# Company Valuation Residual Income Valuation Method Accounting Essay

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These days, identifying appropriate financial methods and applying them on a company has been one of the most popular and reliable ways of evaluating a company. There are various methods that can be used based on the type of valuation that is required. In this paper, methods which can be used to evaluate a company are being discussed. The Residual Income Valuation method is a widely used method through which a company can get its accurate economic value. Capital Asset Pricing model is a model that describes the relationship between risk and expected returnÂ and is used in the pricing of risky securities. Weighted Average Cost of Capital (WACC) is the appropriate discount rate method used for cash flows when the risk involved is similar in the firm. All these approaches are basically used to know and to predict the financial status & stability of a company and their purpose is best served when used appropriately.

## COMPANY VALUATION

## RESIDUAL INCOME VALUATION METHOD

Residual income is net income less a charge (deduction) for common shareholders' opportunity cost in generating net income. Recent years have seen resurgence in its use as a valuation approach, also under names as Economic Profit Model, abnormal earnings and Economic Value Added Method.

Primary uses of residual income

Measurement of internal corporate performance

Estimation of the intrinsic value of common stock

Residual Income Vs Traditional Accounting Income

Traditional financial statements are prepared to reflect earnings available to owners. Net income includes an expense to represent the cost of debt capital (interest expense). Dividends or other charges for equity capital are not deducted. Traditional accounting leaves to the owners the determination as to whether the resulting earnings are sufficient to meet the cost of equity capital.

The economic concept of residual income, on the other hand, explicitly considers the cost of equity capital.

In the Residual Income Model (RIM) of valuation, the intrinsic value of the firm has two components:

The current book value of equity, plus

The present value of future residual income

This can be expressed algebraically as

B0 is the current book value of equity,

Bt is the book value of equity at time t,

RIt is the residual income in future periods,

r is the required rate of return on equity,

Et = net income during period t,

RIt = Et - rBt-1.

## RIM valuation Vs other Discounted Cash Flow (DCF) models

Timing of recognition of value: Forecasting of future dividends and cash flows is often difficult. One key advantage to a residual income model over other models is the timing of the recognition of value. In DCF approaches most of the value is found in future dividends and in the terminal value computation. The longer the forecast period the higher the uncertainty that will exist regarding these future cash flows.

Terminal value: Further in many residual income valuation contexts the terminal value is deemed to be zero. The determination of book value today is much easier than the determination of a terminal value ten or twenty years hence.

A residual income model is most appropriate when:

A firm is not exhibiting an unpredictable dividend pattern.

A firm has negative free cash flow many years out, but is expected to generate positive cash flow at some point in the future (for example, a young or rapidly growing firm where capital expenditures are being made to fuel future growth.

There is a great deal of uncertainty in forecasting terminal values.

Balance sheet adjustments for fair value

In order to have a reliable measure of book value of equity, the balance sheet should be scrutinized for significant off-balance sheet assets and liabilities. Additionally, reported assets and liabilities should be adjusted to fair value where possible. Some common items to review for balance include:

Inventory

Deferred tax assets and liabilities

Pension plan assets and liabilities

Operating leases

Special purpose entities

Reserves and allowances (for example, bad debts)

Intangible assets

## Nonrecurring items

In applying a residual income model, it is important to develop a forecast of future residual income based upon recurring items.

Often companies report non-recurring charges as part of earnings or classify non-operating income (e.g., sale of assets) as part of operating income. These misclassifications can lead to over-estimates and under-estimates of future residual earnings if no adjustments are made. Note that adjustments to book value are not necessary for these items since non-recurring gains and losses do impact the value of assets in place. Non-recurring items sometimes result from accounting rules and at other times result from "strategic" management decisions.

The analyst should examine the financial statement notes and other sources for potential items that may warrant adjustment in determining recurring earnings such as:

Unusual items

Extraordinary items

Restructuring charges

Discontinued operations

Accounting changes

In some cases, management may be recording restructuring or unusual charges in every period. In these cases, the item may be considered an ordinary operating expense and may not require adjustment.

## CAPITAL ASSET PRICING MODEL (CAPM)

A model that describes the relationship between risk and expected returnÂ andÂ that is used in the pricing of risky securities.

Â The general idea behind CAPM is that investors need to be compensated in two ways: time value of moneyÂ and risk.

