Question

Amy was offered two options for a car she was purchasing:

• Lease option: Pay lease amounts of $400 at the beginning of every month for 6 years. At the the end of 6 years, purchase the car for $13,500.

• Buy option: Purchase the car immediately for $25,000.

The money is worth 7.40% compounded monthly.

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

Answer 1

Discounted cash flow of the Lease option = Present value of monthly lease payments + Present value of Cash paid to purchase the car at the end of 6th year

Calculation of Present value of monthly lease payments

As the lease payments are at the beginning of the month , we will use the present value of annuity due formula to calculate the present value.

Present Value of annuity due = P + P x {[1 - (1+r)^-(n-1)]/r}

Present value of annuity due = Present value of monthly lease payments = ?

P = monthly lease payment = $400

r = interest rate per month = 7.40%/12 = 0.006167

n = number of monthly lease payments = 6 years x 12 = 72

Present Value of annuity due = 400 + 400 x {[1 - (1+0.006167)^-(72-1)]/0.006167}

Present Value of annuity due = 400 + 400 x 57.35648

Present Value of annuity due = 400 + 22942.59

Present Value of annuity due = 23342.59

Present value of monthly lease payments = $23,342.59

Calculation of Present value of Cash paid to purchase the car at the end of 6th year

Present value = Cash paid x discount factor @7.40% for 6th year

Present value = $13,500 x (1+0.074)^-6

Present value = $13,500 x 0.65159

Present value = 8796.46

Present value of Cash paid to purchase the car at the end of 6th year = $8,796.46

Discounted cash flow of the Lease option = $23,342.59 + $8,796.46

Discounted cash flow of the Lease option = $32,139.06