Question

Black Oil Company is trying to decide whether to lease or buy a new computer-assisted drilling system for its extraction business. Management has already determined that acquisition of the system has a positive NPV. The system costs $9.4 million and qualifies for a 25% CCA rate. The equipment will have a $975,000 salvage value in five years. Black Oil’s tax rate is 36%, and the firm can borrow at 9%. Cape Town Company has offered to lease the drilling equipment to Black Oil for payments of $2.15 million per year. Cape Town’s policy is to require its lessees to make payments at the start of the year.

What is the NAL for Black Oil Company? What is the maximum lease payment that would be acceptable to the company?

Answer 1

Answers:

        (1)   The forgone salvage value is a cost to the lease decision and the lost tax shield on the resale represents a gain to the lease decision. Also, the salvage value is not really a debt-like cash flow, since there is uncertainty associated with it at year 0. Nevertheless, although a higher discount rate may be appropriate, we’ll use the after tax cost of debt to discount the residual value as is common in practice. We will also assume beginning of year payments.

           

            After-tax cost of debt = Interest rate x (1 – T_c) = .09(1 – .36) = .0576

PV tax shield on CCA=(IdTc/d+k)*(1+0.5k/1+k)-(s_ndT_c)*(1/(1+k)ⁿ

Where: I = Total Capital Investment; d = CCA tax rate; Tc = Corporate Tax Rate; k = Discount rate

            S_n = Salvage value in year n; n = Number of periods in the project

           

PV of CCATS = 9,400,000(.25)(.36) x (1 + .5(.0576) – 975,000(.25)(.36) x                1    

               . 0576 + .25                  1 + .0576             . 0576 + .25          (1 + .0576)⁵

PVCCATS = (2,750,325.10 x 0.97277) - (285,273.08 x 0.75578) = 2,675,429.71 - 215,602.39 = 2,459,827.31

            After-tax lease payment = Lease payment x (1 – T_c) = $2,150,000(1 – .36) = $1,376,000

           

       Net advantage to leasing (NAL) = Investment – PV (After-tax lease payments) - PVCCATS – PV (Salvage)

PV-Annuity=c(1-(1/1+r)^t/r)
Or PV annuity factor = {1 – [1 / (1+r)^t]} / r

PV factor = 1 / (1 + r)^t

NAL = $9.4M – $1,376,000(1.0576)(PVIFA_{5.76%, 5}) - 2,459,827.31 - 975,000 (PVIF_{5.76%, 5})

PVIFA = Present value interest factor of annuity; PVIF = Present value interest factor

= 9,400,000 - [1,376,000 x (4.24001 x 1.0576)] - 2,459,827.31 - (975,000 x 0.75578)

= 9,400,000 - 6,170,306.78 - 2,459,827.31 - 736,885.50 = 32,980.41         

The equipment should NOT be purchased since the net advantage to leasing (NAL) is positive.

Note: If NAL is negative, the asset should be bought. If NAL is positive, the asset should be leased.

(2)

Where: I = Total Capital Investment; d = CCA tax rate; Tc = Corporate Tax Rate; k = Discount rate

            S_n = Salvage value in year n; n = Number of periods in the project

            After-tax cost of debt = Interest rate x (1 – T_c) = .09(1 – .36) = .0576

            PV of CCATS = 9,400,000(.25)(.36) x (1 + .5(.0576))

                                       .0576 + .25                  1 + .0576     

      

       PVCCATS = 2,750,325.10 x 0.972768532 = 2,675,429.71

Net advantage to leasing (NAL) = Investment – PV (After-tax lease payments) - PVCCATS – PV (Salvage)

PV-Annuity=c(1-(1/1+r)^t/r) Or PV annuity factor = {1 – [1 / (1+r)^t]} / r

PV factor = 1 / (1 + r)^t

NAL = 0 = $9.4M – $X(1.0576)(PVIFA_{5.76%, 5}) – 2,675,429.71

PVIFA = Present value interest factor of annuity

= 9,400,000 – X(1.0576 x 4.24001) - 2,675,429.71

X = 6,724,570.29 / 4.48423 = $1,499,604.23       

Maximum pretax lease payment = Lease payment after tax / (1 - T_c) = $1,499,604.23 / (1 - .36) = $2,343,131.61