Let’s face it, the series 79 exam is extremely challenging. You will be required to apply deep analytical reasoning and challenging mathematical concepts. Often understanding what the questions are asking is not enough. It can be difficult to translate key concepts into mathematical equations.
In this article we are going to help test takers master the top math formulas for the series 79 exam.
These math formulas can be used to create a series 79 cheat sheet. This will help you commit the equations to memory. Review your cheat sheet frequently, adding new concepts as your studying progresses.
Investment bankers and analysts developed the PEG ratio. This is used to account for the impact of a company’s growth rate on its future earnings. i. Many market participants consider the PEG ratio to be a better indicator of the true value for a company. The PEG ratio is a relationship between the PE ratio and the forward looking growth rate for the company’s EPS. The formula is as follows:
PE Ratio / EPS Growth Rate
Like the PE ratio, lower PEG ratios represent lower valuations and potentially better values. A company with a PEG ratio of 1 represents a company that is considered to be fairly valued. While PEG ratios greater than 1 would be seen as overvalued. Consider the following example:
SIA Co, Is trading in the market at $50 per share and its EPS for the trailing 12 months is $4.20. SIA is expected to grow earnings by 14 percent. SIA’s PEG ratio would be found as follows:
PE Ratio = 50 / $4.2 = 11.9
PEG Ratio = 11.9 / 14 = .85
With a PEG ratio of less than 1, SIA seems to be undervalued by the market. As with any forward looking projections, the accuracy of the PEG ratio can be negatively affected by unforeseen events. An economic shock or the loss of a major contract could cause a company’s growth to slow or to even turn negative. In these instances, the PEG ratio will have overvalued the stock. Additionally, the valuation or price target placed on the stock is only as good as the analysts’ estimated growth rate. Different analysts often come up with different projected growth rates for a company’s earnings. As a result the valuatations and price targets can vary significantly from one to another. Many investors are willing to pay a premium for companies whose earnings are growing faster than their competitors. As a prospective investment banker being able to calculate the PEG ratio is an important part of the job description.
A company’s enterprise value can be thought of as the sum of all costs a buyer must pay to acquire the assets and financial performance of a business. The total enterprise value or EV includes the core operations, joint ventures, capital leases, non core assets and any non controlling interests. As a prospective investment banker it is important to have a full understanding of different ways to calculate the EV for prospective M&A transactions. Enterprise value is often thought of as the sum of a company’s equity value plus its debt. The formula for calculating enterprise value is :
EV = Equity Value + Debt + Preferred Stock + non controlling interest – Cash and Equivalents
The enterprise value requires the buyer to satisfy or assume the liabilities based on the claims of all capital providers (stockholders, bondholders) creditors and vendors. When considering the enterprise value of a company there are several things to keep in mind:
Let’s take a look at the following information and use it to calculate the enterprise value for SIA.
| Outstanding Common Stock | 10 million |
| Stock Price | $45 |
| Cash | $8 million |
| Short Term Debt | $ 3 million |
| Long Term Debt | $4 million |
| Non Controlling Interest | $ 7 million |
The first step is to calculate the market capitalization for SIA:
$45 X 10 million =$450 million
Next we the total short and long term debt of $7 million
$450 million + $7 million = $457 million
From this figure we subtract the cash of $8 million
$457 million – $8 million – $449 million
Finally we add the value of the non controlling interest of $ 7 million
$449 million + $7 million = $456 million
The total enterprise value of SIA is $456 million. While in theory the enterprise value is what an acquirer would have to pay for a company, it is not actually reflective of what an acquirer would be willing to pay. Further, it is not indicative of what sellers would be willing to accept for the company. In the real world investment bankers often need to calculate the enterprise value based on a company’s fully diluted share count. This assumes that all in the money options, rights and warrants have been exercised and all in the money convertibles have been converted into common shares. In extreme cases a company with a low market capitalization and a high level of net cash could have a negative enterprise value. These could be significant warning signs for a company who is in trouble or close to filing for bankruptcy. It is interesting to note that a company could have a negative enterprise value, but it cannot have a negative equity value, as the stock price can never fall below zero.
