3. cost of capital

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Part VI: Valuation of Part VI: Valuation of Securities and Cost of Securities and Cost of

CapitalCapital

3. The Cost of Capital

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What is the “Cost” of Capital?What is the “Cost” of Capital?

A company’s cost of capital is the average cost of the various capital components (or securities) employed by it.

Put differently, it is the average rate of return required by the investors who provide capital to the company.

Return that an investor receives from a security is the cost of that security to the company that issues it.

Cost of capital associated with an investment depends on the risk of that investment.

It is not right to think that cost of capital for an investment depends primarily on how and where the capital is raised.

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What is the “Cost” of Capital?What is the “Cost” of Capital?

When we talk about the “cost” of capital, we are talking about the required rate of return on invested funds

It is also referred to as a “hurdle” rate because this is the minimum acceptable rate of return

Any investment which does not cover the firm’s cost of funds will reduce shareholder wealth (just as if you borrowed money at 10% to make an investment which earned 7% would reduce your wealth)

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Financial Policy and Cost of Financial Policy and Cost of CapitalCapital

Lets say the financial policy of the firm is given That means firm has fixed debt-equity ratio to

maintain This ratio reflects the firm’s target capital

structure. Given that a firm uses both debt and equity

capital, this overall cost of capital will be a mixture of the returns needed to compensate its creditors and those needed to compensate its stockholders.

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The Appropriate Hurdle Rate: An The Appropriate Hurdle Rate: An ExampleExample

The managers of Rocky Mountain Motors are considering the purchase of a new tract of land which will be held for one year. The purchase price of the land is $10,000. RMM’s capital structure is currently made up of 40% debt, 10% preferred stock, and 50% common equity. This capital structure is considered to be optimal, so any new funds will need to be raised in the same proportions.

Before making the decision, RMM’s managers must determine the appropriate require rate of return. What minimum rate of return will simultaneously satisfy all of the firm’s capital providers?

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RMM Example (cont.)RMM Example (cont.)

Because the current capital structure is optimal, thefirm will raise funds as follows:

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RMM Example (Cont.)RMM Example (Cont.)

The following table shows three possible scenarios:

Obviously, the firm must earn at least 9.8%. Any less,and the common shareholders will not be satisfied.

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The Weighted Average Cost of The Weighted Average Cost of CapitalCapital

We now need a general way to determine the minimum required return

Recall that 40% of funds were from debt. Therefore, 40% of the required return must go to satisfy the debt holders. Similarly, 10% should go to preferred shareholders, and 50% to common shareholders

This is a weighted-average, which can be calculated as:

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Calculating RMM’s WACCCalculating RMM’s WACC

Using the numbers from the RMM example, we can calculate RMM’s Weighted-Average Cost of Capital (WACC) as follows:

Note that this is the same as we found earlier

WACC 0 40 0 07 010 010 0 50 012 0 098. ( . ) . ( . ) . ( . ) .

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Things to rememberThings to remember

For the sake of simplicity, we have considered only three types of capital viz – equity; nonconvertible, non-callable preference; and nonconvertible, non-callable debt.

Debt includes long term debt as well as short-term debt (such as working capital loans and commercial papers)

Non-interest bearing liabilities, such as trade creditors, are not included in the calculation.

Does that mean non-interest bearing liabilities have no cost ?

NO, but this cost is implicitly reflected in the price paid by the firm to acquire goods and services. Hence, it is already taken care of before the cash flow is determined.

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Finding the WeightsFinding the Weights

The weights that we use to calculate the WACC will obviously affect the result

Therefore, the obvious question is: “where do the weights come from?”

There are two possibilities:• Book-value weights• Market-value weights

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Book-value WeightsBook-value Weights

One potential source of these weights is the firm’s balance sheet, since it lists the total amount of long-term debt, preferred equity, and common equity

We can calculate the weights by simply determining the proportion that each source of capital is of the total capital

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Book-value Weights (cont.)Book-value Weights (cont.)

