Question

Your firm specializes in the construction of short track speed skating ice rinks. The popularity of this sport at the Winter Olympics has resulted in lots of new business for your firm. To meet this demand, you've decided to buy or lease a new Terex tower crane for use over the next four years. You have two choices:
1)Buy the crane from Terex for $600,000 and sell it back to them in 48 months for $240,000.
2)Lease the crane from Terex for $11,000 per month for 48 months. If you choose to lease the crane, they will make the first and last payments on your behalf (so that you only have to make payments in months 2 through 47).
Your opportunity cost of capital is 0.8% per month. Should you lease or buy the new crane?

SHOW YOUR WORK, DO NOT USE EXCEl

Answer 1

We have following information -

Opportunity cost of capital (i) = 0.8% per month = 0.008

Life = 48 months.

1. Computation of Present worth of Buying the crane

Initial Purchase cost = $ 600,000

Sale price in 48 months = $ 240,000

Thus, Present worth (PW) of buying can be computed with following equation -

Thus, Present worth of Buying crane is $ 436,278.51

2. Computation of Present worth of leasing the Crane

Lease payment per month = $ 11,000

Payment are made only for 2nd month to 47th month

We can calculate PW of leasing crane with following equation -

Firstly we will calculate the Present value Annuity factor (PVAF) & Present value factor (PVF)

Putting the values in PW equation

Thus, Present worth leasing crane is $ 418,595.67

Conclusion - The Present worth of Leasing crane is less than buying crane which means leasing option would be cheaper. Thus. it is recommended to lease the new crane.

Hope this will help, if you need any further explanation please comment.