PLEASE PROVIDE CASH FLOW DIAGRAM AND SHOW ALL WORK! 3. Automobile dealers are in

Question

PLEASE PROVIDE CASH FLOW DIAGRAM AND SHOW ALL WORK!

3. Automobile dealers are increasingly advertising the leasing of vehicles in lieu of purchasing. In one case, a $20,000 automobile can be leased for $375 per month for 36 months, after which it is returned to the dealer. If the automobile is purchased, it could be financed for 3 years at a 10 percent annual rate with a down payment of 5 percent and 36 equal monthly payments. If at the end of the 36-month period the vehicle is estimated to be worth $8,000, which would be the preferred alternative? Assume that the time value of money to the buyer is also 10 percent per annum. Answer - it is cheaper to lease. The present value of the lease is $11,628, and the present value of the purchase is $14,065.

Explanation / Answer

Solution:

We need to first calculate the Present Value of Both the options i.e. Lease the vehicle or Purchase

Present Value of Lease

Monthly Lease = $375

Number of payments (n) = 36

Annual Interest Rate = 10% or 0.10

Monthly Interest Rate (R) = 0.10/12 = 0.0083

It is the problem of Ordinary Annuity. We need to find out the Present Value of Annuity factor at 0.83% for 36 period

PVIFA (R, n) = (1 – 1/(1+R)n) / R = (1 – 1/(1+0.0083)n) / 0.0083 = 31.00928

Present Value of Lease Rental = Monthly Lease x PVIFA (0.83%, 36) = 375 x 31.00928 = $11,628

Alternative 2 -- Present Value of Purchase

Cost of Vehicle as on today

$20,000

Less: Present Value of Salvage of Vehicle (Refer Note 1)

($5,944)

Present Value of Purchase the vehicle

$14,056

Note 1 – at the end of the period i.e. 36 months the vehicle is estimated to be worth $8,000. It means estimated sale value of vehicle at the end of 36 month is $8,000. It is a cash inflow. We need to find out the Present Value of this $8,000 as on today to find out the net present value of alternative 2.

Present Value interest factor for 36 period at 0.83% = 1 / (1+R)n = 1/(1+0.0083)36

= 0.742623

Present Value of Salvage Value = $8,000 x 0.743 = $5,944

Note --- Present value may be vary due to rounding off of PV factor.

Since, the Present Value of Net Cash Outflow of Lease Payment is less than Purchase, it is cheaper to LEASE.

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Cost of Vehicle as on today

$20,000

Less: Present Value of Salvage of Vehicle (Refer Note 1)

($5,944)

Present Value of Purchase the vehicle

$14,056

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