Question

1. Lease or Buy

You are deciding whether to lease or purchase a car. If you lease the car, your annual payments will be $7,400 for the next four years (due at year end). If you buy the car, you will pay $30,000 to purchase the car. You estimate the car will have a resale value of $12,000 at the end of four years. Assume the appropriate discount rate is 10%.

1. Should you lease or buy the car?

2. To answer this question, assume the NPV of the lease cost is $24,000. At what resale value in four years would you be indifferent between buying and leasing?

3. Instead of buying the car for your personal use, you are buying the car for your business. The annual lease payments of $7,400 can be deducted from taxable income. If you purchase the car, you can depreciate the car straight-line to zero book value over four years. The purchase price of the car is $30,000 and the resale value is $12,000. Your marginal corporate tax rate is 40%. If you are acquiring the car for business, should you buy or lease the car?

Answer 1

Ans Part 1.
Lease or Buy
Purchase cost of Car	$                 30,000
Lease PV:
Discount rate	10%
Lease term in years	4
PV annuity factor @10% for 4 years=(1-1.10^-4)/10%=	3.169865
PV factor @10% for 4 years =1/1.1^4=	0.68301

Let us find PV of Lease and Purchase options
Cash flow	Amt	PV annuity/PV factor	PV of Cash flow
Annual lease payment for 4 years	$                   7,400	3.169865	$               23,457.00
PV of Lease payments =			$               23,457.00
Car purchase
Purchase price	$                 30,000	1.000000	$               30,000.00
Resale Value ay yr 4 end	$               (12,000)	0.68301	$               (8,196.16)
Total PV of Cash flows for Cash purchase			$               21,803.84

So PV of Lease related cash flows =	$            23,457.00
NPV of Cash purchase	$            21,803.84
So Buying the car is preferable

Ans Part 2.
Cash purchase cost of car=	$            30,000.00
NPV of Lease cost	$            24,000.00
for indifference of buying & leasing, the PV of resale
value need to be $6,000
Assume the resale value is R.
PV factor @10% for 4 years =	0.68301
so R*0.68301=6000
R=6000/0.68301=	$              8,784.60
So requited Resale value is $8,784.60

Ans Part 3.
Given Tax rate =	40%
Annual Lease rental	$              7,400.00
Annual Tax savings from Lease rental expense=7400*40%=	$              2,960.00
Assuming 10% discount rate as before :
PV of Annual Tax savings for 4 years =2960*3.169865=	$              9,382.80
PV of lease rentals as calculated above =	$            23,457.00
Net PV of Lease rental over 4 years =23457-9382.8=	$           14,074.20
Purchase Price of car	$            30,000.00
Less salvage value	$            12,000.00
Depreciable value	$            18,000.00
Useful life in years	$                     4.00
Annual depreciation epense =18000/4=	$                   4,500
Annual depreciation tax savings =4500*40%=	$                1,800.0
PV of Annual Tax savings for 4 years =1800*3.169865=	$              5,705.76
PV of Cash purchase as net of salvage as calculated above =	$            21,803.84
NPV of Car purchase after adjusting PV of tax savinsg=21803.84-5705.76=	$           16,098.08
so for acquiring the car for business purpose , leasing is
better option as the net PV of lease and tax
savings is less than that of buying.