JSC Corporation is attempting to determine whether to lease or
purchase research equipment.  The firm is in the 30% tax bracket, and
its after-tax cost of debt is currently 7%.  The terms of the lease
and the purchase are as follows:

Lease Scenario:         Annual end-of-year lease payments of $25,200
are required over the 3-year life of the lease.  All maintenance costs
will be paid by the lessor; insurance and other costs will be borne by
the lessee.  The lessee will exercise its option to purchase the asset
for $5,000 at termination of the lease.

 

Purchase Scenario:    The research equipment, costing $60,000, can be
financed entirely with a 14% loan requiring annual end-of-year
payments of $25,844 for 3 years.  The firm in this case will
depreciate the asset under MACRS using a 3-year recovery period.  The
firm will pay $1,800 per year for a service contract that covers all
maintenance costs; insurance and other costs will be borne by the
firm.  The firm plans to keep the equipment and use it beyond its
3-year recovery period.

 

a)      Calculate the after-tax cash outflows associated with each alternative.

b)      Calculate the present value of each cash outflow stream using
the after-tax cost of debt.

c)      Which alternative, lease or purchase, would you recommend?  Why?

Hi!!


Lease Scenario:

For each year we have the following:
Payments (Pi) of $25,200
Because the lease payments are tax-deductible at a rate of 30%, there
are a recovery from taxes of ($25,200 * 0.30) = $7,560 .
At the end of the third year there is a payment of $5,000 (the use of
the option to purchase the asset).
the cash outflows for each year are:
CF1 = -$25,200 + $7,560 = -$17,640
CF2 = -$25,200 + $7,560 = -$17,640
CF3 = -$25,200 + $7,560 -$5,000 = -$22,640

At the after-tax cost of debt (A) of 7% we have that:
         CF1           CF2            CF3        
PV  = ---------  +  ----------  +  ----------  =
      (1 + A)^1     (1 + A)^2	   (1 + A)^3    

    = (-$16,485.98) + (-$15,407.46) + (-$18,480.98) =

    = -$50,374.42

          -----------------------

Purchase Scenario:

For each year we have:
Payment (Pi) of  $25,844 .
Mantenaince Costs of $1,800 .

Depreciation (MACRS 3-Years recovery period):
The MACRS 3-Years recovery period is a variation on the Declining
Balance with conversion to Straight Line method: it uses 200%
declining balance method but it changes to straight-line when that
method provides an equal or greater deduction.
Straight line depreciation estimates a depreciation for each of the 3
years of $20,000, then MACRS 3-Years recovery period results in:
D1 = 2 * $60,000/3 = $40,000 (>$20,000)
D2 = 2 * ($60,000 - $40,000)/3 = $13,333 (<$20,000) ==> D2 = $20,000
D3 = 0
For references on this depreciation method see the "Double Declining
Balance Depreciation Method": (see pages 1 and 2)
http://beginnersinvest.about.com/cs/investinglessons/l/bldbldeclinebal.htm


Since depreciation is tax deductible at a tax rate of 30%, we will
have depreciation tax credits (DTC) of (0.30 * Di) each year:
DTC1 = $12,000
DTC2 = $6,000
DTC3 = $0


The loan payments are composed of a principal payment of $20,000 and
an interest payment of $5,844 at the end of each year. At this point
we are focused in the interests' tax credits (ITC) that result in a
value of (0.30 * $5,844) for each year.
ITC1 = ITC2 = ITC3 = $1,753.20

In this scenario the cash outflows are:
CF1 = -$25,844 - $1,800 + $12,000 + $1,753.20 = -$13,890.80
CF2 = -$25,844 - $1,800 + $6,000 + $1,753.20 = -$19,890.80
CF3 = -$25,844 - $1,800 + $0 + $1,753.20 = -$25,890.80

At the after-tax cost of debt (A) of 7% we have that:
         CF1           CF2            CF3        
PV  = ---------  +  ----------  +  ----------  =
      (1 + A)^1     (1 + A)^2	   (1 + A)^3    

    = (-$12,982.06) + (-$17,373.40) + (-$21,134.61) =

    = -$51,490.07


        ------------------------

The PVs are both negative but differs in magnitude; their sign are
reflecting PVs of expenditures, in this situation the shortest
negative PV is the better option. In this case is the lease option. We
have just found that it is less expensive to lease the equipment than
purchase it.


I hope that this helps you. Feel free to request for a clarification
if you find something unclear.

Regrds,
livioflores-ga