Simon Benninga. Financial Modelling 3-rd edition

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198 Chapter 5

their investment bankers, that their franchise would be worth more to a

commercial bank whose management could successfully commercialize

First Federal. Moreover, prices being paid for both banks and thrift

franchises were at all time highs, and First Federal’s board believed the

time was right to sell. First Federal’s investment bankers told them that

Fairmont and Clarksburg National Bank would be certain bidders and

that others might bid as well.

First Federal has branches in both Fairmont’s and Clarksburg’s

markets, but more in the latter’s. First Federal expected that if Fairmont

were the winning bidder at least two of its branches would be closed

and consolidate with Fairmont’s. If Clarksburg were the winner, as

many as six of First Federal’s branches would be closed. That difference

meant two things—more First Federal employees would probably lose

their jobs in a merger with Clarksburg, but First Federal’s shareholders

might receive more for their shares in a deal with Clarksburg. According

to First Federal’s investment bankers, however, Fairmont needed the deal

for strategic reasons and for that reason might meet or beat a bid from

Clarksburg.

5.8.3 Clarksburg National Bank

As the ﬁ nancial comparison shows, Clarksburg National Bank underper-

forms Fairmont, but enjoys a higher stock price (in relation to both book

value and earnings). The reasons for this are not clear: Perhaps the

reason is that Clarksburg’s shares have been listed on the Nasdaq

National Market for several years and Fairmont listed only recently. Also,

Clarksburg has often been the subject of takeover rumors while Fair-

mont hasn’t, and such rumors may add something to Clarksburg’s stock

price.

5.8.4 The Cities: Fairmont and Clarksburg

Although Fairmont, with 100,000 residents, is twice as large as Clarksburg,

the two cities share many characteristics. Both are declining in popula-

tion and commerce. Both have lost major manufacturing facilities. Their

most prominent downtown structures are bank headquarter buildings,

but most of those now house branches of large banks headquartered

elsewhere. Both cities have prosperous suburbs served by busy shopping

malls.

199 Bank Valuation

5.8.5 Valuing First Federal Using P/E Ratios

The last rows of the preceding spreadsheet present a solution that is based

on the P/E ratios of the two competing banks. This is a common practice

in the banking industry; small bank boards basically understand only P/E

ratios, and they are afraid of equity dilution—meaning that they will bid

only slightly more than their existing P/E ratio. The P/E-based valuation

assumes that each bank values First Federal at its own price/earnings

ratio, with an addition for a capitalized savings from the merger.

It is clear that under this procedure Clarksburg can bid substantially

more for First Federal than Fairmont Bank. The difference between the

P/E ratios basically settles things: Fairmont will never be able to match

BACD

Fairmont First Federal Clarksburg

Assets 796,866,000 493,466,000 913,480,000

Securities 245,767,000 194,792,000 280,010,000

Residential loans 150,332,000 208,429,000 123,235,000

Other loans 341,156,000 73,667,000 443,257,000

Demand deposits 74,500,000 10,065,000 93,080,000

Passbook savings accounts 195,446,000 69,644,000 155,127,000

Certificates of deposit 195,473,000 239,247,000 390,263,000

Total deposits 545,111,000 276,732,000 703,266,000

Net income 12,941,000 3,538,000 9,510,000

Shareholders' equity 86,579,000 37,329,000 79,428,000

Shares outstanding 6,300,000 869,364 6,900,000

Net interest income/Average assets 4.44% 2.71% 3.87%

Non-interest income/Average assets 1.05% 0.37% 0.96%

Non-interest expense/Average assets 2.66% 1.91% 3.09%

Net income/Average assets 1.67% 0.74% 1.06%

Branch offices 24 7 25

Share price on February 2, 2007 35.00 - 37.25

Estimated cost savings from branch consolidations 450,000 nmf 1,000,000

Price/earnings (P/E) ratio 17.04 27.03 <-- =D23*D14/D11

Valuation of First Federal using P/E ratios

Fairmont Clarksburg

P/E ratio 17.04 27.03

Value of First Federal at each bank's P/E ratio 60,283,518 95,620,868 <-- =D31*$C$11

Capitalized savings @ 10% 4,500,000 10,000,000 <-- =D25/0.1

Valuation of First Federal

64,783,518 105,620,868 <-- =D33+D32

Valuation using earnings/assets ratios

Fairmont Clarksburg

Potential earnings on FF's assets at acquiror's ratio 8,240,882 5,230,740 <-- =$C$3*D19

Valuation of First Federal

140,415,310 141,370,226 <-- =D31*D37

FIRST FEDERAL SAVINGS BANK

Basic data about Fairmont National Bank (our client), First Federal Savings Bank (the target), and

Clarksburg National Bank (the competitor)

200 Chapter 5

Clarksburg’s bid! However, suppose we assume that First Federal can be

made to earn at either Fairmont’s or Clarkburg’s earnings/assets ratio;

then we get the following valuations:

BACDE

Valuation using earnings/assets ratios Fairmont Clarksburg

Potential earnings on FF's assets at acquiror's ratio 8,240,882 5,230,740 <-- =$C$3*D19

Valuation of First Federal

140,415,310 141,370,226 <-- =D31*D37

Going back to the engagement terms, you, as Fairmont’s investment

banker, will have to advise your client how much to bid for First Federal.

