Corporate Finance Lecture Notes 1

7/29/2019 Corporate Finance Lecture Notes 1

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Lecture Notes 1: Net Present Value and Investment Decisions

Corporate Finance

Joao F. CoccoAssociate Professor of Finance at London Business School

MBA Programme

September 2012


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Lecture Notes 1: Net Present Value and Investment Decisions Page 2

The Goal of the Firm


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The objective of a financial decision maker:

MAXIMIZE VALUE

Need to know:

(1) How to make investment decisions?

(2) How to finance the project? Which is the cost of thesources of finance?


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Flow of Cash Between Investorsand the Firms Operations

`

Firms

Operations

Financial

Decision Maker

Investors

(Financial

Institutions,

Individuals,

Other Firms)

(1)

(1) Cash raised from investors by selling financial assets.


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Firms

Operations

Financial

Decision Maker

Investors

(Financial

Institutions,

Individuals,

Other Firms)

(1)

(1) Cash raised from investors by selling financial assets.(2) Cash invested in real assets (some are intangible).

(2)


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Firms

Operations

Financial

Decision Maker

Investors

(Financial

Institutions,

Individuals,

Other Firms)

(1)


(3) Cash generated by operations.

(2)

(3)


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Firms

Operations

Financial

Decision Maker

Investors

(Financial

Institutions,

Individuals,

Other Firms)

(1)


(3) Cash generated by operations.(4) Cash reinvested in the firm (retained earnings).

(2)

(3)

(4)


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Firms

Operations

Financial

Decision Maker

Investors

(Financial

Institutions,

Individuals,

Other Firms)

(1)


(3) Cash generated by operations.(4) Cash reinvested in the firm (retained earnings).(5) Cash repaid to investors (interest, dividends, etc).

(2)

(3)(5)

(4)


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Opportunity cost of capital: The firm canalways give cash back investors.

Projects Investors

Opportunities

for investmentavailable inthe capitalmarkets

The opportunity cost of capital is the expected rate of return

offered by equivalent investments in capital markets. It compensatesinvestors for: The time value of money. The risk of the investment.

Cash


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The Objective: Create Value How?

1. Investment Decisions: How to select projects that increase the valueof the firm?

Need to find projects which are worth more than their requiredinvestment (+ NPV).

2. Financing Decisions: How to finance an investment project? Whichtype of security to choose in order to maximize the value of the firm?

Need to know the cost of the different sources of finance (debt,equity).


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Only one goal can stand the test of time

In some instances maximizing the value of the firm may

not be the same as maximizing the wealth of theshareholders in the firm:

In that case firms should strive to maximize the wealth

of the shareholders In most cases this implies that the firm must be

concerned about the well being of all stakeholders

But what if there are conflicts of interest? Who comesfirst?


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The wrong goals

Size: is bigger necessarily better?

Market share: is a larger market share necessarily better?

Growth: only works if there is value

Profits: not cash and measured at a particular point in time

Most companies could report higher profits in aparticular year if they wanted to

How?

Maximizing cash flows / funds distributed to shareholders: It is OK not to distribute the funds if


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What about the other stakeholders in the firm?

Customers Suppliers Employees

The community Corporate Social Responsibility


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Discounting and Net Present Value


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Introduction

The key driver of the value of any business is making the

right investment decision

Implies: buying and combining assets, ideas, people, sothat they cost less than what they are worth

Goal of this part is to study the process of making theinvestment decision in more detail


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Present Value

Present Value

Value today of a

future cash flow.

Discount Rate

Interest rate used to

compute present

values of future

cash flows.

Discount Factor

Present value of a

$1 future

payment.


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Investment decisions without uncertainty:

Invest $1 today if and only if your return (call it $X) at time T is

worth more than that $1

How do we compare $1 at t = 0 and $X at t = T?

Time value of money: other things equal, having one dollar today is worth

more than having the same dollar next year.Assume, for now, that the interest rate (r) is 5% per year.

