Question

The bank will pay an interest of 10 percent annually. What must Ali’s semi-annual deposit be? A construction company called Albinaa Group is considering buying new machinery for one of its projects. Leasing Company, which deals in heavy machinery, owns that particular equipment and is looking to sell it for $425,000. Albinaa Group offered to buy it today and pay $600,000 over 3 years at a discount rate of 10 percent. Should Leasing Company accept Albinaa’ offer? Why or why not?

Answer 1

Sol :

To determine Albinaa's semi-annual deposit as follows,

Future value (FV) = $600,000

Rate (r) = 5% (Semiannual) 10% / 2 = 5%

Period (n) = 3 years (Semiannual) = 3 x 2 = 6

Semi-annual deposit = FV / (((1 + r)^n - 1) / r)

Semi-annual deposit = $600,000 / (((1 + 5%)^6 - 1) / 5%)

Semi-annual deposit = $88,210.48

Albinaa's semi-annual deposit is $88,210.48

Now to determine present Value of the offer as follows.

Equipment value = $425,000

Semi-annual deposit = $88,210.48

Semiannual rate r = 5%

Period n = 6

Present Value (PV) = Semi-annual deposit x (1 - (1 + r)^-n)/r

PV = $88,210.48 x (1 - (1 + 5%)^-6)/5%

PV = $447,729.24

The present value of the offer is $447,729.24

The Leasing Company should not accept Albinaa's offer as the present value of the offer is less than the value of the equipment.