Solution manual financial management 10e by keown chapter 24

CHAPTER 24

Term Loans and Leases
CHAPTER ORIENTATION
The first section of this chapter provides an overview of the major sources of term loans
and their characteristics. The second section of the chapter provides an overview of lease
financing, including a discussion of leasing arrangements, the accounting treatment of
financial leases, the lease versus purchase decision, and the potential benefits from leasing.

CHAPTER OUTLINE
I.

Term loans
A.

In general, term loans have maturities from one to 10 years and are repaid in
periodic installments over the life of the loan. Term loans are usually
secured by a chattel mortgage on equipment or a mortgage on real property.
The principal suppliers of term credit include commercial banks, insurance
companies and, to a lesser extent, pension funds.

B.

The common attributes of term loans include the following:
1.

2.

The maturities of term loans are usually as follows:
a.

Commercial banks: 1 to 5 years.

b.

Insurance companies: 5 to 15 years.

c.

Pension funds: 5 to 15 years.

The collateral backing term loans:
a.

Shorter maturity loans are usually secured with a chattel
mortgage on machinery and equipment or securities such as
stocks and bonds.

b.

Longer maturity loans are frequently secured by mortgages
on real estate.

65


3.

II.

In addition to collateral, the lender on a term loan agreement will

often require restrictive covenants that are designed to maintain the
borrower's financial condition on a par with that which existed at the
time the loan was made.
a.

Working capital restrictions involve maintaining a minimum
current ratio that reflects the norm for the borrower's
industry, as well as the lender's desires.

b.

Additional borrowing restrictions prevent the borrower from
increasing the amount of debt financing outstanding without
the lender's approval.

c.

A third covenant that is very popular requires that the
borrower supply periodic financial statements to the lender.

d.

Term loan agreements often include a key-man provision that
the borrower requires that the lender approve major personnel
changes and insure the lives of "key" personnel with the
lender named as the beneficiary.

4.

Term loans are generally repaid in periodic installments in

accordance with repayment schedules established by the lender. Each
installment includes both an interest and a principal component.

5.

Frequently a bank will have demand for loans that exceeds its
lending capacity. In order to satisfy the demand, the bank will share
the loan demand with other participating banks. The participating
banks receive a certificate of participation and a commitment from
the lead bank to pay a portion of the loan cash flows as they are
received.

6.

Eurodollar loans are intermediate term loans made by major
international banks to businesses based on foreign deposits
denominated in dollars. The rate of the loan is an amount greater
than the London Interbank Offered Rate. The Eurodollar loan
market is governed by a limited number of regulations.

Leasing
A.

There are three major lease agreements: direct leasing, sale and leaseback,
and leveraged leasing.
1.

In a direct lease the firm acquires the services of an asset it did not
previously own. Direct leasing is available through a number of
financial institutions, including manufacturers, banks, finance

companies, independent leasing companies, and special-purpose
leasing companies. Basically, direct leasing involves the purchase of
the asset by the lessor from a vendor and leasing the asset to the
lessee.

2.

A sale and leaseback arrangement occurs when a firm sells land,
buildings, or equipment that it already owns to a financial institution
and simultaneously enters into an agreement to lease the property

66


back for a specified period under specific terms. The lessee firm
receives cash in the amount of the sales price of the asset sold and
the use of the asset over the term of the lease. In return, the firm
must make periodic rental payments throughout the term of the lease
to the lessor.
3.

B.

C.

In a leveraged lease a third participant is added who finances the
acquisition of the asset to be leased for the lessor. From the lessee's
standpoint, this lease is no different from the two lease arrangements
discussed above. But with a leveraged lease, specific consideration is
given to the financing arrangement used by the lessor in acquiring

the asset to be leased.

The accounting profession through Financial Accounting Statement No. 13
requires the capitalization of any lease that meets one or more of the
following criteria:
1.

The lease transfers ownership of the property to the lessee by the end
of the lease term.

2.

The lease contains a bargain repurchase option.

3.

The lease term is equal to 75 percent or more of the estimated
economic life of the leased property.

4.

The present value of the minimum lease payments equals or exceeds
90% of the excess of the fair value of the property over any related
investment tax credit retained by the lessor.

