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a PV of
AfterTax
cost PV at 7% Cash Outflow
Year Payment Savings
0.9346 $ 80,005
$85,603
$85,603 0
0
3.3872 173,973
$85,603 $34,241 $51,362
14
(24,414)
5 $34,241 ($34,241) 0.7130
$229,564
Lease versus Purchase Decision. The Marijay Co. has selected a machine that will produce
8.38
substantial cost savings over the next 5 years. The company can acquire the machine by outright
purchase for $240,000 or a lease arrangement from the manufacturer.
Marijay could obtain a 5year loan from a local bank to pay for the outright purchase. The
bank would charge interest at an annual rate of 10 percent on the outstanding balance of the loan
and require Marijay to maintain a compensating balance equal to 20 percent of the outstanding
balance of the loan. The principal would be paid in five equal installments, and each annual
payment of principal and interest would be due at the end of each year. In addition to borrowing
the amount needed to purchase the machine, Marijay would have to obtain a loan to cover the
compensating balance required by the local bank.
A local financier and investor heard of Marijayâ€™s need and offered them an unusual
proposition. She would advance the company $240,000to purchase the machine if the company
would agree to pay her a lump sum of $545,450 at the end of 5 years.
The capital lease offered by the manufacturer would allow all the tax benefits of ownership
to accrue to Marijay. The title to the machine would be transferred to Marijay at the end of the
5 years at no cost. The manufacturer would be responsible for maintenance of the machine and
253
CHAP. 81 CAPITAL BUDGETING (INCLUDING LEASING)
has included $8,000per year in the lease payment to cover the maintenance cost. Marijay would
pay $70,175 to the manufacturer at the beginning of each year for the 5year period.
Calculate the beforetax interest rate for each of the three alternatives.
Without prejudice to your answer to (a),what arguments would you present to justify a lease
financing alternative even if that arrangement turned out to have a higher interest cost than
a regular loan?
Compare the relative effect that the three financing alternatives would have on Marijay's
current ratio at the end of the first year. (CMA, adapted.)
SOLUTION
The beforetax interest rates of return for each of the three alternatives are shown below.
For a local financier
principal  $240,000 o.44
PVIF,S = =
total payment $545,450
The beforetax interest rate is 18 percent, which is determined by finding the rate for a PVIF of
0.44 for year 5 in Appendix C.
For a lease:
Annual payment for leasing = $70,175 yearly payment  $8,000 maintenance = $62,175
To find the principal, subtract the first annual payment from the price of the machine, since this
payment is made at the beginning of the year. Therefore,
principal
PVIFA.4 =
annual payment

 $240,000  $62,175 = 2.8601
$62,175
From Appendix D, the beforetax interest rate is 15 percent for a PVIFA of 2.8601 at 4 years (4 years,
not 5, since payments are made at the beginning of each year).
For a purchase:
(2)
(2 t 1)
Interest
(1)
Compensating Principal (10%)on
Beginning Principal Effective
of Year Borrowed ($)" Balance (20%) ($) for Use (80%) ($) Borrowings ($) Rate (%)
1 300,000 60,000 240,000 30,000 14
2 240,000 48,000 192,(xx) 24,000 12;
36,000
3 180,OOO 144,000 18,000 12;
24,000
4 120,000 12,000 12;
96,000
5 60,000 12,000 48,000 60,000 123
"Onefifth of loan repaid each year at the end of the year.
Arguments justifying leases are as follows: The commitment for maintenance is limited, the cash
budgeting impact of maintenance is known, manufacturer may exchange the machine for improved
model at reduced rates, and financing alternatives are expanded.
The effect on the current ratio at the end of the first year differs according to the financing alternative.
For the financier there is no effect because the entire transaction is recorded as a longterm debt and
there is no current asset or current liability until the end of the fourth year. With a loan, the current
ratio will be lower than with the financier arrangement because there will be net cash outlays in the
first year and a current liability recorded at the end of the first year. If a lease is chosen, the current
ratio will be lower than both prior alternatives. There will be a greater net cash outlay in the first year
and a larger current liability recorded at the end of the first year.
Chapter 9
Capital Budgeting Under Risk
9.1 INTRODUCTION
Risk analysis is important in making capital investment decisions because of the large amount of
capital involved and the longterm nature of the investments being considered. The higher the risk
associated with a proposed project, the greater the rate of return that must be earned on the project to
compensate for that risk.
9.2 MEASURES OF RISK
Risk, a measure of the dispersion around a probability distribution, is defined as the variability of
cash flow around the expected value. Risk can be measured in either absolute or relative terms. First,
the expected value, A , is
i= 1
Ai = the value of the ith possible outcome
where
p i = the probability that the ith outcome will occur
n = the number of possible outcomes
Then, the absolute risk is measured by the standard deviation:
J 2 (Ai A ) 2 p i

=
U
i=l
The relative risk is measured by the coeficient of variation,which is CIA.(These three statistics were
also discussed in Chapter 7.)
EXAMPLE 9.1 The ABC Corporation is considering investment in one of two mutually exclusive projects.
Depending on the state of the economy, the projects would provide the following cash inflows in each of the next
5 years:
Proposal A
State Probability Proposal B
$1,000 $ 500
0.3
Recession
0.4
Normal $2,000
$2,000
Boom $3,000
0.3 $5,000
To compute the expected value (A), the standard deviation ( U ) , and the coefficient of variation, it is convenient
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