Question

1. The Promoter Chairperson of a leading Jewellery chain in Kerala had recently procured a Corporate Jet. The purchase price of the Jet is $ 300 million and the pre-tax operational costs of the Jet is $ 50 million per annum. The management of the firm estimates that this asset will be under-utilized. The Jet can be used to fly the management also for important meetings in Mumbai and Delhi, which will reduce the current travel expenses of the management by $ 40 million. However, flying the management along with Chairperson would result in an additional pre-tax operational cost of $ 30 million per annum for the Jet. The management also estimates that this additional activity of flying the management team would force the Jet to be replaced in three years rather than four years, when used only by the Chairperson. Beyond its useful life, the Jet can be sold for $ 100 million, in both the scenarios. The use of corporate Jet is indispensable for the firm and will continue in the future. Assuming the Jet be depreciated using the straight line method to zero book value in both cases, the opportunity cost of capital to be 10%, the corporate tax rate to be 20%, which option should the firm choose?

please solve by formula method and not by excel method

Answer 1

1st option (Jet used only by Chairman for 4 years)

Operating cost per annum= $50 million

Annual Depreciation = $300 million/4 = $75 million

Annual Pre tax cost = $125 million

Annual Post tax cost = $125 million * (1-0.2) = $100 million

Add Depreciation = $75 million

Net annual cost = $25 million

Post tax salvage value in year 4 = $100 million * (1-0.2) = $80 million

So, Equivalent annual cost (EAC) of the option = $300*0.1/(1-1/1.1^4) + $25 - 80*0.1/(1.1^4-1) = $102.40 million

2nd option (Jet used only by both Chairman and management for 3 years)

Normal Operating cost per annum= $50 million

Additional Operating cost per annum= $30 million

Savings per annum = $40 million

Annual Depreciation = $300 million/3 = $100 million

Net Annual Pre tax cost = $140 million

Annual Post tax cost = $140 million * (1-0.2) = $112 million

Add Depreciation = $100 million

Net annual cost = $12 million

Post tax salvage value in year 3 = $100 million * (1-0.2) = $80 million

So, Equivalent annual cost (EAC) of the option = 300*0.1/(1-1/1.1^3) + 12 - 80*0.1/(1.1^3-1) = $108.47 million

As the EAC of the 1st option is only $102.40 million whereas that of the 2nd option is $108.47 million, it means that the 1st option of Jet being used only by Chairman is cheaper and should be selected. So, Jet should be used only by the Chairman