The lease–versus-purchase decision requires a standard capital budgeting
type of analysis, as well as an analysis of two alternative "packages" of
financing. Two models are used to evaluate the lease versus purchase
decision.
1.

The first model computes the net present value of the purchase
option which can be defined as follows:
n

NPV (P)

=

ACF

t

t
t  (1  K)

- IO

1

where ACFt

= the annual after-tax cash flow resulting from the
asset’s purchase in period t

K

= the firm's cost of capital applicable to the project
being analyzed and the particular mix of financing
used to acquire the project

IO

= the initial cash outlay required to purchase the
asset in period zero (now)

n

= the productive life of the project

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2.

In the second model a net advantage to lease (NAL) over purchase
equation is used that indicates the more favorable (least expensive)
method of financing. The equation used to arrive at NAL is as
follows:
n

NAL =

O t (1 - T) - R t (1 - T) - TI t - TD t
(1  rb ) t
1


t
-

Vn
(1  K s ) n

+ IO

where Ot

=

any operating cash flows incurred in period t that are
incurred only when the asset is purchased. Most often
this consists of maintenance expenses and insurance
that would be paid by the lessor.

Rt

=

the annual rental for period t.

T

=

the marginal tax rate on corporate income.

It

=

the tax deductible interest expense foregone in period t
if the lease option is adopted. This level of interest
expense was set equal to that which would have been
paid on a loan equal to the full purchase price of the
asset.

Dt

=

depreciation expense in period t for the asset.

Vn

=

the after-tax salvage value of the asset expected in year
n.

Ks

=

the discount rate used to find the present value of V n.
This rate should reflect the risk inherent in the
estimated Vn. For simplicity, the after-tax cost of
capital is often used as a proxy for this rate.

IO

=

the purchase price of the asset which is not paid by the
firm in the event the asset is leased.

rb

=

the after-tax rate of interest on borrowed funds. This
rate is used to discount the relatively certain after-tax
cash flow savings accruing through leasing the asset.

If NAL is positive, there would be a positive cost advantage to lease
financing. If NAL is negative, then purchasing the asset and
financing with a debt plus equity package would be the preferred
alternative. However, we would lease or purchase the asset in
accordance with the value of NAL in only two circumstances:
a.

If NPV(P) is positive, then the asset should be acquired
through the preferred financing method as indicated by NAL.
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b.

D.

If NPV(P) is negative, then the asset's services should be
acquired via the lease alternative only if NAL is positive and
greater in absolute value than NPV(P). That is, the asset
should be leased only if the cost advantage of leasing (NAL)
is great enough to offset the negative NPV(P). In effect, if a
positive NAL were to more than offset a negative NPV(P),
then the net present value through lease would be positive.

Over the years a number of potential benefits have been offered for lease
financing. Some of the more frequently cited advantages are enumerated and
commented upon here.
1.

Flexibility and convenience. It is often argued that lease financing is
more convenient than other forms of financing because smaller
amounts of funds can be raised at lower cost. In addition, it is often
argued that lease payment schedules can be made to coincide with
cash flows generated by the asset. These may or may not be real
advantages. It depends on the actual circumstances faced by the
lessee firm.

2.

Lack of restrictions. It has been argued that leases require fewer
restrictions on the lessee than do debt agreements.

3.

Avoiding the risk of obsolescence. This argument is generally
conceded to be fallacious because the lessor includes his or her

estimated cost of obsolescence in the lease terms.

4.

Conservation of working capital. Here it is argued that leasing
involves no down payment. However, the borrower could obtain the
same effect by borrowing the down payment.

5.

100-percent financing. The lease involves 100% financing but
purchasing the asset would surely involve some equity. As we noted
above, the down payment could be borrowed to produce 100%
financing via a loan. In addition, it is not clear that 100% lease
financing is desirable because it represents 100% non-owner
financing. Finally the lease agreement does not entitle the lessee to
the asset's salvage value. Thus, the lease provides 100% financing
for the "use value" of the asset but not its "salvage value."

6.

Tax savings. The difference in tax shelters between leasing and other
forms of financing can only be evaluated by using a net advantage of
lease model as we discussed earlier.

7.

Ease of obtaining credit. Lease financing may be more or less
difficult to obtain than other forms of financing. This advantage (or
disadvantage) can only be evaluated on a case-by-case basis.

