	0.00	0.00	886,107.60
Annual Cash Flow	$952,695.00	$1,060,719.00	$1,831,601.00

_____

Step 2: Calculate NPV

The NPV is calculated as follows:

NPV = -Initial Cost + Annual Cash Flow Year 1/(1+Annual Rate of Return)^1 + Annual Cash Flow Year 2/(1+Annual Rate of Return)^2 + Annual Cash Flow Year 3/(1+Annual Rate of Return)^3

Substituting values in the above formula, we get,

NPV = -2,868,000 + 952,695/(1+9.7%)^1 + 1,060,719/(1+9.7%)^2 + 1,831,601/(1+9.7%)^3 = $269,313.09