The Table shows the calculation of the book-value weights for RMM:

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Market-value WeightsMarket-value Weights

The problem with book-value weights is that the book values are historical, not current, values

The market recalculates the values of each type of capital on a continuous basis. Therefore, market values are more appropriate

Calculation of market-value weights is very similar to the calculation of the book-value weights

The main difference is that we need to first calculate the total market value (price times quantity) of each type of capital

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Calculating the Market-value Calculating the Market-value WeightsWeights

The following table shows the current market prices:

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Market vs Book ValuesMarket vs Book Values

It is important to note that market-values is always preferred over book-value

The reason is that book-values represent the historical amount of securities sold, whereas market-values represent the current amount of securities outstanding

For some companies, the difference can be much more dramatic than for RMM

Finally, note that RMM should use the 10.27 WACC in its decision making process

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Which weight to use?Which weight to use?

The appropriate weights are the target capital structure weights stated in the market value terms.

What is the rationale for using the target capital structure ?• Current capital structure may not reflect the capital structure

that is expected to prevail in future with project being employed.

Difficulties in using the target capital structure:1. A company may not have a well-defined target capital structure2. Changing complexion of its business or changing conditions in

the capital market may make it difficult for the company to articulate its target capital structure.

3. If the target capital structure is significantly different from the current capital structure, it may be difficult to estimate what the component capital costs would be.

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Company Cost of Capital vs. Company Cost of Capital vs. Project Cost of CapitalProject Cost of Capital

The company cost of capital is the rate of return expected by the existing capital providers.

It reflects the business risk of existing assets and the capital structure currently employed.

The project cost of capital is the rate of return expected by capital providers for a new project or investment the company proposes to undertake.

It will depend on the business risk and debt capacity of the new project.

If a firm wants to use its company cost of capital (WACC), for evaluating a new investment, two conditions should be satisfied:• The new investment will not change the risk complexion of the

firm.• The capital structure of the firm will not be affected by the new

investment i.e. The firm will continue to follow the same financing policy.

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The Costs of CapitalThe Costs of Capital

As we have seen, a given firm may have more than one provider of capital, each with its own required return

In addition to determining the weights in the calculation of the WACC, we must determine the individual costs of capital

To do this, we simply solve the valuation equations for the required rates of return

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The Cost of DebtThe Cost of Debt

Conceptually, the cost of debt instrument is the YTM of that instrument

Recall that the formula for valuing bonds is:

We cannot solve this equation directly for kd, so we must use an iterative trial and error procedure (or, use a calculator)

Note that kd is not the appropriate cost of debt to use in calculating the WACC, instead we should use the after-tax cost of debt

n

1tt

dt

d0 )k1(

M

)k1(

IP

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ApproximationApproximation

M4.0P6.0n

)PM(I

k0

0

d

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The After-tax Cost of DebtThe After-tax Cost of Debt

Recall that interest expense is tax deductible Therefore, when a company pays interest, the actual

cost is less than the expense The tax rate to be used in is the Marginal Tax Rate

applicable to the company As an example, consider a company in the 34%

marginal tax bracket that pays $100 in interest The company’s after-tax cost is only $66. The

formula is:

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What about Other What about Other Instruments ?Instruments ?

What about bank loan ? Unlike debenture and bond, a bank loan is not

traded in the secondary market. The cost of a bank loan is simply the current

interest the bank would charge if the firm were to raise a loan now. (not the interest rate on the outstanding loan)

What about commercial paper ? A commercial paper is a short-term debt instrument

which is issued at a discount and redeemed at par. Hence the cost of commercial paper is simply its

implicit interest rate.

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IllustrationIllustration

Suppose A ltd has outstanding commercial paper that has a balance maturity of 6 months. The face value of one instrument is Rs 1,000,000 and it is traded in the market at Rs 965,000.

The implicit interest rate for 6 months is:1000,000 / 965,000 – 1 = 0.0363 i.e. 3.63 %

The annualized interest rate works out to:(1.0363)2 -1 = 0.0739 or 7.39 %

When a firm uses different instruments of debt, the average cost of debt has to be calculated.