69


ANSWERS TO
END-OF-CHAPTER QUESTIONS
24-1. Intermediate-term financing includes all those financing arrangements with final
maturities longer than one year and with a maximum of ten years. Short-term
financing is for a period of less than one year and long-term financing generally
involves a period of more than ten years.
24-2. The major types of restrictions usually found in the covenants of term loan
agreements include:
(1)

Working capital requirement. This restriction involves maintaining a
minimum amount of working capital. Very often this restriction takes the
form of a minimum current ratio such as 2 to 1 or 3 1/2 to 1, or a minimum
level of net working capital such as $200,000.

(2)

Additional borrowing. Generally, this type of restriction will require the
approval of the lender before any additional debt is issued. The restriction is
often extended to long-term lease agreements.

(3)

Periodic financial statements. A standard covenant in most term-loan
agreements involves supplying the lender with periodic financial statements.
These usually include annual or quarterly-income statements and balance

sheets.

(4)

Management. Term-loan agreements will sometimes include a provision
requiring prior approval by the lender of major personnel changes. In
addition, the borrower may be required to insure the lives of certain "key"
personnel with the lender named as beneficiary.

24-3. (1)

In a direct leasing agreement the firm acquires the services of an asset it did
not previously own. The lease basically involves purchase of the asset by
the lessor from a vendor and leasing it to the lessee.

(2)

Sale and leaseback arrangements arise when a firm sells land, buildings, or
equipment which it already owns to a financial institution and
simultaneously enters into an agreement to lease the property back for a
specified period under specific terms.

(3)

A net-net lease requires that the lessee maintain the leased asset and return it
to the lessor at the end of the lease term with a value equal to a preestablished amount.

(4)

An operating lease constitutes a cancelable contractual commitment on the

part of the firm leasing the asset (the lessee) to make a series of payments to
the firm which actually owns the asset (the lessor) for use of the asset.

70


24-4. Prior to January, 1977, most financial leases were not included in the balance sheets
of lessee firms. They were instead reported in the footnotes to the balance sheet in
accordance with APB Opinions 5 and 31. In November, 1976, the accounting
profession reversed its long standing position with Statement of Financial Account
Standards No. 13 entitled "Accounting for Leases." Specifically, Statement 13
requires that any lease which meets one or more of the following criteria be
included in the body of the balance sheet of the lessee:
(1)

The lease transfers ownership of the property to the lessee by the end of the
lease term.

(2)

The lease contains a bargain repurchase option.

(3)

The lease term is equal to 75 percent or more of the estimated economic life
of the leased property.

(4)

The present value of the minimum lease payments equals or exceeds 90

percent of the excess of the fair value of the property over any related
investment tax credit retained by the lessor.

24-5. The potential benefits from lease financing include:
(1)

Flexibility and convenience. First, it is argued that leasing provides the firm
with flexibility because it allows for piece-meal financing of relatively small
asset acquisitions.
Second, leasing may allow a division or subsidiary manager to acquire
equipment without the approval of the corporate capital budgeting
committee.
Third, some lease payment schedules may be structured to coincide with the
revenues generated by the asset, or they may be timed to match seasonal
fluctuations in a given industry.
Arguments for the greater convenience of leasing may take many forms. It
is sometimes stated that leasing simplifies bookkeeping for tax purposes
because it eliminates the need to prepare time-consuming depreciation tables
and subsidiary fixed asset schedules. It is also pointed out that the fixed
payment nature of lease rentals allows more accurate forecasting of cash
needs. Finally, it is frequently noted that leasing allows the firm to avoid
the "problems" and "headaches" associated with ownership.

(2)

Lack of restrictions. Lease contracts generally do not contain protectivecovenant restrictions. Furthermore, it is sometimes possible to exclude lease
payments from the firm's debt commitments in calculating financial ratios
under existing covenants.

(3)

Avoiding the risk of obsolescence. This argument states that a lease is
advantageous because it allows the firm to avoid the risk that the equipment
will become obsolete. In actuality, the risk of obsolescence is passed on to
the lessee in any financial lease, except in cases of operating cancelable
operating leases, in which it is sometimes possible to avoid the risk of
obsolescence.

71


(4)

Conservation of working capital. The argument for conservation is that a
lease does not require an immediate outflow of cash to cover the full
purchase price of the asset and, therefore, the funds are retained in the
business.