First Federal has stipulated that the transaction must be tax-free to its

shareholders, and they would prefer to receive 100 percent common

stock in the transaction. They would like the transaction price to be

expressed as an exchange ratio; that is, they would want to know how

many shares of the buyer’s stock they would receive for each share of

First Federal stock.

To solve for the exchange ratio, we have to solve the following

equation:

xN N

∗

∗+

↑

FF Acquirer

Percentage of

First Federal

shareholders inn

combined firm

FF Acquirer

Value of combined



∗+

()

↑

rrm

Acquirer

valuation

of First Federal

 



↑

where x is the exchange ratio (number of shares of acquirer offered for

each share of First Federal), N

, N

Acquirer

is the number of shares of First

Federal and acquirer, V

is the acquirer valuation of First Federal, and

is the market valuation of the acquirer.

This simple algebraic equation has the solution

∗

Acquirer FF

FF Acquirer

Applying this in our spreadsheet gives us the following:

201 Bank Valuation

BACED

Based on valuation using P/E

Fairmont Clarksburg

Acquirer's valuation of First Federal 64,783,518 105,620,868 <-- =D34

Acquirer's market value 220,500,000 257,025,000 <-- =D23*D14

Value of combined entity 285,283,518 362,645,868 <-- =D44+D45

Exchange ratio: Maximum shares of acquirer offered

per share of First Federal

2.13 3.26 <-- =D14*D44/($C$14*D45)

First Federal shareholders' portion of combined firm 22.71% 29.13% <-- =$C$14*D48/($C$14*D48+D14)

Check: Valuation of First Federal in combined firm 64,783,518 105,620,868 <-- =D49*D46

"Valuation" of First Federal shares at acquirer's

preacquisition share price

74.52 121.49 <-- =D48*D23

Based on valuation using

earnings/assets ratios

Fairmont Clarksburg

Acquirer's valuation of First Federal 140,415,310 141,370,226 <-- =D38

Acquirer's market value 220,500,000 257,025,000 <-- =D45

Value of combined entity 360,915,310 398,395,226 <-- =D56+D57

Exchange ratio: Maximum shares of acquirer offered

per share of First Federal

4.61 4.37 <-- =D14*D56/($C$14*D57)

First Federal shareholders' portion of combined firm 38.91% 35.48% <-- =D60*$C$14/(D60*$C$14+D14)

Check: Valuation of First Federal in combined firm 140,415,310 141,370,226 <-- =D61*D58

"Valuation" of First Federal shares at acquirer's

preacquisition share price

161.51 162.61 <-- =D60*D23

Computing the exchange ratio

Row 48 computes the exchange ratio when both Fairmont and Clarks-

burg value the target, First Federal, at their own P/E ratios. Row 60

repeats the exercise when both banks value First Federal based on their

own earnings/assets ratios. Rows 52 and 64 are not strictly scientiﬁ c, but

they are indicative: Each row values the exchange offer at the preacquisi-

tion stock price of the acquirer.

The Financial Analysis of Leasing

6.1 Overview

A lease is a contractual arrangement by which the owner of an asset (the

lessor) rents the assets to a lessee. In this chapter we analyze long-term

leases, in which the asset spends most of its useful life with the lessee. In

economic terms the leases we consider in this chapter are considered by

the lessees as alternatives to purchasing an asset. Thus the analysis of

this chapter ﬁ ts many long-term equipment leases, but not short-term

leasing (car rentals, for example). Financial theory regards such leases as

being essentially debt contracts: For the lessee, the lease is an alternative

to purchasing the asset with debt, and the lessor understands that it is

essentially providing ﬁ nancing for the lessee.

In the example that follows we consider a company that is faced with

the choice of either purchasing or leasing a piece of equipment. We

assume that the operating inﬂ ows and outﬂ ows from the equipment are

not affected by its ownership—irrespective of how the asset is held

(whether owned or leased), the owner/lessee will have the same

sales and must bear the responsibility for maintaining the equipment.