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Free cash flow is the cash flow generated by the enterprise’s operating activities less its capital expenditures. Capital expenditures, usually referred to as CAPEX, includes the payments the company is required to make to purchase and maintain its physical assets such as its plant and equipment. CAPEX will tend to increase during times when the company is expanding its operations or entering new markets. Additionally, most businesses have ongoing CAPEX requirements to simply maintain its current level of production. If a company fails to maintain its assets, the assets’ productivity will decline and the company will see its output and revenue fall. Free cash flow is therefore thought to be the cash flow generated by the business less the cash required to maintain or expand its operations. In turn the free cash generated is available to the providers of capital to the business. The company can use the free cash flow to service its debt (paying interest and principal payments to bondholders), to pay dividends to its shareholders or to repurchase its shares. Free cash flow can be calculated based on the company’s EBITDA or the EBIT. Both of which have already factored in the operating expenses or OPEX of the company. Operating expenses include the day to day expenses of the company such as salaries, rent, utilities and costs of goods sold. The main difference between CAPEX and OPEX is CAPEX are expenses incurred for major long term investments while OPEX are expenses incurred for the daily operations of the company. Operating expenses reduce the taxable income of a company while CAPEX does not. The long term assets acquired as part of CAPEX are traditionally depreciated over the life of the asset. Even though free cash flow is not a GAAP accounting measure, it is very useful as it tells us how much cash a company has left after paying its operating expenses and capital expenditures. The following formulas can be used to calculate the free cash flow for a company :
| Formula | Change in working capital |
| EBITDA – Taxes- CAPEX – increase in working capital | Increased |
| EBITDA – Taxes- CAPEX + decrease in working capital | Decreased |
| EBIT – Taxes-net CAPEX ( CAPEX – Depreciation) – increase in working capital | Increased |
| EBIT – Taxes-net CAPEX ( CAPEX – Depreciation) + decrease in working capital | Decreased |
| EBIT X(1-Tax Rate) + Depreciation and Amortization – Capital Expenditures – Increase in working capital | Increased |
| EBIT X (1-Tax Rate) + Depreciation and Amortization – Capital Expenditures + decrease in working capital | Decreased |
A company’s weighted average cost of capital or WACC, is the weighted average after tax cost of obtaining capital through all capital sources. For most companies these capital sources include the issuance of common and preferred stock and the issuance of bonds. The weighted average cost of capital is the average after tax cost that a company would expect to pay to finance its assets. The WACC is calculated using the cost of each source of capital. The cost of each equity and debt issue is then multiplied by its percentage contribution to the company’s capital base and added together to arrive at the WACC. To simplify the concept the formula is:
WACC = Weighted Average Cost of Debt + Weighted average cost of Equity
There are several factors that can further impact a company’s capital costs. These factors include the expenses incurred to issue and underwrite the securities. These costs are sometimes referred to as flotation expenses. Fees or discounts paid to underwriters and legal costs are just a few of the expenses that can reduce the proceeds to the issuer and increase its capital costs. The cost of issuing debt securities has several additional factors that must be considered. First, the nominal yield is effectively the pre tax cost for borrowing the funds without considering any flotation expenses. However, in addition to the underwriting and floatation expenses any original discount passed on to investors will increase the pre tax cost to the company. The example below illustrates this point.
SIA, Co is seeking to expand its operations and will be issuing $10 million worth of 10 year bonds. The bonds will be issued at par with a 7 percent coupon. SIA’s nominal pre tax cost of capital is $700,000 per year ($10 million X 7%). In order to issue the bonds SIA engaged an underwriting syndicate and the fees paid to the underwriters and other legal and printing costs totaled $400,000. SIA’s proceeds from the bond issuance were therefore reduced by an equal amount resulting in net proceeds of $9.6 million. SIA’ s pre tax cost of issuing the bonds is found as follows:
Annual Interest Expense / Net Proceeds
In this case
$700,000 / $9,600,000
SIA’s pre tax cost of issuing the bonds is 7.29% If bonds in the above example were issued at discount to investors to help market the issue, the discount would further reduce the proceeds to the company and increase its cost of capital. If we keep the flotation costs of $400,000 constant and the bonds were issued at a price of $990 instead of par, the cost of issuing the 7 percent bonds would be 7.36% . The net proceeds to the issuer would be $9.5 million and the annual interest cost remains $700,000. Because the interest payments made to bondholders are made with pre tax dollars. This favorable tax treatment reduces the overall cost of raising capital through the issuance of bonds. Let’s look at the after tax cost of capital for SIA assuming the bonds were issued at par and without considering flotations costs. First we will calculate the after tax cost of capital for the 7 percent bond issue. If SIA pays a corporate tax rate of 28 percent, the after tax cost of the bond issue would be found as follows:
Pre Tax Rate X (100%- Tax Rate)
7% X (100-28)
7% X .72 = 5.04%
A stock’s beta impacts both its expected return and the issuer’s cost of equity capital. A company’s levered beta takes into account the impact of the capital structure and its use of borrowed funds or leverage. Unless stated otherwise, the beta coefficient used in most cases is the levered beta. The greater the company’s leverage the greater its beta and the more of its earnings are committed to servicing debt. The unlevered beta removes the impact of the company’s capital structure and its use of leverage and is based solely on the company’s equity or assets. For this reason unlevered beta is sometimes referred to as asset beta. On your exam you will be required to calculate both the levered and unlevered Beta. You will not be given the formulas and must commit them to memory as follows:
Unlevered Beta = levered Beta / 1+ [(1-tax rate) X (debt/equity)]
Levered Beta = Unlevered Beta X 1+ [(1-tax rate) X (debt/equity)])
Let’s look at how to calculate the unlevered beta given a levered beta.
| Levered Beta | 1.5 |
| Debt/ Equity | 40 % |
| Tax Rate | 28% |
1.5 /1+[(1-28%)x40%)]) =
1.5 / 1+(.72x .4) =
1.5 / 1.288
In this case the unlevered beta would be 1.164. Now lets calculate the levered beta given an unlevered beta
| Unlevered Beta | 1.3 |
| Debt/ Equity | 30 % |
| Tax Rate | 28% |
Using the above formula and information provided we calculate the levered beta as follows:
Levered beta = unlevered beta X (1 + [(1- Tax Rae) X (Debt / Equity)])
1.3X (1+[(1-28%) X 30%)])=
1.3 X (.72 X.30)=
1.3 X1.216 =1.58
We hope that this material has helped you understand these important concepts. The material has been taken from our series 79 textbook.
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