(5)

100 percent financing. Another alleged benefit of leasing is embodied in the
argument that a lease provides the firm with 100 percent financing. It is
pointed out that the borrow-and-buy alternative generally involves a down
payment, whereas leasing does not.

(6)

Tax savings. It is also argued that leasing offers an economic advantage in
that the tax shield generated by the lease payments usually exceeds the tax
shield from depreciation that would be available if the asset were purchased.

(7)

Ease of obtaining credit. This alleged advantage of leasing concerns
assertion that firms with poor credit ratings are able to obtain assets through
leases when they are unable to finance the acquisitions with debt capital.

SOLUTIONS TO
END-OF-CHAPTER PROBLEMS
Solutions to Problem Set A
24-1A.
Interest Rate
Face Amount
Year
0
1
2
3
4
5

10.0%
$325,000.00

Payment

Interest

Principal

50,000.00
50,000.00
50,000.00
50,000.00
268,160.75

32,500.00
30,750.00
28,825.00
26,707.50
24,378.25

17,500.00
19,250.00
21,175.00
23,292.50
243,782.50

Balance
325,000.00
307,500.00
288,250.00
267,075.00
243,782.50
0

Thus, the fifth year balloon payment will equal the principal remaining at the end of
that year of $243,782.50 plus interest for the year of $24,378.25 for a total of
$268,160.75.
24-2A.

Interest Rate
Equipment Price
Number of Payments
Rental Payment

12.0%
100,000.00
10
15,802.16

Present Value of the
Rental Payments

$100,000.00

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5

24-3A.

$100,000 = Payment
Payment =

1


t
t 1 (1.18)

$100,000
= $31,979.53
3.127

24-4A.
Year
1
2
3
4
5

Payment
$31,979.53
31,979.53
31,979.53
31,979.53
31,979.53

Interest
$18,000.00
15,483.68
12,514.43
9,010.71
4,876.33

Principal
$13,979.53
16,495.85

19,465.10
22,968.82
27,103.20

Remaining
Balance
$86,020.47
69,524.62
50,059.52
27,090.70
(12.50)

Rounding errors produced a $12.50 difference in the remaining balance and
principal portion of the fifth year payment.
5

24-5A. (a)

$200,000 = $59,663

1


t
t 1 (1  r)

where r = the effective annual rate on the computer sales firm loan.
5

1


t
t 1 (1  r)

=

$200,000
59,663

= 3.352

Looking in the annuity present value table we find that an r of 15% for a
five year loan is 3.352. Thus, the effective rate on the loan is 15%.
5

(b )

(c)

$250,000

= Payment

Payment

=

$250,000

= $385,080

1
(1  r)

5

Thus, r
(d)

24-6A.

$250,000
3.274

=

$250,000
$385,080

=

9%.

1


t
t 1 (1.16)
= $76,359.19

1
(1  r)5
= .6492

The effective rate of interest is lowest on the insurance company loan. In
addition, the insurance company loan does not require an interim principal
or interest payment during the five-year period.
Bank Loan Alternative: Cost = 14%
73


Manufacturer Financing Alternative:
The cost of this alternative is not immediately apparent and must be
calculated.
We know that the following relationship holds for any equal payment
installment loan:
n
1
Loan Amount = Payment 
t
t 1 (1  k)
where n is the term of the loan and k is the rate of interest charged on the
remaining loan balance.
Using this relationship we can define
4

$400,000
4

Therefore,

= $140,106
1


t
t 1 (1  k)

1


t
t 1 (1  k)

$400,000
$140,106

=

= 2.855

We now know the present value of an annuity factor that corresponds to a
four-year period and the rate of interest on the loan (k). Looking up this
factor in the annuity present value table, we find that k = 15 percent.
Therefore, the bank loan alternative is preferred.
24-7A.(a)

Evaluating the purchase alternative:
IO = $20,000
Annual net cash flows:

Annual cash savings
Less: depreciation
Net revenues before taxes
Less: taxes (50%)

Book profits
$6,000
(4,000)

Cash flows
$6,000

2,000
(1,000)

6,000
(1,000)

Plus: salvage value

$5,000
4,000

Annual after-tax cash flow (4)

$9,000

4

NPV

= $5,000

1


t +
t 1 (1.12)