In the words of Statement 13 of the Financial Accounting Standards

Board, the lease we are considering is one that “transfers substantially

all of the beneﬁ ts and risks incident to the ownership of property” to the

lessor.

The analysis in this chapter concentrates exclusively on the cash ﬂ ows

from the lease. It is assumed that the lessor pays taxes on the income

from the lease rentals and gets a tax shield on the depreciation of the

asset, and that the lessee can claim the rent as an expense. The analysis

implicitly assumes that the tax authorities treat the lessor as the owner

of the asset and the lessee as the user. As is explained in the appendix

to this chapter, this assumption is not trivial. In addition to the cash-ﬂ ow

issues of leasing there are heavy accounting issues, which are also touched

on brieﬂ y in the appendix.

6.2 A Simple Example

The essence of our analysis can be understood from the following simple

example: A company has decided to acquire the use of a machine costing

$600,000. If purchased, the machine will be depreciated on a straight-line

204 Chapter 6

basis to a residual value of zero. The machine’s estimated life is six years,

and the company’s tax rate T

is 40 percent.

The company’s alternative to purchasing the machine is to lease it for

six years. A lessor has offered to lease the machine to the company for

$140,000 annually, with the ﬁ rst payment to be made today and with ﬁ ve

additional payments to be made at the start of each of the next ﬁ ve

years.

One way of analyzing this problem (a misleading way, as it turns out)

is to compare the present values of the cash ﬂ ows to the company of

leasing and of buying the asset. The company feels that the lease payment

and the tax shield from depreciation are riskless. Suppose, furthermore,

that the risk-free rate is 12 percent. On the basis of the following calcula-

tion, the company should lease the asset.

NPV leasing

Lease rental

()

−∗

∑

112

1 140 00

112

386 801

()

=−

∑

NPV buying Asset cost PV(Tax shields

oon depreciation)

,=−

∗

∑

600 000

0 40 100 000

112

435 544

()

In a spreadsheet:

1. At this point we assume that the residual value of the asset at the end of its life is zero.

In section 6.5 we drop this assumption.

CBA

Asset cost 600,000

Interest rate 12%

Lease rental payment 140,000

Annual depreciation 100,000

Tax rate 40%

NPV(leasing) 386,801 <-- =-PV(B3,5,B4*(1-B6))+B4*(1-B6)

NPV(buying) 435,544 <-- =B2+PV(B3,6,B6*B5)

HOW NOT TO ANALYZE A LEASE

This analysis suggests that leasing the asset is preferable to buying it.

However, it is misleading because it ignores the fact that leasing is very

much like buying the asset with a loan. The ﬁ nancial risks are thus dif-

ferent when we compare a lease (implicitly a purchase with loan ﬁ nanc-

205 The Financial Analysis of Leasing

ing) against a straightforward purchase without loan ﬁ nancing. If the

company is willing to lease the asset, then perhaps it should also be

willing to borrow money to buy the assets. This borrowing will change

the cash-ﬂ ow patterns and could also produce tax beneﬁ ts. Hence, our

decision about the leasing decision could change if we were to take the

loan potential into account.

In the following section we present a method of analyzing leases that

deals with this problem by imagining what kind of loan would produce

cash ﬂ ows (and hence ﬁ nancial risks) equivalent to those produced by

the lease. This method of lease analysis is called the equivalent-loan

method.

6.3 Leasing and Firm Financing: The Equivalent-Loan Method

The idea behind the equivalent-loan method is to devise a hypothetical

loan that is somehow equivalent to the lease.

It then becomes easy to

see whether the lease or the purchase of an asset is preferable.

The easiest way to understand the equivalent loan method is with an

example. We return to the previous example:

ABCDEFG

Asset cost 600,000

Interest rate 12%

Lease rental payment 140,000

Annual depreciation 100,000

Tax rate 40%

Year 0123456

After-tax cash flows from leasing

After-tax lease rental -84,000 -84,000 -84,000 -84,000 -84,000 -84,000

After-tax cash flows from buying the asset

Asset cost -600,000

Depreciation tax shield 40,000 40,000 40,000 40,000 40,000 40,000

Net cash from buying -600,000 40,000 40,000 40,000 40,000 40,000 40,000

Differential cash flow: Lease saves lessor

Lease minus buy 516,000 -124,000 -124,000 -124,000 -124,000 -124,000 -40,000

IRR of differential cash flow 8.30% <-- =IRR(B19:H19,0)

Decision?? Buy <-- =IF(B21<(1-B6)*B3,"Lease","Buy")

EQUIVALENT LOAN METHOD

2. This method is due to Myers, Dill, and Bautista (1976). A somewhat more accessible

explanation can be found in Levy and Sarnat (1979).

