B40.2302 Class #9

©The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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B40.2302 Class #9

BM6 chapters 25.2-25.6, 26, 27 25: Leasing 26: Risk management 27: International risk management

Based on slides created by Matthew Will Modified 11/07/2001 by Jeffrey Wurgler

Leasing

Principles of Corporate FinanceBrealey and Myers Sixth Edition

Slides by

Matthew Will, Jeffrey Wurgler

Chapter 25.2-25.6



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Topics Covered

Why Lease? Operating (Short-term) Leases Financial (Long-term) Leases


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Why Lease?

Sensible (Non-tax) Reasons for Leasing

Short-term leases are convenient

Cancellation options are valuable

Maintenance may be provided

Standardization leads to low transaction costs• (Relative to bond or stock issue)


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Why Lease?

Sensible (Tax) Reasons for Leasing

Tax shields can be used• Lessor owns asset, and so deducts its depreciation

• If lessor can make better use of tax shield than lessee, then lessor should own equipment and pass on some tax benefits to lessee (in form of lower lease payments)

• So direct tax gain to lessor, indirect gain to lessee

Reduces the alternative minimum tax (AMT)• Corporate tax = max{regular tax, AMT}

• Leasing (as opposed to buying) reduces lessee’s AMT


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Why Lease?

Dubious Reasons for Leasing

Leasing avoids internal capital expenditure controls

Leasing preserves capital


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Why Lease?

Dubious Reasons for Leasing (contd.)

Leases may be off-balance-sheet financing• In Germany, all leases are off balance sheet• In US, only operating leases are off balance sheet

Leasing affects book income• Leasing reduces book income bec. lease payments are

expensed• Buy-and-borrow alternative reduces book income

through both interest and depreciation


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Operating Leases

Review: Suppose you decide to lease a machine for one year

Q: What is the rental payment in a competitive leasing industry?

A: The lessor’s equivalent annual cost (EAC)


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Operating LeasesExample: Calculate a competitive lease payment / EAC

Acme Limo has a client who will sign a lease for 7 years, with lease payments due at the start of each year. The following table shows the NPV of the limo if Acme purchases the new limo for $75,000 and leases it out for 7 years.

(amounts in 000s) Year0 1 2 3 4 5 6

Initial cost -75Maintenance, insurance, selling, -12 -12 -12 -12 -12 -12 -12

and administrative costsTax shield on costs 4.2 4.2 4.2 4.2 4.2 4.2 4.2Depreciation tax shield 0 5.25 8.4 5.04 3.02 3.02 1.51Total -82.8 -2.55 0.6 -2.76 -4.78 -4.78 -6.29

PV @ 7% = - $98.15

Break even rent(level) 26.18 26.18 26.18 26.18 26.18 26.18 26.18Tax -9.16 -9.16 -9.16 -9.16 -9.16 -9.16 -9.16Break even rent after-tax 17.02 17.02 17.02 17.02 17.02 17.02 17.02

PV @ 7% = $98.15


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Operating Leases

Bottom line for lessee: Operating lease or buy?

Buy if the lessee’s equivalent annual cost of ownership and operation is less than the best available operating lease rate

Otherwise lease

Complication: If operating lease includes option to cancel/abandon, need to factor that in


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Financial LeasesExample - cont

Greymare Bus Lines is considering a lease. Your operating manager wants to buy a new bus for $100,000. The bus has an 8 year life. An alternative is to lease the bus for 8 years at $16,900 per year, but Greymare still assumes all operating and maintenance costs.

Should Greymare buy or lease the bus?

Cash flow consequences of the financial lease contract:

•Greymare saves the $100,000 cost of the bus.

•Loss of depreciation benefit of owning the bus.

•$16,900 lease payment is due at the start of each year.

•Lease payments are tax deductible.


