# Lease or Buy Decision

Lease or buy decision involves applying capital budgeting principles to determine if leasing as asset is a better option than buying it.

Leasing in a contractual arrangement in which a company (the lessee) obtains an asset from another company (the lessor) against periodic payments of lease rentals. It may typically also involve an option to transfer the ownership of the asset to the lessee at the end of the lease.

Buying the asset involves purchase of the asset with company’s own funds or arranging a loan to finance the purchase.

In finding out whether leasing is better than buying, we need to find out the periodic cash flows under both the options and discount them using the after-tax cost of debt to see where does the present value of the cost of leasing stands as compared to the present value of the cost of buying. The alternative with lower present value of cash outflows is selected.

## After-tax cash flows of lease

Determining periodic cash flows in case of leasing is easy. Most leases involve periodic fixed payments and an optional one-time terminal payment. They may also involve payment of insurance, etc. associated with the asset which also need to be accounted for. These payments have associated tax shield, i.e. they are allowed as deduction from the company’s taxable income which results in a decrease in net tax liability of the company.

Periodic after-tax cash flows of lease = (maintenance costs + lease rentals) * (1 – tax rate)

Terminal after-tax cash flows = periodic after-tax cash flows + amount paid at purchase the asset

## After-tax cash flows of purchase

The most significant component of cash outflows in case of purchase of asset is the payment for cost of the asset. If the company uses its own funds, the total cost is assumed to be paid at the time 0, however, if the company obtains a loan to finance the purchase, the loan repayment and associated tax shield on interest shall appear in all the periods of the lease analysis.

Other cash flows include the tax shield on depreciation, any potential savings, maintenances costs, insurance, etc. associated with the purchase and use of the asset.

Once we know the after-tax cash flows under both the alternatives, we just need to find present values for each option using the company’s after-tax cost of debt and choosing the option that has lower present value of cash outflows.

## Example

B-Tel, Inc. is a telecommunication services provider looking to expand to a new territory Z; it is analyzing whether it should install its own telecom towers or lease them out from a prominent tower-sharing company T-share, Inc.

Leasing out 100 towers would involve payment of $5,000,000 per year for 5 years.

Erecting 100 news towers would cost $18,000,000 including the cost of equipment and installation, etc. The company has to obtain a long-term secured loan of $18 million at 5% per annum.

Owning a tower has some associated maintenance costs such as security, power and fueling, which amounts to $10,000 per annum per tower.

The company’s tax rate is 40% while its long-term weighted average cost of debt is 6%. The tax laws allow straight-line depreciation for 5 years.

Determine whether the company should erect its own towers or lease them out.

## Solution

Annual cash out flows of leasing (Year 1 to Year 5) = $5,000,000 * (1 – 40%) = $3,000,000

Annual cash flows of purchasing have three components: the loan amount to be repaid in each period, the maintenance costs to be borne each year, the tax shields associated with maintenance costs, depreciation expense and interest expense. The following table summarizes the calculation of cash flows under this alternative.

Period | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|

Loan repayment | A | 4,157,546 | 4,157,546 | 4,157,546 | 4,157,546 | 4,157,546 |

Maintenance costs | B | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 |

Depreciation | D | 3,600,000 | 3,600,000 | 3,600,000 | 3,600,000 | 3,600,000 |

Interest expense | I | 900,000 | 737,123 | 566,101 | 386,529 | 197,978 |

Total tax deductions | T = B+D+I | 5,500,000 | 5,337,123 | 5,166,101 | 4,986,529 | 4,797,978 |

Tax shield @ 40% | t = 0.4×T | 2,200,000 | 2,134,849 | 2,066,441 | 1,994,612 | 1,919,191 |

Net cash flows | N = A+B–t | 2,957,546 | 3,022,697 | 3,091,106 | 3,162,935 | 3,238,355 |

Annual loan repayment is based on present value calculation; it is the amount paid at the end of each year for 5 years that would write off the loan completely. It is calculated using the following MS Excel function: PMT (5%,5,-18000000).

Interest expense are calculated in the following debt amortization table:

Period | Opening Principal | Total Repayment | Interest | Principal Repayment | Closing Principal |
---|---|---|---|---|---|

0 | 18,000,000 | - | - | - | 18,000,000 |

1 | 18,000,000 | 4,157,546 | 900,000 | 3,257,546 | 14,742,454 |

2 | 14,742,454 | 4,157,546 | 737,123 | 3,420,424 | 11,322,030 |

3 | 11,322,030 | 4,157,546 | 566,101 | 3,591,445 | 7,730,585 |

4 | 7,730,585 | 4,157,546 | 386,529 | 3,771,017 | 3,959,568 |

5 | 3,959,568 | 4,157,546 | 197,978 | 3,959,568 | - |

It is necessary to prepare amortization table because tax laws do not allow deduction of total loan amount, instead only interest expense is allowed as deduction.

Depreciation is calculated on straight-line basis using the 5-year useful life (i.e. $18,000,000/5 = $3,600,000).

Tax shield is subtracted from loan repayments and maintenance costs while calculating the net cash outflows because tax shield represents a cash inflow which arises due to tax deductibility of the expenses.

Now, we have to calculate the present value of cash outflows under both the options using the after-tax cost of debt which is 3.6% (6% * (1-40%))

Present value of leasing at 3.6% = $13,545,157

Present value of purchasing at 3.6% = $13,950,176

Since leasing has a lower present value of cash outflows, it should be the preferred option.

Written by Obaidullah Jan, ACA, CFA <--- Hire me on Upwork