$4,000

1
(1.12) 4

- $20,000

= $5,000 (3.037 )+ $4,000 (0.636) - $20,000
= $15,185 + $2,544 - $20,000
= $17,729 - $20,000 = $-2,271
Thus, the asset should not be purchased.
(b)

Evaluating the lease alternative:
Calculating principal and interest on a loan of $20,000 at 10%.
74


4

Annual payment = $20,000 /

Year
0
1
2
3
4

1


t =
t 1 (1.10)

$6,309.15

Payment

Interest

Principal

$6,309.15
6,309.15
6,309.15
6,309.15

$2,000.00
1,569.09
1,095.08
573.67

$4,309.15
4,740.06
5,214.07
5,735.48

Remaining Balance
$20,000.00
15,690.85
10,950.79
5,736.72
1.24

Rounding errors produced a $1.24 difference in the remaining balance and principal portion
of the fourth year payment.
4

(1)

Year
1
2
3
4

Solving for


t 1

Ot(1-T) - R(1-T)
$500
500
500
500

$3,000
3,000
3,000
3,000

O t (1  T)  R t (1  T)  I t T  D t T
(Term one)
(1  rb ) t
-

It T
$1,000
785
548
287

Vn
(1  k s ) n

(2)

Solving for -

(3)

Adding IO

(4)

Net advantage of leasing

-

DtT
$2,000
2,000
2,000
2,000

Discount
= SUM Factor
5%
-$5,500
0.952
- 5,285
0.907
- 5,048
0.864
- 4,787
0.823

Present
Value
-$ 5,236

- 4,794
- 4,361
- 3,940

(Term one)

=

-$18,331

(Term two)

=

-2,544
20,000
($875)

Since the asset's NAL is negative, the asset should not be leased.

75


24-8A.(a) The basic analytical relationship needed to solve for installment payments is
found below:
n

Loan Amount

1


t
t 1 (1  k)

= Payment

Thus, for the first part of this exercise
10

$100,000

1


t
t 1 (1.15)

= Payment

or
10

Payment

= $100,000 ÷ ( 

t 1

1

)
(1.15) t

10

We recognize the summation term

1


t as a present
t 1 (1.15)

value annuity factor which is found in Appendix E. Thus,
Payment

= $100,000 ÷ 5.019
= $19,924.29

(b)

In this problem we must recall the procedure for quarterly compounding. In
general, the payment relationship in (a) becomes
mn

Loan Amount

= Payment

1


t
t 1 (1  k/m)

where m is the number of compounding periods in a year (e.g., m = 4 for
quarterly compounding). Thus,
20

$100,000

= Payment

1


t
t 1 (1.0375)

Since the tables in Appendix E do not have fractional rates we must solve
for the present value annuity interest factor algebraically.
Payment

= $100,000 ÷ 13.8962
= $7,196.21

76


(c)

This problem requires that we first solve for the annual installment
payments for each of the next five years based upon a 30-year installment
period, i.e.,
30

Payment

= Loan amount ÷


t 1

1
(1  .15) t

or
Payment

= $100,000 ÷ 6.566
= $15,229.97

Next, we have to calculate the outstanding or remaining balance of the loan
at the end of the fifth year where five annual installments of $15,229.97
have been made. To do this, we must go through the calculations outlined in
Table 24-1.
Remaining
Year
Loan Payment
Interest

Principal
Balance
0
$100,000.00
1
$15,229.97
$15,000.00
$ 229.97
99,770.03
2
15,229.97
14,965.50
264.47
99,505.56
3
15,229.97
14,925.83
304.14
99,201.42
4
15,229.97
14,880.21
349.76
98,851.66
5
113,679.41
14,827.75
98,851.66
0
Thus, the fifth year balloon payment will equal the principal remaining at

the end of that year of $98,851.66 plus interest for the year of $14,827.75
for a total of $113,679.41.
This type of loan agreement is frequently used by homeowners who give
buyers a second loan on a home purchase. The loan will usually be
amortized or have installment payments calculated over a 30-year period but
require full repayment in a 5- or 10-year period.

