Question

Tiong Nam Tonic (TNT) needs to expand its production capacity. To do so, the company must acquire a machine costing $120,000. The machine can be leased or purchased. The terms of the lease and purchase plans are as follows:- Lease: The leasing arrangement requires beginning-of-year payments of $40,000 over 4 years. Under the leasing arrangement, the lessee is required to insure the machine during the contract period. TNT insurance broker has informed that the annual insurance premium is about $1,200, on cash before cover basis. All other costs will be paid by the lessor. Purchase: If TNT were to purchase the machine, its cost of $120,000 will be financed with a 4-year loan, with a fixed annual repayment, interest calculated on a yearly rest basis. The after-tax cost of borrowing is 8.05%. The machine will be depreciated using straight line method towards a zero salvage value. TNT will pay $10,000 per year for the service contract that covers maintenance and other related costs. The lender, SME Bank, also requires TNT to insure the machine and the annual insurance premium and terms of payment is similar, as advised by TNT insurance broker. TNT plans to dispose the machine for an estimated value of $15,000 at the end of year 4. TNT cost of capital is 12% and its tax rate is 30%. Which alternative - lease or purchase - would you recommend?

Answer 1

Machine Cost = $120,000

Lease Conditions :
Start of year payment 40,000 for 4 years
Annual insurance premium = 1200, cash before cover basis

Purchase Condition :
Financed through 4 year loan
After tax cost of borrowing = 8.05%
Straight Line depreciation with 0 salvage value
Service contract = 10,000 per year
Insurance premium = 1200
Machine disposed at value = 15000

Cost of capital k = 12%
Tax Rate t = 30%

Leasing Option:
Cashflow from lease rental = -40,000
Cashflow from insurance premium = -1,200

Total Net cashflow per year = cashflow from lease rental + cashflow from insurance premium = -40,000-1,200 = -41,200

Also, these cashflow at the begining of the year, or can be assumed at the end of previous year.

PV of Cash flow at year n = Net Cash flow at year n/(1 + k)ⁿ
Net NPV of all cashflows = _{i = 1 to n} (PV of Cashflow at year i)

Calculations in excel will look like below. Formulas in excel are -

Values in Excel are -

Hence, net cost with leasing = $140,155.45

Using Purchase method:
We assume that loan principal repayment, interest payment and payment for service contract happens at the end of the year.
Also, remember that depreciation is a non-cash expense, so we need not consider this in cash flow calculation.

Loan at the end of year = Loan at beginning of year - Principal Repayment
Loan at the beginning of year = Loan at the end of previous year
Interest Cost = Loan at beginning of year * Interest Rate

Total Cashflow in an year = cashflow from loan repayment + cashflow from interest cost + cashflow from service contract + Cashflow from insurance premium + cashflow from salvage value.

Remember that in above equation other than salvage value, all other cashflows are negative.

PV of Cash flow at year n = Net Cash flow at year n/(1 + k)ⁿ
Net NPV of all cashflows = _{i = 1 to n} (PV of Cashflow at year i)

Excel formulas for above calculation look like below -

values in Excel look like below -

Hence, cost of Purchase option = $135,416.74.

Comparing 2 Options:
Cost Of Lease = $140,155.45
Cost of Purchase = $135,416.74

It is clear that Purchase option is less costly than the lease option, so company must go for purchase of the machine.