The time value of money is represented by the risk-free (Rf) rateÂ in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking onÂ additional risk. This is calculated by taking a risk measure (beta)Â that compares the returns of the asset to the market over a period of time and to the market premium (Rm - Rf).

## Compounded Annual Growth Rate (CAGR)

This is the year after year growth rate of an investment over a specified period of time.

The compound annual growth rate is calculated by taking the nth root of the total percentage growth rate, where n is the number of years in the period being considered.

This can be written as follows:

## Continuing Value

To estimate a company's value, we separate a company's expected cash flow into two periods and define the company's value as follows:

Value = {Present Value of Cash Flow during Explicit Forecast Period} + {Present Value of Cash flow after Explicit Forecast Period}

The second term is the Continuing Value: the value of the company's expected cash flow beyond the explicit forecast period.

If the RE is expected to be same after the forecast period to eternity,

CVt = REt / WACC

If RE is expected to grow at the rate 'g' after the forecast period,

CVt = REt / (WACC - g)

Where, WACC is the Weighted Average Cost of Capital which is generally used for discounting all cash flows while evaluating a project / company.

## WEIGHTED AVERAGE COST of CAPITAL:

"The weighted average cost of capital (WACC) is the discount rate used in value management, including project appraisal" (Arnold, 2002). In WACC, the cost of capital of each category is proportionally weighted. This method can be used to calculate the interest the company would pay for its finances.

Arnold (2002) has classified the capital structure of companies into two types,

All equity &

Mixed, where debt and equity are held in varying proportions.

The all equity firm is appropriate when new investments do not increase the overall risk of the company. For the second type, the discount rate is calculated by weighting the debt and equity costs in proportion. This method is useful for calculating the average capital of an investment. WACC can be calculated by using the following formula,

WACC

Where,

k1, k2.... kn = individual cost of capital

v1, v2,.....vn = market values

This method can also be used for verifying the capital after the deduction of tax. The following formula can be used for serving this purpose,

WACC = kb(1-tc)(B/V) + kp(P/V) + ks(S/V)

Where,

kb = pre-tax market yield

Tc = marginal tax rate of entity valued

B = market value of interest bearing debt

V = market value of enterprise valued

Kp = after tax capital of non-convertible stock

P = market value of preferred stock

Ks = market determined opportunity cost of equity

S = market value of equity

Like other valuating methods, WACC has its own drawbacks as well. Some of them that need to be mentioned are,

Does not consider discount factors.

Based more on assumptions and judgment rather than scientific precision.

Risks like inflation which are considered in other models while making investment are not considered here.

## B. Yolanda Valuation Report

As a part of the valuation method for Yolanda plc, the history of the company and the industry has been studied. The observations of this study are as mentioned below.

## Table 1: Earnings of Yolanda Ltd

Year

Earnings

2005

47,000

2006

51,000

2007

59,000

2008

68,000

2009

75,000

## Table 2: Balance sheet of Yolanda Ltd (as on Dec 2009)

Assets

## £

Net Fixed assets

850,000

Net current assets

150,000

## 1,000,000

Liabilities

## £

5% Debentures 2012/13

100,000

Ordinary shares of £1 each

100,000

Profit & Loss account

800,000

## 1,000,000

## Yolanda Ltd.

Rate of return

15%

Authorised share capital

200,000

Market Value of Fixed Assets

1,000,000

Premium Payable for the redemption of Debentures

20%

Goodwill as perceived by Mgmt of Yolanda

100,000

Face Value of each share

1

## Table 3: P/E Ratio

Industry Average

12

Ashraf plc

15

Bronagh plc

8

Conrad plc

12

Risk-free return (Rf)

2%

Market Return (Rm)

6%

Beta for the Industry

1.5

## Compounded Annual Growth Rate (CAGR) of Yolanda Ltd

CAGR = {(Earnings in 2009 / Earnings in 2005)^(1/4)} - 1

= {(75000/47000)^(1/4)} - 1

= 12.39%

## Excess Return (Re) of Yolanda Ltd:

Re = Rf + Beta * (Rm - Rf)

= 2% + 1.5 x (6% - 2%)

= 8%

Weighted Average Cost of Capital (WACC) has been taken as the IRR of Xavier Ltd. (15%), which the company uses to evaluate any new project or investment.