77


SOLUTION TO INTEGRATIVE PROBLEM
(a)

Initial outlay (IO) = $60,000
Computing annual net cash flows
Book profits
$27,000
(12,500)

Annual cash savings
Less: depreciation
Net revenues before taxes
Less: taxes (50%)

Cash flows
$27,000

14,500
(7,250)

27,000
(7,250)

Annual after-tax cash flows (1-3)
Plus: salvage value

$19,750
10,000

Annual after-tax cash flow (4)

$29,750

Years
1-3
Year
4

Calculating NPV (P):
4

NPV(P)

= $19,750

1


t
t 1 (1.12)

+ $10,000 - $60,000

= $19,750(3.037) + $10,000(0.636) - $60,000
= $59,980.75 + $6,360 - $60,000
= $6,340.75
Thus, the computer should be acquired via normal purchase financing, as it
has a positive NPV(P) of $6,340.75.
(b)

Calculating principal and interest components of a loan equal to the full
$60,000 purchase price of the asset:
4

Loan payment = $60,000 ÷
Year
0
1
2
3
4

1


t =
t 1 (1.08)

$18,115.94

Payment

Principal

Interest

$18,115.94
18,115.94
18,115.94
18,115.94

$13,315.94
14,381.22
15,531.71
16,774.25

$4,800.00
3,734.72
2,584.23
1,341.69

Remaining
Balance
$60,000.00
46,684.06
32,302.84
16,771.13
(3.12)

Rounding errors produced a $3.12 difference in the remaining balance and principal portion

of the fourth year payment.

78


4

(1)

Year

After-tax
operating expenses
paid by lessor
Ot(1-T)

1
2
3
4

After-tax
rental
expenses
-

1,000
1,000
1,000
1,000


t 1

Solving for

Rt(1-T)

O t (1  T)  R t (1  T)  I t T  D t T
(1  rb ) t

Tax Shelter on
loan (interest
lost by leasing)
-

$9,000
9,000
9,000
9,000

It T

(Term one)

Depreciation
Tax Shelter
-

$2,400

1,868
1,292
671

TDt

Total
SUM

=

$6,250
6,250
6,250
6,250

Discount
Factor
4%
x

-$16,650
-16,118
- 15,542
- 14,921

(Term one)

591
(c)

Vn

Solving for: -

(3)

Adding: IO:

(4)

Net Advantage of Leasing (NAL)

(1  k s )

n

= -

10,000

(2)

(1.12) 4

= (Term two)
(Term three)

DF
0.962

0.925
0.889
0.855

=

Present
Value
=

PV
-$16,017
- 14,909
- 13,817
- 12,757

- $57,500

=

- 6,360

=

60,000
$ (3,860)

The NAL is negative, indicating that lease financing is not preferred to normal purchase
financing. That is, the net present value of the asset, if leased, is equal to NPV(P) + NAL or
$6,340 - $3,860 = $2,480. The asset should not be leased.

Solutions to Problem Set B
24-1B.
Interest Rate
Face Amount
Year
0
1
2
3
4
5

Payment

12.0%
$300,000.00
Interest

60,000.00
60,000.00
60,000.00
60,000.00
207,531.67

Principal

36,000.00
33,120.00

29,894.40
26,281.73
22,235.54

24,000.00
26,880.00
30,105.60
33,718.27
185,296.13

Balance
300,000.00
276,000.00
249,120.00
219,014.40
185,296.13
0

Thus, the fifth year balloon payment will equal the principal remaining at the end of that
year of $185,296.13 plus interest for the year of $22,235.54 for a total of $207,531.67.
24-2B.
Interest Rate
Equipment Price
Number of Payments
Rental Payment

15.0%
250,000.00
10
43,315.67

Present Value of the
Rental Payments

$250,000.00
7

24-3B.

$100,000 = PAYMENT

1


t
t 1 (1.16)

Payment = $24,761.27
24-4B.
Year
1
2
3
4
5
6
7

Payment
$24,758.60

24,758.60
24,758.60
24,758.60
24,758.60
24,758.60
24,758.60

Interest
$16,000.00
14,598.62
12,973.03
11,087.34
8,899.93
6,362.55
3,419.18

Principal
$8,758.60
10,159.98
11,785.57
13,671.26
15,858.67
18,396.05
21,339.42

Remaining
Balance
$91,241.40
81,081.42
69,295.85

55,624.59
39,765.92
21,369.87
30.45

Rounding errors produced a $30.45 difference in the remaining balance and principal portion of
the seventh year payment.

