Question

Chad was offered two options for a car he was purchasing:

• Lease option: Pay lease amounts of $400 at the beginning of every month for 4 years. At the the end of 4 years, purchase the car for $10,500.

• Buy option: Purchase the car immediately for $23,500.

The money is worth 7.70% compounded monthly.

a. What is the Discounted Cash Flow (DCF) for the lease option?

b. Which is the better option?

Lease Option or Buy Option

Answer 1

(a) Discounted Cash Flow of Lease option comprise of 2 parts-

(i) PV of monthly payments calculated as that of an Annuity Due. The amount arrived at is $16,585.40 as follows:

(ii) Preset value of terminal payment of $10,500 at the end of 4 years, which is arrived at $7,724.21 as follows:

PV= FV/(1+r)^n Where FV= Future Value ($10,500), r= rate of interest per period (7.7%/12 =0.00641667) and n= number of months (48)

Therefore, PV= $10,500/(1.00641667)^48 = $10,500/1.35936277 =$7,724.21

Total Discounted Cash Flow of Lease Option= $16,585.40 + $7,724.21 = $24,309.61

(b)  Since immediate purchase of the car costs only $23,500 which is less than the discounted value of lease option ($24,309.61), immediate purchase is the better option.