206 Chapter 6

Rows 2–6 give the various parameters of the problem. The spreadsheet

then compares two after-tax cash ﬂ ows, that of the lease and that of the

buy; we write outﬂ ows with a minus sign and inﬂ ows (such as the tax

shield from the depreciation) with a plus sign.

•

The cash ﬂ ow from leasing the asset is (1 − Tax rate)

Lease payment,

in each of years 0–5.

•

The cash ﬂ ow from buying the asset is the asset cost in year 0 (an

outﬂ ow, hence positive) and the tax shield on the asset’s depreciation,

tax rate

depreciation, in years 1–6 (an inﬂ ow, hence written here with a

negative sign).

Line 19 of the spreadsheet shows the differential cash ﬂ ow between

the lease and the buy decision. This line shows that leasing the asset,

instead of buying it, results in the following cash ﬂ ows to the lessor:

•

A cash inﬂ ow of $516,000 in year 0. This inﬂ ow is the cash saved at time

0 by the lease: Purchasing the asset costs $600,000, whereas leasing the

asset costs only $84,000 on an after-tax basis.

•

A cash outﬂ ow of $124,000 in years 1–5 and an outﬂ ow of $40,000 in

year 6. This outﬂ ow corresponds to the marginal after-tax cost of the lease

versus the buy in these years. This marginal cost has two components: the

after-tax lease payment ($84,000) and the fact that when we lease we do

not get the tax shield on the asset’s depreciation ($40,000).

Thus leasing instead of purchasing the asset is like getting a loan of

$516,000 with after-tax repayments of $124,000 in years 1–5 and an after-

tax repayment of $40,000 in year 6. The lease, in other words, can be

viewed as an alternative method of ﬁ nancing the asset. In order to compare

the lease to the buy, we should compare the cost of this ﬁ nancing with the

cost of alternative ﬁ nancing. The internal rate of return of line 21—8.30

percent—gives us the cost of the ﬁ nancing implicit in the lease; this is

larger than the after-tax cost of ﬁ rm borrowing, since in this case (where

the ﬁ rm’s tax rate is 40 percent and its borrowing cost is 12 percent), this

cost is 7.20 percent. Thus our conclusion: Buying is preferable to leasing.

6.3.1 Why We Decided Against the Lease

Not everyone is fully convinced by the preceding argument. We therefore

present an alternative argument in this subsection. We show that if the

207 The Financial Analysis of Leasing

ﬁ rm can borrow at 12 percent, it can borrow more money with the same

schedule of after-tax repayments as that which resulted from the lease

versus the buy. This hypothetical loan is shown in the following table:

ABCDEF

Year

Principal at

beg. year

Loan

payment,

end year

Interest

Repayment

of principal

After-tax

loan

repayment

Lease minus

buy cash

flows, years

1-6

1 532,070 149,539 63,848 85,691 124,000 124,000

2 446,379 145,426 53,565 91,861 124,000 124,000

3 354,518 141,017 42,542 98,475 124,000 124,000

4 256,044 136,290 30,725 105,565 124,000 124,000

5 150,479 131,223 18,057 113,166 124,000 124,000

6 37,313 41,791 4,478 37,313 40,000 40,000

Split of loan repayment

between:

=NPV((1-$B$6)*$B$3,G28:$G$33)

=D28+B28-B29

=$B$3*B28

=B28-B29 =(1-$B$6)*D28+E28

The table (a version of the loan tables discussed in Chapter 1) shows the

principal of a hypothetical bank loan bearing a 12 percent interest rate.

At the beginning of year 0 (that is, at the time when the ﬁ rm either pur-

chases or leases the asset), for example, the ﬁ rm borrows $532,070 from

the bank. At the end of the year, the ﬁ rm repays $149,539 to the bank,

of which $63,848 is interest (since $63,848 = 12 percent

$532,070) and

the remainder, $85,691, is repayment of principal. The net, after-tax,

repayment in year 1—assuming full tax deductibility of the interest

payment—is (1 − 40 percent)

$63,848 + $85,691 = $124,000, which is, of

course, the same after-tax differential cash ﬂ ow calculated in our original

spreadsheet.

Payments in subsequent years are calculated similarly to the illustra-

tion in the preceding paragraph. At the beginning of year 6, there is still

$37,313 of principal outstanding; this is fully paid off at the end of the

year with an after-tax payment of $40,000.

The point of this example? If the ﬁ rm is considering leasing the

asset in order to get the ﬁ nancing of $516,000 that the lease gives, it

should instead borrow $532,070 from the bank at 12 percent; it can repay

this larger loan with the same after-tax cash ﬂ ows as are implicit in the

lease. The bottom line: Purchasing is still preferable to leasing the

asset.