80


24-5B.
5

(a)

1


t
t 1 (1  r)

$250,000

= $69,000

where r

= the effective annual rate on the loan.

5

1


t
t 1 (1  r)

=

$250,000
= 3.623
69,000

Looking in the annuity present value table we find that an r of 12% for a fiveyear loan is 3.605. Thus, the effective rate on the loan is approximately 12%.
Actually, it is 11.79% (found using the Rate function in a financial spreadsheet).
5

(b )

(c)

= Payment

Payment

= $91,631.03

$300,000

= $425,000

1
(1  r)

5

Thus, r
(d)

=

1


t
t 1 (1.16)

$300,000

1
(1  r)5

$300,000
= .7059
$425,000

= 7.21%.

The effective rate of interest is lowest on the insurance loan.

24-6B.
Bank Loan Alternative: Cost = 14%
Manufacturer Financing Alternative:
The cost of this alternative is not immediately apparent and must be calculated.
We know that the following relationship holds for any equal payment installment
loan:
n

Loan Amount

= Payment

1


t
t 1 (1  r)

where n is the term of the loan and r is the rate of interest charged on the
remaining loan balance.

81


Using this relationship we can define
4

$500,000
4

Therefore,

= $175,000
1


t
t 1 (1  r)

=

1


t
t 1 (1  r)

$500,000
$175,000

= 2.857

We now know the present value of an annuity factor that corresponds to a fouryear period and the rate of interest on the loan (r). Looking up this factor in the
annuity present value table, we find that r = 15 percent.
Therefore, bank loan alternative is preferred.
24-7B.
(a)

IO = $25,000

Annual net cash flows:
Annual cash savings
Less: depreciation

Book profits
$7,000
(5,000)

Cash flows
$7,000

2,000
(1,000)

7,000
(1,000)

Net revenues before taxes
Less: taxes (50%)
Annual after-tax
Cash flows
Plus: salvage value

$6,000
5,000

Annual after-tax cash flow (4)
4

NPV

= $6,000

1


t
t 1 (1.13)

$11,000
+ $5,000

1
(1.13) 4

- $25,000

= $6,000 (2.974) + $5,000 (0.613) - $25,000

= -$4,091.00

Thus, the asset should not be purchased.

82

Years
1-3
Year
4

(b)

Calculating principal and interest on a loan of $25,000 at 10%.
4

Year
0
1
2
3
4

Payment

Interest

$8,058.16
8,058.16
8,058.16
8,058.16

$2,750.00
2,166.10
1,517.98
798.56
4

(1)

Solving for



t 1

Year
1

1


t =
t 1 (1.11)

Annual payment = $25,000/

$8,058.16

Principal
$5,308.16
5,892.06
6,540.18
7,259.60

Remaining Balance
$25,000.00
19,691.84
13,799.78
7,259.60

0.00

O t (1 - T) - R(1 - T) - I t T - D t T
(1  rb )t

Ot(1-T) - R(1-T) It T
DtT
625.00
3,500
1,375.00
2,500.00

= SUM
-6,750.00

PV Factor
.9479

PV
-6,398.32

2

625.00

3,500

1,083.05

2,500.00

-6,458.05

.8985

-5,802.56

3

625.00

3,500

758.99

2,500.00

-6,133.99

.8516

-5,223.71

4

625.00

3,500

399.28

2,500.00

-5,774.28

.8072

-4,661.00

Term one=
(Term two)

=

-22,085.59

(2)

Solving for -

-3,065.00

(3)

Adding IO

25,000.00

(4)

Net advantage of leasing

- $ 150.59

Since the asset's NAL is negative, the asset should not be leased.
24-8B.
(a)

The basic analytical relationship needed to solve for installment payments is
found below:
Loan Amount

n

1

t 1

(1  k) t

= Payment 

83


Thus, for the first part of this exercise
$125,000

12

1

t 1

(1.13) t

= Payment 

or
Payment

12

1

t 1

(1.13) t

= $125,000 ÷ 

12

1

t 1

(1.13) t

We recognize the summation term 

as a present

value annuity factor which is found in Appendix E. Thus,
Payment

= $125,000 ÷ 5.918
= $21,122.00

(b)

In this problem we must recall the procedure for quarterly compounding. In
general, the payment relationship in (a) becomes
mn

