Question

Two different companies provide maintenance services and their pricing offers are as follows: For both options, the initial payment is at the beginning of the contract, and the monthly payments are at the end of each month.

Company 1) An eight-year contract with an initial payment of $12,000, and $2,000/month for the first three years, a payment of $3000 at the end of year 3, and $2,500/month in years 4 to 8.

Company 2) A six-year contract, with an initial payment of $6,000, and $4,000/month.

Considering that the interest rate is 12% compounded monthly, which company provides a better offer?

Answer 1

Company 1:

Net Present Value of Cash Flow = Initial Payment + PV of payment for first 3 years + PV of Payment at the end of year 3 + PV of Payments for year 4 to 8

PV of Payment for first 3 years = P*[1-{(1+i)^-n}]/i = 2000*[1-{(1+0.01)^-36}]/0.01 = $60215.01

PV of Payment for years 4 to 8, at the end of 3rd year = P*[1-{(1+i)^-n}]/i = 2500*[1-{(1+0.01)^-48}]/0.01 = $94934.9

PV of 3rd year Payment and PV above PV = (3000+94934.9)/[(1+0.01)^36] = $39793.63

Net Present Value = 12000+60215.01+39793.63 = $112008.64

Company 2:

Net Present Value of Cash Flows = Initial Payment + PV of Monthly Payments

PV of Monthly Payments = P*[1-{(1+i)^-n}]/i = 4000*[1-{(1+0.01)^-72}]/0.01 = $204601.57

Net Present Value = 6000+204601.57 = $210601.57

As Company 1 has Lower Cost and also higher term of contract, Company 1 provides a better offer.