Question

LuLuLime (LLL) is a company that sells modern equipment. To purchase a new equipment for your company from LLL, you as a financial manager have narrowed down two equipment models which meet your performance requirements equally. However, the schedule of payments of two models are different.

Model A requires yearly payment of $15,000 for 5 years with the first payment to be made today.

Model B requires yearly payment of $15,500 for 5 years with the first payment to be made end of year 1.

Given yearly interest rate of 5.5%, which model would you recommend to purchase and why?

Answer 1

Present Value of Model A

P = Yearly payment = $15,000

n = 5 years

r = interest rate = 5.5%

Present Value of the payments = P + [P * [1 - (1+r)^-(n-1)] / r]

= $15,000 + [$15,000 * [1 - (1+5.5%)^-(5-1)] / 5.5%]

= $15,000 + [$15,000 * 0.192783257 / 0.055]

= $15,000 + $52,577.252

= $67,577.252

Present value of payments for Model A is $67,577.25

Present Value of Model B

P = Yearly payment = $15,500

n = 5 years

r = interest rate = 5.5%

Present Value of the payments = [P * [1 - (1+r)^-(n-1)] / r]

= [$15,500 * [1 - (1+5.5%)^-5] / 5.5%]

= [$15,500 * 0.234865646/ 0.055]

= $66,189.4093

Present value of payments for Model B is $66,189.41

Model B should be choosed since Present value of payments for Model B is lower than Model A