Leases R Us, Inc. (LRU) has been contracted by Robotics (RBH) to
provide lease financing for a machine that would assist in automating
a large part of their current assembly line. Annual lease payments
will start at the beginning of each year. The purchase price of this
machine is $200,000, and it will be leased by RBH for a period of 
years. LRU will utilize straight line depreciation of $40,000 per year
with a zero book salvage value.  However, salvage value is estimated
to actually be $35,000 at the end of 5 years. LRU is required to earn
a 14% after-tax rate of return on the lease. LRU uses a marginal tax
rate of 40%.  Calculate the annual lease payments (these payements are
to be considered at the beginning of each year-annuity due)

The net present value of the after-tax cash flows associated with the
lease must result in a 14% rate of return on the lease, meaning that
after purchasing the machine, LRU must net $200,000(0.14) or $28,000.

In Years 0-3, LRU buys the machine for $200,000 and receives the after
tax lease payment net of depreciation of L-(L-$40,000)*0.4 because the
lease is paid at the beginning of the year and the machine depreciates
during that year, generating a tax deduction.

In Year 4, LRU receives the after tax lease payment of only L-L*0.4
because the machine is already fully depreciated.

In Year 5, LRU receives the after tax salvage value of $35,000*0.6
that is a taxable gain because the machine was fully depreciated
earlier

Therefore, using the after tax rate of return as the discount value,
the net present value formula looks like this:

$28,000 = -$200,000 + L-(L-$40,000)*0.4+
[L-(L-$40,000)*0.4][1/(1.14)^1]+L-[(L-$40,000)*0.4][1/(1.14)^2]+L-[(L-$40,000)*0.4][1/(1.14)^3]+L-[L*0.4][1/(1.14)^4]+$35,000*0.6[1/(1.14)^5].

$228,000 = 0.6L-$16,000 + (0.6L-$16,000 )*.8772 + (0.6L-$16,000
)*.7695 + (0.6L-$16,000 )*.6750 + (0.6L-$16,000 )*.5921 + $18177.90.

$228,000 = 2.348L - $62620.8 + $18177.90

L = $116,018.06 (some rounding error is generated by not carrying more
digits of the time value of money reduction factor).

Sincerely,

Wonko

For information regarding the NPV formula, see:

"Primer on the Time Value of Money"
http://pages.stern.nyu.edu/~adamodar/New_Home_Page/PVPrimer/pvprimer.htm