Question

1. Your firm is purchasing a new telephone system that will last for four years. You can purchase the system for an up-front cost of $150,000, or you can lease the system from the manufacturer for $4,000 paid at the end of each month. The lease price is offered for a 48-month lease with no early termination – you cannot end the lease early. Your firm can borrow at an interest rate of 6% APR with monthly compounding. Should you purchase the system outright by paying $150,000 now or pay $4,000 per month?

   		You should choose to pay $4,000 per month.
   		You should choose to purchase the system outright by paying the upfront cost of $150,000.
   		You can either choose to purchase the system outright by paying the upfront cost of $150,000 or choose to pay $4,000 per month, because the present values of these two choices are the same.
   		None

Answer 1

The present value of the leasing alternative is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 6% / 12 (Since the interest is compounded monthly, hence divided by 12)

= 0.5% or 0.005

So, the present value will be computed as follows:

= $ 4,000 x [ (1 - 1 / (1 + 0.005)⁴⁸ ) / 0.005 ]

= $ 4,000 x 42.58031778

= $ 170,321.2711

The present value of upfront value of $ 150,000 will be $ 150,000 since it is paid upfront or today.

So, the correct answer is option of You should choose to purchase the system outright by paying the upfront cost of $150,000 since the present value of cost of paying upfront is less than the present value of cost of leasing alternative.

Feel free to ask in case of any query relating to this question