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IAI Actuarial Core Principles · Business Finance · Financial instruments issued or used by companies

A firm can buy a machine for Rs 10,00,000 or lease it for 5 annual payments of Rs 2,60,000 made at the start of each year. Its post-tax cost of debt is 10% and tax is ignored for the comparison. The present value of Rs 1 paid at the start of each of 5 years at 10% is 4.1699. Which conclusion is correct?

Buying is cheaper. The present value of the lease payments is 2,60,000 multiplied by 4.1699, about Rs 10,84,000, which exceeds the Rs 10,00,000 purchase cost, so leasing costs roughly Rs 84,000 more in present value terms.

  1. ALeasing is cheaper, as the present value of lease payments is about Rs 10,84,000
  2. BLeasing is cheaper, as the present value of lease payments is about Rs 9,50,000
  3. CBuying is cheaper, as the present value of lease payments is about Rs 10,84,000Correct
  4. DBuying is cheaper, as the present value of lease payments is about Rs 13,00,000
  5. The two are equal in present value terms

Explanation

PV of lease payments = 2,60,000 x 4.1699 = 10,84,174, about Rs 10,84,000. This exceeds the purchase price of Rs 10,00,000, so buying is cheaper. The 13,00,000 option simply sums payments undiscounted, and the 9,50,000 option is not supported by the data.

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