Financial Math for Calculating Cost of Capital
Chapter 8
This lecture
• In Chapter 3 it was demonstrated that there are two techniques of valuing an entire corporation:
1. Estimating the value of equity and debt separately, by calculating the present value of dividends and interest and debt repayments, respectively 2. Calculating the present value of free cash flows (total cash flows after capital expenditure)
• These two techniques should produce the same result because free cash flows are eventually distributed to equity holders and debtholders
This lecture (cont’d)
• The value of a corporation is a function of: – The return required by the providers of capital – The corporation’s future cash flows The return required is known as the company cost of capital and is some combination of the cost of debt and cost of equity The three broad steps in valuing a company are: 1. Estimation of the company cost of capital 2. Preparation of cash flow forecasts 3. Discounting cash flows at the company cost of capital
•
•
This lecture (cont’d)
• In this lecture we will discuss the company cost of capital, with regard to:
– Estimation of the cost of debt capital – Estimation of the cost of equity capital – The impact of corporate tax on the company cost of capital – Calculation of the company cost of capital
• We will also discuss the calculation and forecasting of free cash flows, including:
– Cash flow reporting in financial statements – Preparation of free cash flow forecasts
The cost of capital
• In Chapter 3, the following expression for the value of a corporation was presented:
V
1 r
Ft
t 1
t
(3.2)
where: Ft = the net cash flows after tax generated by the
r =
company for its owners (free cash flow) the company cost of capital
The latter variable r is the focus of this lecture
The Cost of Capital (cont’d)
• The cost of capital is a combination of the equity cost of capital and the debt cost of capital • The cost of capital lies between these two values, and is actually a weighted average of these values
• As a result, it is commonly referred to as the weighted average cost of capital (or WACC)
The WACC
• The WACC for a corporation funded by debt and equity capital is given by the following expression:
D E WACC rd re DE DE
(8.1)
where: re = the cost of equity capital rd = the cost of debt capital D = the value of debt used by the company E = the value of equity used by the company
The WACC (cont’d)
Example: Debtholders have contributed $8 million to a company and charge an interest rate of 10% p.a. Equity holders have contributed $2 million and require a return of 15% on their investment. What is the company cost of capital?
D E WACC rd re DE DE 8 2 0.10 0.15 82 82 0.10 0.80 0.15 0.20 0.11 11% p.a.
The Cost of Capital (cont’d)
Example:
CAPITAL
Equity Debt
AMOUNT
$2 million $8 million
ANNUAL COST
15% 10%
ANNUAL COST
$0.3 million $0.8 million
Total
$10 million
?
$1.1 million
The opportunity cost for equity holders is 15% and the interest rate charged by debtholders is 10% The total annual cost of capital in dollar terms is $1.1m, which is 11% of the total capital of $10m This is the weighted average of the equity cost of capital and the debt cost of capital
The cost of debt capital
• In Chapter 3 we used the following expression for the value of a debt security:
D
1 r
F
t 1
n
d
t
1 rd
B
n
(3.3)
where: D = the market value of the debt n = the time to maturity of the debt F = the dollar interest paid on the debt B = the face value of the debt rd = the discount rate
The cost of debt capital (cont’d)
• The cost of the debt is the discount rate (rd) in the previous equation • It is the return built into the cash flows of the debt security by the purchasers of the debt • It can also be seen as the discount rate that makes the present value of the debt’s future cash flows equal to its market value
Estimating the cost of debt (cont’d)
• Number of approaches are used to estimate the cost of debt, including:
– Assuming the debt is risk-free, and using the 10-year government bond yield – Adding 100 – 200 basis points (1 – 2%) to the 10-year bond yield to allow for risk – Applying the following equation:
net interest rd average net debt
(8.2)
Estimating the cost of debt (cont’d)
Example:
At 30 June 2007 and 30 June 2008, 10-year bond yields were 5.01% and 5.87%, respectively. Use this information and the information below to estimate Tabcorp Holdings Ltd’s risk premium on its debt and current cost of debt.
