Question

A company is considering the possibility of acquiring new manufacturing unit for $6,000,000 cash. The scrap value is estimated to be $500,000 at the end of the 10-year life of the equipment. The firm could lease the equipment for $1,000,000 per year, payable at the start of each year. The equipment will be returned to the lessor at the expiry of the lease. If the firm can earn 15% pa on its capital, advise whether it should buy or lease.

Answer 1

For taking the decision on whether the firm should buy or lease the unit, we have to compare both scenarios in terms of the sum of present values of the total price which is to be paid. Since the life of the unit is 10 years, we are taking time duration in each scenario as 10 years.

Consider the first case, where the unit is acquired for $6,000,000 cash. In this case, in the 0^th year the payment is made (beginning of first year). Also, at the end of the 10^th year, the salvage value of the unit is $500,000, which can be realized at the end of tenth year. Considering the salvage value to be a negative value for the total price to be paid, we can obtain the present value of the total price to be paid by the firm, with a hurdle rate of 15% (as this is what the firm can earn on its capital). I have shown the present value of the total price to be paid in the below excel.

In the second case, when the unit is leased at $1,000,000 per year, the lease amount is to be paid at the start of each year. For calculation purposes, I have considered as the start of 1^st year as the 0^th year. So, at the start of the 10^th year, the firm would have paid the lease. Hence we will calculate the leased amount for the 0-9 year duration. Also, the hurdle rate in this case also would be 15%. Please see the excel below for calculations on both cases –

Please note that present value for an investment (P) invested in the nth year, with hurdle rate (R) is given by – P/((1+R)^N). So the present value of the salvage value of the unit after end of 10 years would be 500000/((1+15%)^10) = $123592.35. I have shown salvage value as negative with reference to price to be paid.

As we can see from the calculation, the present value for the scenario 1 is $5,876,407.65 whereas the present value of scenario 2 is $5,771,583.92. Since the present value of scenario 2 is less than the present value of scenario 1, the firm should lease the manufacturing unit.

Hope the explanation and the excel calculation answers your question.