Quantum $\text{'}$R Us has a physics research lab which would like to use a specialized machine for its quantum computers research program. The company will either need to lease the machine for the lab or it will buy the machine for the lab. Which one is better? Here's what's known about the machine and about the Quantum $\text{'}$R Us company:

Quantum $\text{'}$R Us's pre$-$tax borrowing rate is $4\%$ per year.

Quantum $\text{'}$R Us pays a $22\%$ tax rate on its corporate taxable income.

The machine for the research lab would cost $$14,000,000$ to buy. It depreciates straight$-$line to zero over its $7$ year economic life. After that, the lab's research project would end, and the machine will have no selling value.

If the machine for the research lab is leased, Quantum $\text{'}R$ Us would need to pay $$2,400,000$ at the end of every year in pre$-$tax lease payments, for $7$ years.

Calculate the following:

Each year, the depreciation of the machine would equal & and the tax savings from depreciation $($or the "tax shield"$)$ would equal $

$.$ That's if the machine is purchased.

Each year, Quantum $\text{'}$R Us would need to make a $ lease payment after taxes. That's if the machine is leased.

Based on Quantum $\text{'}$R Us's calculations of "leasing instead of buying" incremental cash flows for each year, in "Year $0"$ it would equa

$,$ and at the end of each future year it would equal

As part of this valuation analysis, the appropriate discount rate for these cash flows would equal

Based on the above, the calculations show that Quantum $\text{'}$R Us's estimated net advantage to leasing, or NAL $($i$.$e$.,$ the NPV of leasing instead of buying$),$ is

In addition $($no math!$)$:

In general, if Quantum $\text{'}$R Us's calculated NAL is negative, then it should the machine. And in this case, in order for Quantum $\text{'}$R Us to be indifferent between leasing and purchasing the machine, the lease payment would have to

In general, if Quantum $\text{'}$R Us's calculated NAL is negative, then the other company that would be leasing the machine to Quantum $\text{'}$R Us would to sign the lease agreement with Quantum $\text{'}$R Us$.$