Putting $1 in the bank gets you $1 1.05 = $1.05 a year from now.

Present Value


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Future Value of $y in T years at an interest rate of r:

FV ($y, T, r) = $y (1 + r)T (e.g $15 (1.05)4 = $18.23)

How much is having $x at time t = T (say in 4 years) worth today?

Answer: How ever much I would have to invest today to get $x at time t =

T.

Present Value: PV ($x, T, r) = $x / (1 + r)T (e.g. $20/(1.05)4 == $16.45)

Call 1/(1+r)T thePresent Value Factor, orDiscount Factor.

Present and Future Value


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Valuing an Office Building

Step 1: Forecast cash flows

Cost of building = C0 = 350

Sale price in Year 1 = C1 = 400

Is it a good investment?

Step 2: We need the opportunity cost of capital

If equally risky investments in the capital market

offer a return of 7%, then

Cost of capital = r = 7%


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Valuing an Office Building

Step 3: Discount future cash flows

Step 4: Go ahead if PV of payoff exceeds investment

37)07.1(

400)1(

1 rC

PV

24374350 NPV


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Net Present Value

Present Value = PV = Discount Factor1 * C1 Discount Factor1 = DF1 = 1/(1+r)

Net Present Value = Required Investment + PV

= C0 + C1/ (1+r)

Decision Rule: Accept investments that have

positive net present value.


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Risk and Present Value

Higher risk projects require a higher rate of return

Higher required rates of return cause lower PV

1PV of C $400 at 12%$400

PV $357

1 .12


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Discount Factor more generally

Discount Factors can be used to compute the presentvalue of any cash flow.

Replacing 1 with t allows the formula to be used forcash flows that exist at any point in time

tt

ttr

CCDFPV)1(


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Present Values

Present values can be added together to evaluatemultiple cash flows.

....22

1

1

)1()1(

r

C

r

CPV


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Present Values

Example

Assume that the cash flows from the

construction and sale of an office buildingare as follows. Given a 7% required rateof return, create a present valueworksheet and show the net presentvalue.

000,300000,100000,150

2Year1Year0Year


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Present Values

Example - continued

Assume that the cash flows from the construction and sale of an office building is asfollows. Given a 7% required rate of return, create a present value worksheet and show

the net present value.

400,18$

900,261000,300873.2

500,93000,100935.1000,150000,1500.10

Value

Present

Flow

Cash

Factor

DiscountPeriod

207.1

1

07.11

TotalNPV


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Why do we use the NPV Rule?

Assume we showed that a project had an NPVof 138. So what?

Share value will rise by NPV:

Market capitalization increases from 1,000 to 1,138

Share price increases from 1 to 1,138/1,000 = 1.14

If:

The stock market is efficient The market agrees with the assessment of project

The project NPV had not already been anticipated

When:

On announcement Not when profits are subsequently realized


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Project Evaluation Techniques


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Applying the methods

The Net Present Value:

Present value of inflows - present value of outflows

Recognizes time value of money: a Pound today is worth more than a Pound tomorrow if you have a Pound today, you can invest it, which will return more

than a Pound tomorrow Takes into account compounding effect: you earn interest oninterest

Recognizes the risk of the project:

the discount rate is higher than the interest rate for a risk-lessinvestment

Net present value = measure of wealth you created


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Example

A project requires an initial investment of 1 million.

The project will generate 500,000 per year for the next 4years assume the cash flows occur at year end(common practice)

Compute: The Net Present Value, assuming a required rate of

return of 20%


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NPV of this project


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Internal Rate of Return

The rate of return that makes the Net Present Value equal to zero

Relation between Discount Rate and Net Present Value

-400,000.00

-200,000.00

0.00

200,000.00

400,000.00

600,000.00

800,000.00

1,000,000.00

1,200,000.00

1% 6% 11% 16% 21% 26% 31% 36% 41% 46% 51%

Discount Rate


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Internal Rate of Return

Methods to calculate the IRR: Method 1: use a calculator (spreadsheet) with the IRR function. Method 2: by trial and error.

