Question

High electricity costs have made Farmer Corporation’s chicken-plucking machine economically worthless. Only two machines are available to replace it. The International Plucking Machine (IPM) model is available only on a lease basis. The lease payments will be $83,000 for five years, due at the beginning of each year. This machine will save Farmer $30,500 per year through reductions in electricity costs. As an alternative, Farmer can purchase a more energy-efficient machine from Basic Machine Corporation (BMC) for $387,000. This machine will save $32,500 per year in electricity costs. A local bank has offered to finance the machine with a $387,000 loan. The interest rate on the loan will be 6 percent on the remaining balance and will require five annual principal payments of $77,400. Farmer has a target debt-to-asset ratio of 62 percent and a tax rate of 23 percent. After five years, both machines will be worthless. The machines will be depreciated on a straight-line basis. a. What is the NAL of leasing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. How much debt is displaced by this lease? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

Answer 1

A.   

.

Cost of buying =   -387000
Annual lease payment=   -83000
After tax lease payment = 83000*(1-23%)=   -63910
Borrowing rate is cost of capital that is 6% or 0.06.

After tax rate (i) = 6% *(1-23%)=   4.62%
Time (n)=   5
          
Present value of Lease payment=    Annual lease cost * PVIFA due, 4.62%, 5

PVIFA due, 4.62%, 5 = 4.5774759

   .
Present value of Lease payment= -63910 * 4.5774759 = -292546.48

.

Present value of Annual saving calculation

Annual saving = 30500

After tax saving = 30500 - 23% = 23485

PV of After tax annual saving =   After tax saving * PVIFA, 4.62%, 5

   PVIFA, 4.62%, 5 = 4.375335

PV of After tax annual saving = 23485 * 4.375335 = 102754.74

.

Net present value of lease = Present value of Lease payment + PV of After tax annual saving

Net present value of lease = -292546.48 + 102754.74 = -189791.74
          .

Depreciation tax benefit per year = Cost of asset/no of years* tax rate          
387000 / 5 *23% =   17825 ( depreciation tax shield )
Present value of tax benefit of depreciation =   depreciation tax shield    * PVIFA, 4.62%, 5
Present value of tax benefit of depreciation =  17825 * 4.375335 = 77990.35

.       

Present value of Annual saving calculation

Annual saving = 32500

After tax saving = 32500 - 23% = 25025

PV of After tax annual saving =   After tax saving * PVIFA, 4.62%, 5

   PVIFA, 4.62%, 5 = 4.375335

PV of After tax annual saving = 25025 * 4.375335 = 109492.76

.

Total cost of buying ( initial cash flow) = -387000

.

Net Present value of Buying = initial cash flow + PV of tax benefit of depreciation           + Present value of Annual saving

.

Net Present value of Buying = - 387000 + 77990.35 + 109492.76

Net Present value of Buying = -199516.89
.

      
Net advantage to leasing = Net Present value of lease - Net Present value of buying

.

Net Present value of lease =   -189791.74

Net Present value of buying =   -199516.89
.

Net advantage to leasing =     -189791.74 -   -199516.89 = 9725.15
          
So Net advantage to Lease is    $9725.15.

.

B. Farmer has a target debt-to-asset ratio of 62 percent.

.

PV of lease payment is the debt of farmer

PV of lease payment = 292546.48