## For the purpose of valuation, two cases have been considered:

Case 1 - Assumes that the company continues to operate as Yolanda Ltd. with the same management team. This will lead to the following incidents.

Dividend per share (DPS) in 2010

0.80

Growth in DPS till 2012

10%

Growth in DPS after 2012

0%

Earnings in the next few years are forecast based on the assumption that the Earnings in 2009 will grow at the CAGR of the period 2005 - 2009, i.e. 12.39%.

Earnings in 2010 = 75,000 * (1 + 12.39%)

= 84,295

Earnings in 2011 = 84,295 * (1 + 12.39%)

= 94,742

Earnings in 2012 = 94,742 * (1 + 12.39%)

= 106,484

Earnings in 2013 = 106,484 * (1 + 12.39%)

= 119,681

Earnings in 2014 = 119,681 * (1 + 12.39%)

= 134,513

Earnings in 2015 = 134,513 * (1 + 12.39%)

= 151,184

Dividend Expenses = DPS * No of shares

Residual Earnings = Earnings - Dividend expenses

## Continuing Value

Earnings forecast have been made till year 2015. So a continuing value has been arrived at as on 2016. For this purpose the Residual Earnings as on 2015 has been considered to be growing at the Excess Return as calculated to be 8% earlier. Thus, Continuing Value (CV) = {Earnings in 2015 * (1 + Re)} / (WACC - Re)

This has resulted in the following calculations.

## Table 4: Total Present Value

Year

2010

2011

2012

2013

2014

2015

2016

Expected Earnings

84,295

94,742

106,484

119,681

134,513

151,184

Dividend Expenses

80,000

88,000

96,800

96,800

96,800

96,800

Net Earnings

4,295

6,742

9,684

22,881

37,713

54,384

PV(Net Earnings)

3,735

5,098

6,367

13,082

18,750

23,512

Total PV(Net Earnings)

70,544

Continuing Value (CV)

839,070

PV(CV)

315,438

## Total Present Value

## 385,982

Case 2 - Yolanda Ltd is acquired and reorganization is effected so that the following events take place subsequently.

Expected Earnings in 2010

90,000

Dividend per share (DPS) till 2012

0.00

Dividend per share (DPS) in 2013

1.20

Growth in DPS till 2015

10%

Growth in DPS after 2015

0%

Again the Earnings are forecast till year 2015 and expected to grow at the CAGR of 12.39%. This has resulted in the following calculations.

## Table 5: Total Present Value

Year

2010

2011

2012

2013

2014

2015

2016

Expected Earnings

90,000

101,154

113,691

127,781

143,617

161,416

Dividend Expenses

## -

## -

## -

120,000

132,000

145,200

Net Earnings

90,000

101,154

113,691

7,781

11,617

16,216

PV(Net Earnings)

78,261

76,487

74,753

4,449

5,776

7,011

Total PV(Net Earnings)

246,736

Continuing Value (CV)

250,191

PV(CV)

94,056

## Total Present Value

## 340,792

Based on the above two cases, we have calculated two values. This can be used as a reference point to arrive at a price band for the acquisition of Yolanda Ltd.

Lower Limit - To find the lower limit of the price band the lower of the two values is considered and added with the book value of the assets. Also the liabilities like debentures and the premium payable for the redemption of these debentures are subtracted. The assets are taken at the book value only and the goodwill is not being accounted for, since the market value and goodwill values are debatable. Thus the following lower limit was computed.

## Table 6: Lower Limit

Book Value

1,000,000

Debentures

(100,000)

Payables (for Debenture Redemption)

(20,000)

Total Present Value

340,792

Market Value Adjustment

## -

Perceived Goodwill

## -

Price of total shares

## 1,220,792

Or Price per share

## 12.20

Upper Limit - The higher value of the two cases has been considered and maximum allowance has been given for the market value adjustment and goodwill has also been accommodated. Thus the following upper limit was computed.

## Table 6: Upper Limit

Book Value

1,000,000

Liabilities

(100,000)

Payables (for Debenture Redemption)

(20,000)

Total Present Value

385,982

Market Value Adjustment

150,000

Perceived Goodwill

100,000

Price of total shares

## 1,515,982

Or Price per share