In this example?

Decision rule: Invest if IRR > required rate of return

Remark: The IRR rule gives the same answer as the NPV rule if theNPV of a project is a smoothly declining function of the interest rate (asin previous example).

What if the NPV of the project is not a smoothly declining function ofthe interest rate?


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Internal Rate of Return:

No solution

Example 1:

There are no solutions: NPV never becomes zero.

C0 C1 C2Project -100 +120 -90

2

2

120 90100

1 1

120 900 100

1 1

NPV

r r

irr irr

-85

-80

-75

-70

-65

-60

0 1 2 3 4 5 6r


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Internal Rate of Return:

Multiple solutions

Example 2:

Two solutions: 25% and 400%.

C0 C1 C2

Project -4,000 +25,000 -25,000

2

2

25,000 25,0004000

11

25,000 25,0000 4,000

1 1

NPVr

r

irr irr


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Payback

Count the number of years until you get your money back

A project requires an initial investment of 1 million andgenerates 500,000 per year for the next 4 years assume the cash flows occur at year end (common

practice). Payback?


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What are the proper criteria?

NPV > 0

IRR > required rate of return

Be careful when there is no solution or when there aremultiple solutions

Why is the payback method not a proper method?

Does not take into account the time value of money

Cut-off period (benchmark) is arbitrary Ignores cash flows beyond cut-off period


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Example

C0 C1 C2 C3 Payback Time NPV

ProjectA -2,000 +2,000 0 0 1 year -182

ProjectB -2,000 +1,000 +1,000 +5,000 2 years +3,492

2 3

2 3

2, 000 0 0

2, 000 182.821 0.10 1 0.10 1 0.10

1, 000 1, 000 5, 0002, 000 3, 492.11

1 0.10 1 0.10 1 0.10

A

B

NPV

NPV

Based on Payback Rule, Project A is preferable since it has a smaller paybacktime (it takes a shorter amount of time start generating positive profits). However theNPV of Project A is negative!


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Exercise

A project requires an initial investment of 400,000. Theproject will generate 200,000 per year for the next 2

years, and 100,000 in 3 years assume the cash flowsoccur at year end (common practice). Compute:

The Net Present Value, assuming a required rate ofreturn of 10%

The Internal Rate of Return

The Payback Period


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Exercise solution


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Keep in mind

Investment decisions should not be made without a proper

valuation and NPV analysis

Investment decision should not be made without having

a champion to support this project and who is heldaccountable

a reasonable story: the champion has to be able to

explain why the NPV is positive


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Summing Up

Net present value is the best technique to evaluate

investment projects Internal rate of return and benefit/cost ratio are acceptable

in most cases

Payback has important limitations


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Perpetuities and Annuities


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In Capital Budgeting sometimes computations become easier. This can be the casewhen cash flows are perpetuities, growing perpetuities or annuities.

Example: Consider the case of the purchase of a machine that costs today $5,000, withrunning costs equal to $2,000 which generates revenues equal to $5,000. Supposethat as long as we keep maintaining the machine, we will be able to sustain theprevious revenues. If the interest rate is 10%, what is the Net Present Value of theinvestment?