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Debt Instrument Face Value

Market Value

Coupon Rate

YTM or Current

Rate

Non-convertible Debentures

Rs 100 Mln

Rs 104 Mln 12 % 10.7 %

Bank Loan Rs 200 Mln

Rs 200 Mln* 13 % 12.0 %

Commercial Paper Rs 50 Mln Rs 48.25 Mln

N.A 7.39 %

Total Rs 352.25 Mln

*Since the bank loan doesn’t have a secondary market, we have, for the sake of simplicity, equated market value with face value.

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Solution:Solution:

Average Cost of Debt for A ltd:

10.7 % [104 / 352.25] + 12.0 % [200/352.25] + 7.39 % [48.25 / 352.25] = 10.98 %

Note that we use the YTM or the Current Rates as they reflect the rates at which the firm can raise new debt.

Coupon rates that reflect historical or embedded interest rates at the time the debt was originally raised are not relevant for our purposes.

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The Cost of Preferred EquityThe Cost of Preferred Equity

As with debt, we calculate the cost of preferred equity by solving the valuation equation for kP:

Note that preferred dividends are not tax-deductible, so there is no tax adjustment for the cost of preferred equity

If a company has more than one issue of preference stock outstanding, the average yield on all preference issues may be calculated.

0p P

Dk

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Cost of EquityCost of Equity

Equity finance may be obtained in two ways:1. Retention of Earnings2. Issue of additional equity

The cost of equity is same in both the cases When a firm decides to retain earnings, an

opportunity cost is involved. Shareholders could receive the earnings ad

dividends and invest the same in alternative investments of comparable risk to earn a return.

So, irrespective of whether a firm raises equity finance by retaining earnings or issuing additional equity shares, the cost of equity is the same.

The only difference is in floatation cost.

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The Dividend Growth Model The Dividend Growth Model ApproachApproach

.......)k1(

)g1(D...........

)k1(

)g1(D

)k1(

)g1(D

)k1(

)g1(D

k1

DP

1nc

n1

4c

31

3c

21

2c

1

c

10

gP

g)1(Dg

P

Dk

g-k

D

g-k

g)1(DP

0

0

0

1c

c

1

c

00

• We know the value of equity stock according to dividend growth model is:

If dividends are expected to grow at a constant rate of g % per year then :

The expected return of shareholders is the required return which is equal to the dividend yield plus the expected growth rate.

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Estimating gEstimating g

Relying on analyst’s forecast for the future growth rates. Obtain multiple estimates from various sources and then average them.

Look at the dividends for the preceding 5-10 years, calculate annual growth rates, average them. For egYear Dividend Rupee Change Growth %

1 Rs 3.00 - -2 Rs 3.50 Re 0.50 16.7 %3 Rs 4.00 Re 0.50 14.3 %4 Rs 4.25 Re 0.25 6.3 %5 Rs 4.75 R Re 0.50 11.8 %

Average = 12.3 % Use Retention Growth Rate Method (Sustainable Growth Rate)

g = b x ROE

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The SML (Security Market Line) The SML (Security Market Line) ApproachApproach

According to SML, the required return on company’s equity is:

rE = Rf + βE (RM - Rf)

Where, Rf = Risk-free rate

βE = Systematic Risk (un-diversifiable risk) of the asset relative to average, which we call beta of the equity of the company

RM= Expected return on the market portfolio

(RM – Rf) = Market Risk Premium

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Inputs for SML approachInputs for SML approach

The risk-free rate may be estimated as the yield on a long-term government bond that has maturity of 10 years or more.

The market risk premium may be estimated as the difference between average return on the market portfolio and the average risk free rate over the past 10 to 30 years – the longer the period, better it is.

The beta of the stock may be calculated by regressing the monthly returns on the stock over the monthly return on the market index over the past 60 months or more

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Bond Yield Plus Risk Premium Bond Yield Plus Risk Premium ApproachApproach

Cost of Equity = Yield on Long Term Bonds + Risk Premium

Logic:• Firms that have risky and consequently high cost of debt

will also have risky and consequently high cost of equity.• So it makes sense to base the cost of equity on a readily

observable cost of debt. Problem is how to determine risk premium There’s no objective way of determining it. Most analyst look at the operating and financial

risks of the business and arrive at a subjectively determined risk premium (2 % - 8 %)

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Flotation CostsFlotation Costs

When a company sells securities to the public, it must use the services of an investment banker

The investment banker provides a number of services for the firm, including:• Setting the price of the issue, and• Selling the issue to the public

The cost of these services are referred to as “flotation costs,” and they must be accounted for in the WACC

Includes underwriting costs, brokerage expenses, fees, advertising expenses etc.

