Big Sky Hospital plans to obtain a new MRI that costs $1.5 million and has an estimated four-year useful life. It can obtain a bank loan for the entire amount and buy the MRI or it can lease the equipment. Assume that the following facts apply to the decision:
* The MRI falls into the three-year class for tax depreciation, so the MACRS allowances are 0.33, 0.45,0.15, and 0.07 in Years 1 through 4, respectively.
* Estimated maintenance expenses are $75,000 payable at the beginning of each year whether the MRI is leased or purchased.
* Big Sky's marginal tax rate is 40 percent.
* Big Sky's cost of debt is 15 percent.
* If leased, the lease (rental) payments would be $400,000 payable at the end of each of the next four years.
* The estimated residual (and salvage) value is $250,000.
What is the IRR of the lease?
Answer (2)
The question revolves around evaluating the financial decision Big Sky Hospital faces: whether to lease or buy a new MRI machine, and specifically, it asks for the internal rate of return (IRR) of the lease.
Calculating the IRR of the lease involves comparing cash flows of leasing the MRI and its effective cost versus the alternative of purchasing the equipment outright. Let's examine this step-by-step:
1. Leasing Cash Flows
Lease payments are $400,000 paid at the end of each year for four years.
Maintenance expenses are $75,000 paid at the beginning of each year.
2. Tax Effects
Lease payments reduce taxable income, thus creating tax savings. Tax savings per year = Lease payment x Tax rate = 400 , 000 × 0.40 = 160 , 000 .
Net lease cash outflow (cost of lease per year) = Lease payment - Tax savings = 400 , 000 − 160 , 000 = 240 , 000
3. Maintenance Cash Flows
Maintenance costs do not change between leasing and buying, but they do affect tax payments. Tax savings for maintenance = Maintenance cost x Tax rate = 75 , 000 × 0.40 = 30 , 000 .
Net maintenance cost per year = 75 , 000 − 30 , 000 = 45 , 000 .
4. Total Cash Outflows per Year
Total cash outflow per year from leasing: Net lease cost + Net maintenance cost = 240 , 000 + 45 , 000 = 285 , 000 .
5. Organizing Cash Flows
End of Year 0 : Outflow for maintenance = 45,000
End of Year 1-4 : Outflow = 285,000 each year
6. Calculating IRR
The IRR can be calculated by finding the rate at which the present value of cash outflows equals zero:
NPV = -45,000 / (1+IRR)^0 - 285,000 / (1+IRR)^1 - 285,000 / (1+IRR)^2 - 285,000 / (1+IRR)^3 - 285,000 / (1+IRR)^4 = 0
Calculating IRR in a manual process might involve trial and error, but typically you would use financial calculator tools or software like Excel with the IRR function, inputting the sequence of cash flows:
=IRR([-45000, -285000, -285000, -285000, -285000])
Conclusion
Thus, by determining this IRR, Big Sky Hospital can compare it against their hurdle rate or cost of borrowing (15%) to assess whether leasing is a financially viable option.
Remember: The IRR is the rate at which the hospital would be indifferent to leasing versus not engaging in this financial activity when only considering this isolated decision.
To determine the IRR of leasing the MRI, we calculated the cash flows from lease payments and associated maintenance costs. Using these cash flows in financial software, such as Excel, will yield the IRR value, which should be compared with the hospital's cost of debt to evaluate the financial viability of the lease. This process involves considering tax implications and the total costs associated with leasing.
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