Question

Hartwick is considering leasing a new equipment. The lease lasts for 5 years. The lease calls for 5 payments of $11,300 per year with the first payment occurring immediately. The equipment would cost $44,000 to buy and would be straight-line depreciated to a zero salvage value over 5 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 6%. The corporate tax rate is 25%. What is the NPV of the lease relative to the purchase if the asset had a pretax salvage value of $800 (ignoring any possible risk differences)?

-$4,462.19

-$4,736.80

-$5,018.70

$1,097.38

$3,110.25

Answer 1

Solution :

The NPV of the lease relative to the purchase if the asset had a pretax salvage value of $800 is = - $ 5,018.70

Thus the solution is option 3 = - $ 5,018.70

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 % ; Tax rate = 25 % = 0.25

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

= 6 % * ( 1- 0.25 ) = 6 % * 0.75 = 4.5 %

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

06.04.2019- Excel FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Statement showing calculation of NPV of the Lease Option Sl.No. Particulars After Tax Lease | PVF @ 4.5 % | Discounted Cash outflows Tax @25 % 1Lease payment Year 0 2 Lease payment Year 1 3 Lease payment Year 2 4 Lease payment Year 3 5Lease payment Year 4 -11,300.00 $ -11,300.00 $ $-11,300.00 $ $-11,300.00 $ $11,300.00 $ 2,825.00 $ 2,825.00 $ 2,825.00 S 2,825.00 S 2,825.00 S 8,475.00 8,475.00 8,475.00 8,475.00 8,475.00 1.0000$ 0.9569 $ 0.9157$ 0.8763 $ 0.8386$ -8,475.00 -8,110.05 7,760.81 7,426.61 7,106.81 38,879.28 NPV of the lease option Statement showing calculation of NPV of the Purchase option SI.No. Particulars Depreciation -$ 44000/5-$(3)(21*0.25 Tax shield @ 25 % | Total of cash | PVF @ 4.5 % Discounted Cash 1 Cash Outflow-Initial Investment - Year O 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 $ $44,000.00 $ 8,800.00 S 8,800.00 S 8,800.00 S 8,800.00 $ 8,800.00 $ -$-44,000.00 2,200.00 2,200.00 2,200.00 2,200.00 2,200.002,200.00 2,200.002,200.00 2,200.002,200.00 0.9569 S 0.9157 $ 0.8763 $ 0.8386 $ 0.8025 -44,000.00 2,105.26 2,014.61 1,927.85 1,844.83 1,765.39 15 Post Tax Salvage value Year 5 7 Pre tax salvage value (1-tax rate) 0.8025$ 481.47 -$8001 0.25) $ 800 0.75 $ 600 NPV of the Purchase Option 33,860.58 20 Statement showing NPV of the lease relative to the purchase SI.No. Particulars Amount S -38,879.28 S -33,860.58 $ -5,018.70 23 1|NPV of the Lease Option Less NPV of the purchase option 3 NPV of the lease relative to the purchase 25 26 27