Generally, we do this by reducing the proceeds from the issue by the amount of the flotation costs, and recalculating the cost of capital

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The Cost of Debt with Flotation The Cost of Debt with Flotation CostsCosts

Simply subtract the flotation costs (F) from the price of the bonds, and calculate the cost of debt as usual:

Note that we still must adjust this calculation for taxes

n

1tt

dt

d0 )k1(

M

)k1(

IFP

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The Cost of Preferred with Flotation The Cost of Preferred with Flotation CostsCosts

Simply subtract the flotation costs (F) from the price of preferred, and calculate the cost of preferred as usual:

FP

Dk

0p

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The Cost of Common Equity with Flotation The Cost of Common Equity with Flotation CostsCosts

Simply subtract the flotation costs (F) from the price of common, and calculate the cost of common as usual:

gFP

g)1(Dg

FP

Dk

g-k

D

g-k

g)1(DFP

0

0

0

1c

c

1

c

00

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A Note on Flotation CostsA Note on Flotation Costs

The amount of flotation costs are generally quite low for debt and preferred stock (often 1% or less of the face value)

For common stock, flotation costs can be as high as 25% for small issues, for larger issue they will be much lower

Note that flotation costs will always be given, but they may be given as a dollar amount, or as a percentage of the selling price

The cost of retained earnings is exactly the same as the cost of new common equity, except that there are no flotation costs

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Approach 1Approach 1

Cost Floating -1

WACC WACCRevised

A better approach is to leave the WACC unchanged but to consider floatation costs as part of the project cost.

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Better Approach (Illustration)Better Approach (Illustration)

A ltd, an all equity firm has WACC of 18 % (cost of equity) Its considering a Rs 200 million expansion project which will be

funded by selling additional equity. Based on the advice of its merchant banker, A ltd believes that

its floatation costs will be 8 % of the amount issued. This means that the net proceeds will only be 92 % of the

amount of equity raised. What is the cost of expansion, considering the floatation

costs ?Rs 200 million = 0.92 x Amount RaisedAmount Raised = Rs 217.39 millionHence, Floatation cost of A ltd = Rs 17.39 million andTrue cost of expansion project is Rs 217.39 million

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Floatation Cost and WACCFloatation Cost and WACC

If the firm raises a mixture of capital then find weighted average floatation cost which is defined as:

FA = wrFr + weFe + wpFp + wdFd

FA of 5.1 % means that for every rupee of financing needed by the firm for its investments, the firm must rise

1 / (1- 0.051) = Rs 1.054 Use the weights in the target capital structure, even

though the specific investment under consideration is financed entirely by debt or equity (because firm has to maintain its constant financial policy)

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Floatation Costs and NPV Floatation Costs and NPV (Illustration)(Illustration)

B ltd is currently at its target debt-equity ratio of 4:5 It is evaluating a proposal to expand capacity which

is expected to cost Rs 4.5 million and generate after-tax cash flows of Rs 1 million per year for the next 10 years.

The tax rate for the company is 25 %. Two financing options are being looked at:

• Issue of equity stock. The required return on company’s new equity is 18 %. The issuance cost will be 10 %

• Issue of debentures carrying a yield of 12 %. The issuance cost will be 2 %.

What is the NPV of the expansion project ?

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Solution:Solution:

WACC = (5/9) x 18 % + (4/9) x 12 % (1-.025) = 14 % NPV = Rs 1,000,000 x PVIFA ( 14 %, 10 yrs) – Rs 4,500,000

= Rs 716,000 What will be the effect of floatation cost ? Weighted average floatation cost is:

FA = (5/9) x 10 % + (4/9) x 2 % = 6.44 % Note that B ltd can finance the project entirely with equity

or debt is irrelevant. What matters is the target capital structure ?