Interest paid during 2008 = 105,195 Interest received during 2008 = 6,188 Net interest2008 = 105,195 – 6,188 = 99,007 Net debt at the end of 2007 = 647,109 Net debt at the end of 2008 = 1,674,956 Average net debt = (647,109 + 1,674,956) / 2 = 1,161,033
Estimating the cost of debt (cont’d)
Example:
At 30 June 2003 and 30 June 2004, 10-year bond yields were at 5.01% and 5.87%, respectively. Use this information and the information below to estimate Tabcorp Holdings Ltd’s risk premium on its debt and current cost of debt.
rd,2004 = net interest / average net debt = 99,007 / 1,161,033 = 8.53% Average 10-year bond yield2004 = (5.01 + 5.87) / 2 = 5.44% Tabcorp risk premium = 8.53 – 5.44 = 3.09% Tabcorp’s current cost of debt (rd) = 10-year bond yield + risk premium = 5.87 + 3.09 = 8.96%
The cost of equity capital
• The cost of equity is the minimum rate of return required by a company’s shareholders, given its risk • The risk is derived from the business risk of the company
• There are two general ways of estimating the required return on shares: – The required rate of return can be implied from the stock price and fundamentals of the company – The CAPM can be used to estimate the required rate of return
Estimating the cost of equity
• In Chapter 3 we learnt that the value of a company’s shares is given by the present value of future dividends, as follows:
dt P 1 re t t 1
where: P = the current price of shares dt = the dividend paid in year t re = the required return on shares
(3.4)
Estimating the cost of equity (cont’d)
Example:
On 30 December 2005, the following information was available for Tabcorp Holdings Ltd: • Forecast growth for next two years = 6.7% • Dividend for year ended 30 June 2006 = 81 per share • Stock price = $15.57 Calculate the implied cost of equity capital.
dt 0.081 P 15 .57 r g r .067 r 0.119 11 .9%
Estimating the cost of equity (cont’d)
• An alternative method of estimating the cost of equity is the CAPM:
Eri rf Erm rf i
(7.4)
where: E(ri) =required return on the equity of stock i E(rm – rf) = expected return on the market over and above the risk-free rate rf = risk-free rate βi = beta of stock i
Estimating the cost of equity (cont’d)
Example:
Using one year of monthly data to June 2007, the beta of Tabcorp Holdings Ltd is estimated to be 0.84. The yield on 10-year bonds is 5.87%. The market risk premium is believed to be 5.2% p.a. What is the cost of equity for Tabcorp?
Eri rf Erm rf i
0.0587 0.052 0.84 0.1024 10.24%
Estimating the cost of equity (cont’d)
• The following steps are required to use the CAPM to estimate the cost of equity:
1. Estimate the beta of the stock using historical data 2. Determine the current risk-free rate 3. Determine the expected market risk premium 4. Substitute these values into the CAPM equation
Estimating the cost of equity (cont’d)
• The first step was discussed at the end of the previous chapter, and steps 2. and 4. are relatively straightforward • We will consider three different approaches to Step 3. - determining the market risk premium
Historical average stock market returns
• In the examples we have used so far we have relied on estimates of the market risk premium based on long-term average returns on equities in excess of bond rates • This approach assumes that: – Realised returns are equivalent to the returns expected by market participants for bearing risk in the future – The market risk premium is constant over time
• Since these assumptions may be untenable, alternative approaches have been developed
Stock prices and analysts’ forecasts
• The market risk premium can also be implied using analysts’ forecasts of earnings and dividends, using a rearrangement of the constant dividend growth model
rei
d1i gi Pit
where: rei = the equity cost of capital for stock i d1 = the one-year-ahead forecast dividend for stock i gi = the constant growth rate for stock i Pit = the current price of stock i
Stock prices and analysts’ forecasts
• To estimate the market risk premium, we:
– Use analysts’ forecast earning (for gi), dividend forecasts (for d1i) and stock price data (for Pit) to estimate rei for each stock – Estimate the required rate of return for the market by calculating the weighted average required rate of return (rei) across all stocks – Subtract the bond yield from the required return on the market to find the market risk premium
• Whilst this avoids the assumption that the market risk premium is constant, it is only accurate if analysts’ forecasts are accurate
37. Consider the following information on Astral Accounting Pty Ltd. Extract of Astral Accounting Pty Ltd Balance Sheet as at June 2006 2006 $000 Current Assets: Cash 12,874 Current Liabilities: Borrowings 5,789 Current Liabilities: Accounts 564 payable Non-current Liabilities: 125,785 Borrowings Non-current Liabilities: 458 Provisions Extract of Astral Accounting Pty Ltd Income Statement as at June 2006 2006 $000 Revenue 54,781 Interest Received 1,884 Interest Paid 15,784 Depreciation 40,874
2005 $000 11,984 8,458 984 114,489 448
2005 $000 43,984 1,485 12,485 38,578
Calculate the cost of debt for Astral Accounting using book values and then determine the current cost of debt using the risk premium approach given the yield on 10-year bonds was 6.50% at June 2005 and 7.25% at June 2006.
