Question

Q3: A computer dealer offers to lease a system to you for $100 per month for three years. At the end of three years, you have the option to buy the system for $700. You will pay at the end of each month. He will sell the same system to you for $1,200 cash. If the going interest rate is 10%, which is the better offer?

(I want to solve the method by law and not by using Excel)

Answer 1

So we need to calculate the present value of the first option and then we can compare it with the second option. The one which will be cheaper should be opted for.

The discount rate used for the first option will be 10%. But it will be converted to monthly by 10%/12 and period will be 3*12 = 36 months.

NPV of option 1 i.e. lease and buy = 100/(1+0.1/12)^1 + 100/(1+0.1/12)^2 + 100/(1+0.1/12)^3 + 100/(1+0.1/12)^4 + 100/(1+0.1/12)^5 + 100/(1+0.1/12)^6 +.................100/(1+0.1/12)^36 + 700/(1+0.1/12)^36

The above series is a GP series, whose sum can be calculated by using the sum of GP formula.

NPV = 100/(1+0.1/12)^1 { (1 - 1/(1+0.1/12)^36)/(1 - 1/(1+0.1/12)) } + 700/(1+0.1/12)^36 = 3618.341

So the first option is way costlier than the second option. So the second option i.e. buying for 1200 cash is recommendable.