Question

Healthsouth Company is considering leasing a new equipment. The lease lasts for 8 years. The lease calls for 8 payments of $111,000 per year with the first payment occurring immediately. The equipment would cost $724,000 to buy and would be straight-line depreciated to a zero salvage value over 8 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 6.5%. The corporate tax rate is 25%. What is the NPV of the lease relative to the purchase? $8,115.44 $11,257.63 $9,872.66 -$12,648.23 -$17,041.66

Answer 1

Solution :

The NPV of the lease relative to the purchase = $ 9,872.66

Thus the solution is Option 3 = $ 9,872.66

Note :

The discount rate used in the solution is the after tax discount rate.

As per the information given in the question we have

Discount rate = 6.5 % ; Tax rate = 25 % = 0.25

Thus, after tax discount rate = Discount rate * ( 1 - Tax rate )

= 6.5 % * ( 1 - 0.25 ) = 6.5 % * 0.75 = 4.875 %

Please find the attached screenshots of the excel sheet containing the detailed calculation for the solution.

04.11.2019 - Microsoft Excel FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW D Sl.No. Particulars 1 Lease payment Year 0 2 Lease payment Year 1 Lease payment Year 2 4 Lease payment Year 3 5 Lease payment Year 4 6 Lease payment Year 5 Lease payment Year 6 8 Lease payment Year 7 Statement showing calculation of NPV of the Lease Option Amount Tax @25% After Tax Lease (1) (2) = (1) * 0.25 payment (3) = (1)-(2) $ -111,000.00 $ -27,750.00 $ -83,250.00 -111,000.00 $ -27,750.00 $ -83,250.00 $ -111,000.00 $ -27,750.00 $ -83,250.00 $ -111,000.00 $ -27,750.00 $ -83,250.00 $ -111,000.00 $ -27,750.00 $ -83,250.00 $ - 111,000.00 $ -27,750.00 $ -83,250.00 $ - 111,000.00 $ -27,750.00 $ -83,250.00 $ - 111,000.00 $ -27,750.00 $ -83,250.00 NPV of the lease option PVF @ 4.875 % Discounted Cash outflows (5) = (3) * (4) 1.0000 $ -83,250.00 0.9535 $ -79,380.21 0.9092 $ -75,690.31 0.8669 $ -72,171.93 0.8266 $ -68,817.10 0.7882 $ -65,618.21 0.7516 $ -62,568.02 0.7166 $ -59,659.61 $ -567,155.39

04.11.2019 - Microsoft Excel ? a - XES FILE HOME A B INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Sl.No. Particulars 1 Cash Outflow - Initial Investment - Year 0 2 Cash Inflow - Depreciation Tax Shield - Year 1 3 Cash Inflow - Depreciation Tax Shield - Year 2 4 Cash Inflow - Depreciation Tax Shield - Year 3 5 Cash Inflow - Depreciation Tax Shield - Year 4 6 Cash Inflow - Depreciation Tax Shield - Year 5 7 Cash Inflow - Depreciation Tax Shield - Year 6 8 Cash Inflow - Depreciation Tax Shield - Year 7 9 Cash Inflow - Depreciation Tax Shield - Year 8 Statement showing calculation of NPV of the Purchase option Amount Depreciation Tax shield @ 25 Total of cash PVF @ 4.875 % Discounted Cash (1) = $ 724000/ 8 = $ 90,500 % Flows (5) flows (2) (3)=(2)*0.25 (4) = (1) + (3) (6) = (4) * (5) $ -724,000.00 $ - $ - $ -724,000.00 1.0000 $ -724,000.00 90,500.00 $ 22,625.00 $ 22,625.00 0.9535 $ 21,573.30 90,500.00 $ 22,625.00 $ 22,625.00 0.9092 $ 20,570.49 90,500.00 $ 22,625.00 $ 22,625.00 0.8669 $ 19,614.29 90,500.00 $ 22,625.00 $ 22,625.00 0.8266 $ 18,702.54 90,500.00 $ 22,625.00 $ 22,625.00 0.7882 $ 17,833.18 90,500.00 $ 22,625.00 $ 22,625.00 0.7516 $ 17,004.22 IS 90,500.00 $ 22,625.00 $ 22,625.00 0.7166 $ 16,213.80 1 $ $ 90,500.00 $ 22,625.00 $ 22,625.00 0.6833 $ 15,460.12 NPV of the Purchase Option $ -577,028.06 Statement showing NPV of the lease relative to the purchase Sl.No. Particulars Amount 1 NPV of the Lease Option $ -567,155.39 2 Less : NPV of the purchase option $ -577,028.06 3 NPV of the lease relative to the purchase = (1) - (2) $ 9,872.66