The constant stream of cash flows equal to +$3,000 that start in period 1 and last for

ever is a perpetuity.

time 0 1 2 3 forever

Capital Expenditure -$5,000

Running Costs -$2,000 -$2,000 -$2,000 -$2,000

Revenues $5,000 $5,000 $5,000 $5,000

Cash Flows -$5,000

Perpetuities


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0

0

$3,000

0.10

$3,000$5,000

0.10

$25,000

PV

NPV

0

0

$3,000

0.10

$3,000$5,000

0.10

$25,000

PV

NPV

Instead of calculating the PV with long calculations, we can use theshort cut:


Capital Expenditure -$5,000

Running Costs -$2,000 -$2,000 -$2,000 -$2,000

Revenues $5,000 $5,000 $5,000 $5,000

Cash Flows -$5,000

Perpetuities


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Definition: A Perpetuity is a financial Asset that promises to pay a fixed nominal amountC forever

The Present Value at time t= 0 of a perpetuity that starts paying C next period is:

Example 1: What is the Present Value of a Perpetuity that pays $50 forever starting nextperiod? Assume that the opportunity cost of capital is 1%

Example of perpetuities: UK government securities.

time 0 1 2 3 4 .. forever

Cash-flow C C C C .. C

0CPVr

0 CPVr

0

$50$5000

0.01PV 0

$50$5000

0.01PV

Perpetuities


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0 44 4

1 $ 5 0 0 0$ 4 8 0 4 . 9

( 1 ) ( 1 . 0 1 )P V P V

r

0 44 4

1 $ 5 0 0 0$ 4 8 0 4 . 9

( 1 ) ( 1 . 0 1 )P V P V

r

4

$ 5 0$ 5 0 0 0

0 . 0 1

CP V

r 4

$ 5 0$ 5 0 0 0

0 . 0 1

CP V

r


Cash-flow C C

Example 2: What is the Present Value of a Perpetuity that pays $50 foreverstarting in period 5? Assume r = 1%.

Perpetuities


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Example: Consider the case of the purchase of a machine that costs today $5,000,with running costs equal to $2,000 growing at a rate of 2% every year and thatgenerates revenues equal to $5,000 growing at rate of 2% forever. Suppose that as

long as we keep maintaining the machine, we will be able to sustain the previousrevenues. If the interest rate is 10%, what is the Net Present Value of theinvestment?

The stream of cash flows equal to +$3,000 starting in period 1 and growing at aconstant rate forever is a growing perpetuity.

time 0 1 2 3 . forever

Cap. Exp. -$5k .Costs -$2k -$2k (1.02) -$2k (1.02)2 -$2k (1.02)t

Revenues $5k $5k (1.02) $5k (1.02)2 $5k (1.02)t

Cash Flows -$5k

Growing Perpetuities


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0

0

$3,000

0.10 0.02

$3,000$5,0000.10 0.02

$32,500

PV

NPV

0

0

$3,000

0.10 0.02

$3,000$5,0000.10 0.02

$32,500

PV

NPV

Instead of calculating the PV with long calculations, we can use the far simpler short cut:

time 0 1 2 3 . forever

Cap. Exp. -$5k .

Costs -$2k -$2k (1.02) -$2k (1.02)2 -$2k (1.02)t

Revenues $5k $5k (1.02) $5k (1.02)2 $5k (1.02)t

Cash Flows -$5k



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A Growing Perpetuity is a financial Asset that gives the right to receive acash flow growing at a rate equal to gforever.

EXAMPLE:

Next Years Cash Flow = $100Constant Expected Growth Rate = 10%

Cost of Capital = 15%

CPV

r g

CPV

r g

$1002000

0.15 0.10

$1002000

0.15 0.10



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An Annuity is a financial asset that gives the right to receive a constant cash-flow C for tperiods starting next one.

EXAMPLE: Consider a 20-year mortgage. The Annual Payment is equalto $100,000. If you were the Chief Financial Officer of Barclays and theinterest rate were 20%, what is the maximum amount you would lend at the

previous annual payment schedule?You would lend at most the Present Value of thefuture Cash Flows from the mortgage payments. Using the shortcut the result can beeasily obtained:

Yr 0 Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr 6 Yr 7

C C C C C C 0

0

1 1

1

tPV C

r r r

0

1 1

1

tPV C

r r r

20

1 1100, 000 $487, 000

0.2 0.2 1 0.2PV

20

1 1100, 000 $487, 000

0.2 0.2 1 0.2PV

Annuities


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Example: You are offered a building for $5Ml today (Year 0). After some extensiveresearch on the housing market and on interest rates, your expectations are thatyou will be able to sell the building for $7Ml in 10 years from now (Year 10). If the

Cost of Capital is 15%, what is the smallest fixed rent that does not make the dealunprofitable?