1

t 1

(1  k/m) t

Loan Amount = Payment 

where m is the number of compounding periods in a year (e.g., m = 4 for
quarterly compounding). Thus,
$125,000

24

1

t 1

(1.0325) t

= Payment 

Since the tables in Appendix E do not have fractional rates we must solve for the
present value annuity interest factor algebraically or using the "payment"
function in a financial spreadsheet software package.
Payment

= $7,581.11

84


(c)

This problem requires that we first solve for the annual installment payments for
each of the next five years based upon a 30-year installment period, i.e.,
30

Payment

= Loan amount ÷



t 1

1
(1  .13) t

or
Payment

= $125,000 ÷ 7.496
= $16,675.56

Next, we have to calculate the outstanding or remaining balance of the loan at
the end of the fifth year where five annual installments of $16,675.56 have been
made. To do this, we must go through the calculations outlined in Table 24-1.

Year

Loan Payment

Interest

0
1
3
4
5

$16,675.56
16,675.56
16,675.56
16,675.56

138,917.82

$16,250.00
16,194.68
16,132.16
16,061.52
15,981.70

Principal
$

425.56
480.88
543.40
614.04
122,936.12

Remaining
Balance
$125,000.00
124,574.44
124,093.56
123,550.16
122,936.12
0.00

Note that the fifth year balloon payment will equal the principal remaining at the
end of that year of $122,936.12 plus interest for the year of $15,981.70 for a
total of $138,917.82.
This type of loan agreement is frequently used by homeowners who give buyers

a second loan on a home purchase. The loan will usually be amortized or have
installment payments calculated over a 30-year period but require full repayment
in a 5- or 10-year period.

85


24-9B.
(a)

Initial outlay (IO) = $65,000
Computing annual net cash flows
Book profits
$29,000
(14,250)

Annual cash savings
Less: depreciation
Net revenues before taxes
Less: taxes (50%)

Cash flows
$29,000

14,750
(7,375)

29,000
(7,375)

Annual after-tax cash flows (1-3)

$21,625

Plus: salvage value

Years
1-3

8,000

Annual after-tax cash flow (4)

$29,625

Year
4

Calculating NPV (P):
NPV(P)

1

4

= $21,625 

t 1

(1.14)

t

+ $8,000

1
(1.14) 4

- $65,000

= $21,625 (2.914) + $8,000 (0.592) - $65,000
= $2,751.25
Thus, the computer should be acquired via normal purchase financing, as it has a
positive NPV(P) of $2,745.67.
(b)

Year
0
1
2
3
4

Calculating principal and interest components of a loan equal to the full $65,000
purchase price of the asset:
4
1
Loan payment = $65,000 / 
t = $19,624.85
t 1 (1.08)

Payment

Principal

Interest

$19,624.85
19,624.85
19,624.85
19,624.85

$14,424.85
15,578.84
16,825.15
18,171.16

$5,200.00
4,046.01
2,799.70
1,453.69

86

Remaining
Balance
$65,000.00
50,575.15
34,996.31
18,171.16
0.00

4

(1)

Solving for



t 1

Year

After-tax
operating expenses
paid by lessor
Ot(1-T)

1
2
3
4

1,125
1,125
1,125
1,125

After-tax

rental
expenses
-

Rt(1-T)
$10,000
10,000
10,000
10,000

599
(c)

O t (1  T)  R t (1  T)  I t T  D t T
(1  rb ) t
Tax Shelter
on loan (interest
lost by leasing)
-

It T

Depreciation
Tax Shelter
-

$2,600.00
2,023.01
1,399.85
726.85

8,000

(2)

Solving for - = -

(3)

Adding: IO:

(4)

Net Advantage of Leasing (NAL)

(1.14) 4

TDt
$7,125
7,125
7,125
7,125

=

Discount
Factor
4%

Total

=

SUM

x

-$18,600.00
-18,023.01
- 17,399.85
- 16,726.85

DF

Present
Value
=

0.962
0.925
0.889
0.855

(Term one)

=

-$64,333

(Term two)

=

- 4,736

(Term three)

=

65,000
$ (4,069)

The NAL is negative, indicating that lease financing is not preferred to normal purchase financing.

PV

-$17,893
- 16,671
- 15,468
- 14,301