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Financial Leases

(amounts in 000s) Year0 1 2 3 4 5 6 7

Cost of new bus 100.00 Lost Depr tax shield (7.00) (11.20) (6.72) (4.03) (4.03) (2.02) - Lease payment (16.90) (16.90) (16.90) (16.90) (16.90) (16.90) (16.90) (16.90) Tax shield of lease pmt. 5.92 5.92 5.92 5.92 5.92 5.92 5.92 5.92 Net cash flow of lease 89.02 (17.98) (22.18) (17.70) (15.01) (15.01) (13.00) (10.98)

Cash flow consequences of the financial lease contract


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Financial Leases

How to discount CFs?

Since lessor is essentially lending money to lessee, appropriate rate is the equivalent lending/borrowing rate• Lender pays tax on interest it receives: net return is after-tax interest rate• Borrower deducts interest from taxable income: net cost is after-tax interest rate• Thus, after-tax interest rate is effective rate at which company can transfer debt-equivalent cash flows across time• Suppose Greymare can borrow at 10%. Then the lease payments should be discounted at (1-.35)*.10 =.065.


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Financial LeasesExample – contd.

Greymare Bus Lines can borrow at 10%, thus the value of the lease should be discounted at 6.5% or .10 x (1-.35). The result will tell us if Greymare should lease or buy the bus.

Buy, don’t lease

$700-or 70.

1.065

10.98-

1.065

13.00-

1.065

15.02-

1.065

15.02-

1.065

17.71-

1.065

22.19-

1.065

17.99-89.02lease NPV

765

432


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Financial LeasesExample – Equivalent loan cash flows

Another way to think about where the lease value comes from (or goes) is to imagine a loan that generates exactly the same year 1 - 7 cash outflows as the lease.

This costs same, but brings in 89.72 in year 0 (vs. 89.02 in the lease).

Thus, borrowing-and-buying is 89.72-89.02=0.70=$700 better than lease.

(amounts in 000s) Year0 1 2 3 4 5 6 7

Amount borrowed at year end 89.72 77.56 60.42 46.64 34.66 21.89 10.31 0.00Interest paid @ 10% -8.97 -7.76 -6.04 -4.66 -3.47 -2.19 -1.03Tax shield @ 35% 3.14 2.71 2.11 1.63 1.21 0.77 0.36Interest paid after tax -5.83 -5.04 -3.93 -3.03 -2.25 -1.42 -0.67Principal repaid -12.15 -17.14 -13.78 -11.99 -12.76 -11.58 -10.31Net cash flow of equivalent loan 89.72 -17.99 -22.19 -17.71 -15.02 -15.02 -13.00 -10.98


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Financial Leases

Bottom line for lessee: Financial lease or buy-and-borrow?

Buy-and-borrow if can devise a borrowing plan that gives same cash flow as lease in every future period, but higher immediate cash flow (equivalently, buy-and-borrow if incremental lease cash flows are NPV<0)

Otherwise lease


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Leases in APV framework

lease of NPV project of NPVAPV

• Can think of leases as financing that may have side effects.

• Thus, the APV of a project financed by a lease:

• This is consistent with all the previous examples.

Managing Risk


Slides by


Chapter 26



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Topics Covered

Insurance Futures contracts Forward contracts Swaps How to set up a hedge


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Insurance

Most businesses insure against fire, theft, environmental liability, vehicle accidents, etc.

Insurance transfers risk from company to insurer

Insurers pool risks The claims on any individual policy are very risky… … but the claims on a large portfolio of policies may be

quite predictable This gives insurers a risk-bearing advantage Of course, insurers cannot diversify away macro risks

• In same way that investors can’t diversify away systematic risk


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Insurance

ExampleAn offshore oil platform is valued at $1 billion. Expert

meteorologist reports indicate that a 1 in 10,000 chance exists that the platform may be destroyed by a storm over the course of the next year. What is the “fair price” of insurance?

Answer:There is no systematic risk; it’s all due to the weatherTherefore no systematic risk premium required

The expected loss per year is = (1/10,000)*$1 billion = $100,000 = “fair price”

But for several reasons we’d expect a higher price …


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Insurance

Why would an insurance company probably not offer a policy on this oil platform for $100,000/yr?

