Question

A firm is negotiating a lease on a new piece of equipment that would cost $1,000,000 if purchased. The equipment falls into the MACRS 3-year class. The depreciation would be 33%, 45%, 15%, and 7% for years 1, 2, 3, and 4 respectively. The equipment would be used for 3 years and sold. It is estimated that it would be sold after three years for $300,000. A maintenance contract on the equipment would cost $30,000 per year if purchased. Conversely, the firm could lease the equipment for a lease payment of $290,000 per year. The lease payment would include maintenance. The firm is in the 20% tax bracket, and it could obtain a loan to purchase the equipment at a before-tax rate of 10%. What is the NAL?

Please show calculation. Thank you

Answer 1

As question has mentioned before-tax rate of 10%.

So we'll now calculate the discount rate.

Discount rate = After tax cost of debt

= 10% * ( 1 - tax rate )

= 10% * ( 1 - 20% )

= 10% * 0.8

Discount rate = 0.08 i.e 8%.

a) Purchasing an equipment :

Cost of purchasing a new piece of equipment is $1,000,000.

Depreciation of the equipment will be as follows -

year 1 : 33% * $1,000,000 = $330,000.

year 2 : 45% * $1,000,000 = $450,000.

year 3 : 15% * $1,000,000 = $150,000.

year 4 : 7% * $1,000,000 = $70,000.

Now present value of depreciation is

= ( 330,000/1.08) + ( 450,000/1.08² ) + (150,000/1.08³ ) + (70,000/1.08⁴ )

= $305,555.56 + $385,802.47 + $119,074.84 + $51,452.09

= $861,884.96

So depreciation tax shield is

= $861884.96 * 0.2 - As 20% is the tax rate

= $172376.99

After 3 years

Salvage value after selling an equipment = $300,000.

Present value of salvage is = (300,000/1.08³ )

= $238,149.67

Now maintenance cost of an equipment is $30,000 per year for 3 years

So PV of maintenance cost is = $78106.74

We got this value using financial calculater

So total cost of purchasing an equipment at time 0 = -Investment + Depreciation tax shield + Salvage value - Maintenance

= -$1,000,000 + $172376.99 + $238,149.67 - $78,106.74

= - $667580.08

b) Leasing of an equipment

After tax lease payment per year = $290,000 * (1-0.2)

= $232,000

So now PV of leasing for three years is can be found using financial calculator

So PMT = $232,000

I = 8, N = 3, FV = 0

So PV = -$598,680.33

So NPV of leasing is -$598,680.33

So now NAL = NPV leasing - NPV purchasing an equipment

=- $598,680.33 - (- $667,580.08)

NAL = $68900.46

So Leasing an equipment is a cheaper option as net advantage in leasing is $68900.46.