Answer: Net interest2006 = 15,784 – 1,884 = 13,900 Net debt2005 = 8,458 + 114,489 – 11,984 = 110,963 Net debt2006 = 5,789 + 125,875 – 12,874 = 118,790 Average net debt = (110,963+118,790)/2 = 114,876.50 rd = 13,900/114,876.50 = 0.1210 or 12.10 per cent Average 10-year bond yield = (6.50 + 7.25)/2 = 6.875 giving a risk premium of 12.10 – 6.875 = 5.225 per cent Adding this to the current yield on 10-yeilds bonds gives a cost of debt of 12.475 per cent. Difficulty: 3 Page: 237
Corporate financial reporting System
Free cash flows before tax
Government
Free cash flows after tax
Shareholders Real assets Debtholders
Capital expenditure
• Free cash flows after tax are then distributed to capital providers (shareholders and debtholders)
Corporate financial reporting (cont’d)
• The financial statements of a company include a Statement of cash flows prepared in accordance with Accounting Standards • These standards promote the reporting of historical cash flows in a similar form across companies • The cash flows usually form the basis for forecasting future cash flows for the purpose of valuing a company
Statement of cash flows (cont’d)
• The cash flow statement is divided into three sections:
Cash flows from operating activities Cash flows used in investment activities Cash flows used in financing activities Examples:
Cash receipts and payments in the course of operations
Income tax paid
Dividends received
Interest received or paid
Statement of cash flows (cont’d)
• The cash flow statement is divided into three sections:
Cash flows from operating activities Cash flows used in investment activities Cash flows used in financing activities Examples:
Purchases of property, plant and equipment
Sales of property, plant and equipment Purchases and sales of businesses
Statement of cash flows (cont’d)
• The cash flow statement is divided into three sections:
Cash flows from operating activities Cash flows used in investment activities Cash flows used in financing activities Examples:
Funds lent, borrowed or repaid
Proceeds of share issues
Funds used for share buybacks
Dividends paid
Calculation of free cash flows
• Only a few items are required for the calculation of free cash flows:
Cash flows from operating activities
This item represents all of the cash flows generated by the firm’s real assets
Examples:
Cash receipts and payments in the course of operations
Income tax paid Dividends received Interest received or paid
These items all represent distributions to shareholders, debtholders and the government
Calculation of free cash flows (cont’d)
• Only a few items are required for the calculation of free cash flows:
Cash flows used in investment activities Examples:
Purchases and sales of property, plant and equipment
Purchases and sales of business
The net expenditure on investment activities (the bottom line from this section of the cash flow statement) represents capital reinvested in real assets
Total
Calculation of free cash flows (cont’d)
• Only a few items are required for the calculation of free cash flows:
Cash flows used in financing activities Examples:
Funds lent, borrowed or repaid
Proceeds of share issues
All items in this section represent distributions to shareholders or debtholders, and are not as relevant in the calculation of free cash flows
Funds used for share buybacks
Dividends paid
Calculation of free cash flows (cont’d)
• Hence, the free cash flows can be calculated from a company’s cash flow statement using the following calculation:
Cash receipts from operations Less: Cash payments from operations Less: Net capital expenditure Equals:Free cash flows before tax
• The corporate tax rate is then applied to free cash flows before tax to find free cash flows after tax • Note that all other items on the cash flow statement relate to distribution of cash flows to owners and are irrelevant to valuing the firm
Calculation of free cash flows (cont’d)
Example: Calculate the free cash flows for Tabcorp Holdings for the year ended 30 June 2007, given the following information from the cash flow statement: ● Cash receipts from operations = $2,510.0m ● Cash payments from operations = $1,798.9m ● Net capital expenditure = $101.2m
$ million
Cash receipts from operations 2510.0 Less: cash payments from operations 1798.9 net capital expenditure 101.2 Free cash flows before tax 609.9
Calculation of free cash flows (cont’d)
Example:
Estimate the value of each Tabcorp share, given: ● Estimated real after-tax company cost of capital = 8.38% ● Forecast real economic growth = approximately 3% ● Number of shares = 423.48 million ● Net debt = $1675m
(i) Free cash flows after tax: F FCF before tax 1 t t c
609 .9 1 0.30 426 .9
(ii) Value of firm using constant dividend growth model:
Ft 1 g 426 .91.03 V $8173 .0 WACC g 0.0838 0.03
Calculation of free cash flows (cont’d)
Example:
Estimate the value of each Tabcorp share, given: ● Estimated real after-tax company cost of capital = 8.38% ● Forecast real economic growth = approximately 3% ● Number of shares = 423.48 million ● Net debt = $1675m (iii) Value of equity = value of firm – net book value of debt
$8173.0 $1675 $6498
(iv) Value of each share = value of equity / number of shares
$6498 423 .48 $15 .34