Administrative costs Adverse selection Moral hazard

If these costs are large, there may be cheaper ways to protect against risk


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Insurance: British Petroleum

During the 1980s BP paid out $115m/year in insurance, recovered $25m/year in claims

BP has decided to cut down insurance BP felt it was better-placed to assess risk And insurance was not competitively priced

So now BP assumes more risk than when it insured BP guesses a big loss of $500m happens every 30 years Even so, this is <1% of BP market equity ! BP can afford not to insure against these risks


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Hedging

Hedging Taking on one risk to offset another

Some basic tools for hedging Futures Forwards Swaps


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Futures

Futures contract - A contract between two parties for the delivery of an asset, at a negotiated price, on a set future date

Example: Wheat farmer expects to have 100,000 bushels of wheat next Sept. He’s worried that price may decline in the meantime To hedge this risk, he can sell 100,000 bushels of Sept. wheat futures

at a price that is set today Bottom line -- perfect hedge

• If price rises, value of his wheat goes up but futures contract value falls

• If price falls, value of his wheat falls but futures contract value rises


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Futures

Futures are standardized contracts,

traded on organized futures exchanges

Commodity Futures

-Sugar -Corn -OJ -Lumber

-Wheat -Soybeans -Pork bellies

-Oil -Copper -Silver -...

Financial Futures

-Tbills -Japanese govt. bonds

-S&P 500 -DJIA index -...

SUGAR


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Futures

When you buy a financial future, you end up with the same security that you would have if you bought in the “spot market” (i.e. on-the-spot today)

Except: You don’t pay up front, so you earn interest on purchase price You miss out on any dividend or interest in interim

Therefore for a financial future:

Futures price/(1+rf)t

= Spot price – PV(foregone interest or dividends)


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FuturesFutures price/(1+rf)t

= Spot price – PV(foregone interest or dividends)

Example: Stock index futures

Q: Suppose 6-month stock index futures trade at 1,235 when index is at 1,212. 6-month interest rate is 5% and average dividend yield of stocks in index is 1.2%/year. Are these #s consistent?

A: Yes:

Futures price/(1+rf)t = 1,235/(1.05)1/2 = 1,205

Spot price – PV(foregone interest or dividends)

= 1,212 – 1,212*(1/2)*(.012)/(1.05)1/2 = 1,205


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Futures When you buy a commodities future, you end up with the same

commodity that you would have if you bought in the “spot market”

Except: You don’t pay up front, so you earn interest on purchase price You don’t have to store the commodity in the interim; saves on storage

costs You don’t get a “convenience yield” – the value of having the real thing

So for a commodities future:

Futures price/(1+rf)t

= Spot price + PV(storage costs) – PV(convenience yield)


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Forwards

Futures contracts are standardized, exchange traded

Forward contracts are tailor-made futures contracts, not exchange traded

Main forward market is in foreign currency Also forward interest-rate contracts


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ForwardsExample: Lock in a rate today on a loan tomorrow (“a homemade forward loan”)

Suppose you borrow $90.91 for one year at 10%, and you lend $90.91 for two years at 12%

These are interest rates today, i.e. spot interest rates

Net cash flow Year 0: 90.91 – 90.91 = 0 Year 1: -90.91*1.10 = -100 Year 2: 90.91*1.12*1.12 = 114.04

So paid out 100 at year 1, take in 114.04 at year 2, essentially you made a “forward loan” at locked-in interest rate of

Fwd. rate = (1+r2)2/(1+ r1) – 1 = (1.12)2/(1.1) – 1 = .1404


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Swaps

Swap contract - An agreement between two parties (“counterparties”) lend to each other on different terms, e.g. in different currencies, or one at fixed rate and the other at a floating rate


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Swaps

Example: Currency swap

USA Inc. wants to borrow euros to finance European operations, but it gets better rates in US

So it issues US debt (say $10M of 8%, 5-year notes) And contracts with a bank to swap its future dollar

liability for euros Combined effect: convert an 8% dollar loan into a 5.9%

euro loan (see next page)


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Swaps

Year 0 Years 1-4 Year 5

Dollars Euros Dollars Euros Dollars Euros

Dollar loan +10 -.8 -10.8

Swap dollars for euros

-10 +8.5 +.8 -.5 +10.8 -9.0

Net cash flow 0 +8.5 0 -.5 0 -9.0

Net cash flow to USA Inc. after the currency swap

Bottom line: currency swap turned dollar debt into euro debt


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Swaps

Example: Fixed-to-floating interest rate swap

Bancorp has made a 5-year, $50m loan at a fixed rate of 8%; annual interest payments are $4m

Bank wants to swap the $4m, 5-year annuity (the fixed interest payments) into a floating rate annuity

Bank has ability to borrow at 6% for 5 years. So $4m interest annuity could support a fixed-rate loan of 4/.06 = $66.67m.