True cost of project = Rs 4,500,000 / 0.9356 = Rs 4,809,748 NPV = Rs 1,000,000 x PVIFA ( 14 %, 10 yrs) – Rs 4,809,748

= Rs 406,252 The project is still worthwhile

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Marginal Cost of CapitalMarginal Cost of Capital

At the outset we assumed, inter alia, that the adoption of new investment proposals will not change either the risk complexion or the capital structure of the firm.

Does it mean that the WACC will remain the same irrespective of the magnitude of financing ?

Apparently not. Generally, WACC tends to rise as the firm seeks

more and more capital. As financers provide more capital , the rate of return

required by them tends to increase. A schedule or graph showing the relationship

between additional financing and the WACC is called the Weighted Marginal Cost of Capital Schedule.

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Determining the WMCC Determining the WMCC ScheduleSchedule

1. Estimate the cost of each source of financing for various levels of its use through an analysis of current market conditions and an assessment of the expectation of investors and lenders.

2. Identify the levels of total new financing at which the cost of the new components would change, given the capital structure policy of the firm. These levels, called breaking points can be established using the following relationships:

BPj = TFj/ wj

where, BPj = breaking point on account of financing source j

TFj = total new financing from source j at the breaking pointwj = proportion of financing source j in the capital

structure3. Calculate the WACC of various ranges of total financing

between breaking points.4. Prepare the WMCC schedule which reflects the WACC for each

level of total new financing.

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Electronics Ltd plans to use equity and debt in the proportion of 40:60

Cost of each source of finance for various levels of use: Based on its discussions with its merchant bankers and lenders Electronics estimates –

Sources of Finance Range of New financing (Rs Mln) Cost

Equity 0 -30 18 %

> 30 20 %Debt 0 -50 10 %

> 50 11 %

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Illustration (contd…)Illustration (contd…)

Breaking Points: Column 3

Sources

Cost(1)

Range of new

Financing (2)

Breaking Point(3)

Range of Total New Financing

(4)

Equity 18 % 0 – 30 30 / 0.4 = 75 0 -75

20 % > 30 - Above 75

Debt 10 % 0 -50 50 / 0.6 = 83.3

0 – 83.3

11 % 50 - > 83.3

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WACC for various ranges of total financing:• Column shows that the firm’s WACC will change at Rs 75

Mln and Rs 83.3 Mln.Range of total new financing

Source of capital

(1)

Proportion(2)

Cost (3)

Weighted Cost

(2 x 3) (4)

0 -75 EquityDebt

WACC

0.40.6

18 %10 %

7.2 %6.0 %

13.2 %

75 – 83.3 EquityDebt

WACC

0.40.6

20 %10 %

8.0 %6.0 %

14.0 %

> 83.3 EquityDebt

WACC

0.40.6

20 %11 %

8.0 %6.6 %

14.6 %

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Range of Total Financing(Rs in Mln)

WMCC

0 – 75 13.2 %

75 -83.3 14.0 %

> 83.3 14.6 %

Weighted Marginal Cost of Capital Schedule

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5.6 Determining the Optimal 5.6 Determining the Optimal Capital BudgetCapital Budget

Compare the expected return on proposed capital expenditure projects with the WMCC schedule.

Illustration: Electronics Ltd is developing its capital budget for the forthcoming year. The company’s proposed capital expenditure projects for the coming year is as follows:

Project Amount (Rs Mln) IRR

A 30 18.0 %

B 40 16.5 %

C 25 15.3 %

D 10 13.4 %

E 20 12.0 %

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The expected returns from the proposed capital expenditures are plotted against the cumulative funds required and shown as the investment opportunity curve

Also WMCC cost of capital curve is plotted.

The optimal capital budget is reflected by the point at which the investment opportunity curve and the marginal cost of capital curve intersect.

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Determining optimal capital Determining optimal capital budgetbudget

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SolutionSolution

Thus, the optimal capital budget for Electronics totals Rs 95 million and includes Projects A, B and C. Projects D and E are excluded as their expected returns are lower than marginal cost of capital.

3. cost of capital

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