Let xbe the rent such that:

time 0 1 2 3 4 5 6 7 8 9 10

sale $7Ml

rent x x x x x x x x x x

9

11

1 0 . 1 5o

xP V

r

10.15 910

$7 1$5

1.15 0.15 1 0.15

MlMl x x

10.15 910

$7 1$5

1.15 0.15 1 0.15

MlMl x x

Annuities: Example


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1 0

75 / 5 . 7 7 1 6 $ 5 6 6 , 5 2 0

1 . 1 5

M lx M l

1 0

75 / 5 . 7 7 1 6 $ 5 6 6 , 5 2 0

1 . 1 5

M lx M l

Solving forx:

Annuities: Example


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Summary

Growing Perpetuities, first payment year 1: Growing Perpetuities, first payment year 1:C

PVr g

CPV

r g

Growing Perpetuities, first payment year (t+1): Growing Perpetuities, first payment year (t+1): 1

(1 )t

CPV

r g r

1

(1 )t

CPV

r g r


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Compound Interest and Inflation


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Compound Interest

Most interest rates are stated in annual terms. This does not,however, mean that interest is paid only once a year. Many securities

pay interest semi-annually (e.g. corporate Bonds), monthly (somesavings accounts), daily, or even continually.

If the compounding frequency is not annual, then the stated interestrate is not equal to the actual return you are earning (effective annualyield). If the compounding frequency increases, so does the effectiveannual yield.


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Compound Interest

i ii iii iv v

Periods Interest Value Annually

per per after compounded

year period (i x ii) one year interest rate

1 6% 6% 1.06 6.000%

2 3 6 1.032 = 1.0609 6.090

4 1.5 6 1.0154 = 1.06136 6.136

12 .5 6 1.00512 = 1.06168 6.168

52 .1154 6 1.00115452

= 1.06180 6.180365 .0164 6 1.000164365 = 1.06183 6.183


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Compound Interest

0

2

4

6

8

10

12

14

16

18

0 3 6 9 12 15 18 21 24 27 30

Number of Years

F

V

of$1

10% Simple

10% Compound


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Compound Interest

We can convert r (as stated by the bank) into the effective annualyield.

We can then use the effective annual yield in order to compareinterest rates that are paid with differing compounding frequencies.

Example:Suppose you are offered an automobile loan at an APR of6% per year. What does that mean, and what is the true rate ofinterest, given monthly payments?


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Compound InterestExample - continued

Suppose you are offered an automobile loan at 6% per year. What does thatmean, and what is the true rate of interest, given monthly payments?Assume$10,000 loan amount.

12Loan Pmt 10, 000 (1.005)

10,616.78

6.1678%Effective Rate

Inflation


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Inflation

Inflation - Rate at which prices as a whole are increasing.

We should distinguish between real and nominal cash flows

Always discount nominal cash flows with the nominal rate

and real cash flows with the real rate.

Nominal Interest Rate - Rate at which money invested grows.

Real Interest Rate - Rate at which the purchasing power of aninvestment increases.

Inflation


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Inflation

rateinflation+1

rateinterestnominal+1

=rateinterestreal1

Approximation formula:

Real int. rate nominal int. rate - inflation rate

Inflation


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Inflation

Example: If the interest rate on one year govt. bonds is 5.9% and theinflation rate is 3.3%, what is the real interest rate?

1

1

+

+

real interest rate =

real interest rate = 1.025

real interest rate = .025 or 2.5%

Approximation =.059-.033 =.026 or 2.6%

1+.0591+.033

Corporate Finance Lecture Notes 1

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