Bank can construct “homemade swap” by borrowing $66.67m at 6% for 5 years, then simultaneously lend this amount at LIBOR (a floating rate)

Bottom line: bank’s fixed rate interest stream has been converted into a floating-rate stream

(Easier way to do all this: Bank could just call a swap dealer)


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Setting up a hedge

In our futures examples, firm has hedged by buying one asset and selling an equal amount of another

In practice, the appropriate “hedge ratio” may not be 1.0 The asset to be hedged may not move 1-to-1 with the available hedge

contract

Suppose you own A and you want to hedge by making an offsetting sale of B. If percentage changes in value of A and B are related as follows:

Expected change in A = a + *(change in B)

Then delta is the hedge ratio – the # of units of B that should be sold to hedge each unit of A


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Setting up a hedge

You can calculate deltas by brute force, or you can use finance theory to set up a hedge

Example: Suppose a leasing company has a lease contract to receive a fixed $1m for 5 years.

If interest rates go up (down), the value of the lease payments go down (up)

The company can hedge this interest rate risk by financing the leased asset with a package of debt that has exactly the same duration as the lease payments

So if interest rates change, the lease payments’ value changes, but the debt obligations change by an equal amount

We say the company is immunized against interest rate risk

Managing International Risk


Slides by


Chapter 27



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Topics Covered

Foreign Exchange Markets Some Basic Relationships Hedging Currency Risk International Capital Budgeting


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Foreign Exchange Markets

Exchange Rate - Amount of one currency needed to purchase one unit of another.

Spot Exchange Rate – Price of currency for immediate delivery.

Forward Exchange Rate – Price for future delivery.


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Foreign Exchange Markets

Example - The yen spot price is 112.645 yen per dollar and the 3 month forward rate is 111.300 yen per dollar. What is the forward premium, expressed as an annual rate?

So yen trades at a “4.8% forward premium relative to dollar”

(could also say dollar sells at a 4.8% forward discount)

4.8%=100x 111.300

111.300-112.6454

)(-Discountor Premium= PriceForward

PriceForward-Spot Price


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Exchange Rate Relationships How are these various quantities related?

(i = inflation, f=forward rate, s=spot rate, r=interest rate)

$

foreign

r+1

r+1

)i+E(1

)i+E(1

$

foreign

foreign/$

foreign/$

s

f

foreign/$

foreign/$)E

s

(s

?

?

? ?


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Exchange Rate Relationships In simplest world (people are risk-neutral and face no

transaction costs for international trade), they are all equal (!)

$

foreign

r+1

r+1

)i+E(1

)i+E(1

$

foreign

foreign/$

foreign/$

s

f

foreign/$

foreign/$)E

s

(s

=

=

= =


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Exchange Rate Relationships

Leg #1) “Interest Rate Parity Theory” links interest rates and exchange rates

It says that the ratio between the interest rates in two different countries is equal to the ratio of the forward and spot exchange rates.

1 + r

1 + r=

foreign

$ foreign/$

foreign/$

s

f


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Interest Rate Parity Example - You have $1,000,000 to invest for one year. You can buy a 1- year Japanese bond (in yen) @ 0.25 % or a 1-year US bond (in dollars) @ 5%.

The spot exchange rate is 112.645 yen:$1.

The 1-year forward exchange rate is 107.495 yen:$1

Which bond will you prefer?


