Question

Aaron Co. needs a machine for a 5-year project. It can either (1) buy a machine without borrowing for $500,000 or (2) enter into a 5-year operating lease for an annual payment of $105,000. The machine has an estimated useful life of 5 years, after which it can be sold for $15,000. The average tax rate is 30%, and the discount rate for the project is 6%. Relevant discount factors are below: Present value of 1 at 6% in 1 year: 0.943 Present value of 1 at 6% in 2 years: 0.890 Present value of 1 at 6% in 3 years: 0.840 Present value of 1 at 6% in 4 years: 0.792 Present value of 1 at 6% in 5 years: 0.747 What is the present value of the relevant net cash outflows of the operating lease

Answer 1

Answer:

The present value of the relevant net cash outflows of the operating lease is $434,416.50.

Explanation:

Salvage value after tax = Salvage value * (100% - Tax rate) = $15,000 * (100% - 30%) = $10,500

Present value of salvage value after tax = Salvage value after tax * Present value of 1 at 6% in 5 years = $10,500 * 0.747 = $7,843.50  

Present value of a Year annual operating lease = Annual operating * Present value of 1 at 6% in the years ………… (1)

Using equation (1), we have:

Present value of Year 1 annual operating lease = $105,000 * 0.943 = $99,015

Present value of Year 2 annual operating lease = $105,000 * 0.890 = $93,450

Present value of Year 3 annual operating lease = $105,000 * 0.840 = $88,200

Present value of Year 4 annual operating lease = $105,000 * 0.792 = $83,160

Present value of Year 5 annual operating lease = $105,000 * 0.747 = $78,435

Therefore, we have:

Present value of net cash outflows of the operating lease = Present value of Year 1 annual operating lease + Present value of Year 2 annual operating lease + Present value of Year 3 annual operating lease + Present value of Year 4 annual operating lease + Present value of Year 5 annual operating lease - Present value of salvage value after tax = $99,015 + $93,450 + $88,200 + $83,160 + $78,435 - $7,843.50 = $434,416.50

Therefore, the present value of the relevant net cash outflows of the operating lease is $434,416.50.