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Next year’s payoff to dollar bond = $1,000,000 x 1.05 = $1,050,000

Next year’s payoff to Yen bond = $1,000,000 x 112.645 x 1.0025

= 112,927,000 yen

= 112,927,000/107.495 = $1,050,000

In other words, you are indifferent only if the interest rate differential (1.0025)/(1.05) equals the difference between the forward and spot exchange rates (107.495/112.645), as it does here. (If this “interest rate parity” doesn’t hold, you’d have an arbitrage opportunity. Hence, it must hold.)


Interest Rate Parity Example - You have $1,000,000 to invest for one year. You can buy a 1- year Japanese bond (in yen) @ 0.25 % or a 1-year US bond (in dollars) @ 5%. The spot exchange rate is 112.645 yen:$1. The 1-year forward exchange rate is 107.495 yen:$1. Which bond to prefer?


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Leg #2) “Expectations Theory of Forward Rates” links forward rates to expected spot rates

It says that in risk-neutral world, the expected future spot exchange rate equals the forward rate

foreign/$

foreign/$

s

f

foreign/$

foreign/$)E

s

(s


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Expectations theory logic

Suppose one-year forward rate on yen is 107.495

But that traders expect the future spot rate to be 120.

Then no trader would be willing to buy yen forward, since would get more yen by waiting and buying spot.

Thus the forward rate will have to rise until the two rates are equal


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Leg #3) “Purchasing Power Parity (PPP)” implies that

And so the expected difference in inflation rates equals the expected change in spot rates

foreign/$

foreign/$)E

s

(s

)i+E(1

)i+E(1

$

foreign


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PPP intuitionIf $1 buys a McDonald’s hamburger in the USA, it also buys (after currency conversion) a hamburger in Japan

So spot exchange rates should be set such that $1 has the same “purchasing power” around the world – else, there would be import/export arbitrage – buy goods where $1 buys a lot, sell them where $1 doesn’t buy much.

And if this relationship is to hold tomorrow as well, then the expected change in the spot rate must reflect relative inflation.


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Leg #4) “International Fisher Effect” relates relative interest rates to inflation

rates

Says that expected inflation accounts for differences in current interest rates, i.e. real interest rates are the same across countries

1 + r

1 + r=

foreign

$ )i+E(1

)i+E(1

$

foreign


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Example: International Fisher effect Claims that the real interest rate in each country is about equal. Suppose Japan

and US, interest rates as before, expected deflation in Japan is 2.5%, inflation in US is 2%. Then real interest rates are about equal, Intl. Fisher effect holds.

.028 =.975

1.0025=

)i+E(1

r+1)(

foreign

foreignforeign realr

.029 =1.02

1.05=

)i+E(1

r+1)(

$

$$ realr


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Hedging Currency Risk

Outland Steel: Current situation

Has profitable export business

Contracts involve substantial payment delays

Company invoices in $, so it is naturally protected against exchange rates

But wonders if it’s losing sales to firms that are willing to accept foreign currencies…


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Outland Steel: Proposal #1

Accept foreign currency payments…• But if value of that currency declines before payment is made,

company may suffer a big loss in dollar terms

… and hedge by selling the currency forward• If contract is to receive X yen next year, then sell X yen forward

today. Lock in dollar rate today.

Cost of this “insurance” is the difference between the forward rate and the expected spot rate next year

• Cost =0 if these are equal, as in expectations theory (“leg #2”)


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Outland Steel: Proposal #2

Accept foreign currency payments…

… and hedge by borrowing foreign currency against foreign receivables, sell the currency spot, invest dollar proceeds in the US

• Interest rate parity theory (“leg #1”) says that the difference between selling forward and selling spot equals the difference between foreign interest that you pay, and dollar interest you receive

This should be equally effective as proposal #1


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International Capital Budgeting

Equivalent Intl. Capital Budgeting Techniques

1) (Easy) Discount foreign CFs at foreign cost of capital. (Can then convert this present value to $ using spot exchange rate.)

2) (Hard) Convert to $ assuming all currency risk was hedged (use forward exchange rates), and then discount with $ cost of capital.

These techniques are equivalent (verify BM6 p. 806-807)

Thus, hedging allows you to separate the investment decision from decision to take on currency risk

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B40.2302 Class #9