ACCT 451 Notes Exam 3 PDF

10/30 Forecasting Financial Statements 1. Forecasting Lecture 17 Approaches 2. Adjusting FS 1. Forecasting Approaches before a. Detailed forecast...

10/30 Forecasting Financial Statements 1. Forecasting Lecture 17 Approaches 2. Adjusting FS 1. Forecasting Approaches before a. Detailed forecast of operating and non-operating accounts Forecasting b. Detailed forecast of operating accounts and summary forecast of non 3. Two-Stage operating accounts Approach i. Recognizes significance of operating accounts 4. Forecasting ii. Reduced effort because non-operating accounts not in detailed growth rate for c. Parsimonious Method next year i. Uses NOPAT and NOA 5. Finding growth ii. Less effort, not necessarily less accurate rate example iii. Direct inputs to two major valuation models 6. Organic Growth 1. DCF model 7. Forecasting 2. Adjusting F/S before Forecasting growth rates for a. Analysts adjust NOPAT and NOA for forecasting purposes other years i. Income statement might include non-recurring (transitory) items 8. Parsimonious ii. Balance sheet might not measure economic resources (AKA assets) Method and obligations (AKA liabilities) accurately and comparably due to GAAP limitations/accounting choices b. Common adjustments i. Remove non-recurring operating expenses (discontinued/extraordinary) 1. Restructuring expense a. Should be a one time item, unlikely to recur 2. Asset impairment loss/expense a. More likely to occur when economic going downturn, theoretically nonrecurring 3. G/L on asset disposal a. During restructuring you may have more of this 4. Unusual tax expense or benefit a. Ex. When the tax law changes (such as from 35% - 21%) ii. Inventory (LIFO to FIFO) iii. Pro forma consolidation: Equity Method Investments iv. Pro forma capitalization of R&D expenditures v. Intangibles 3. Two-Stage Approach (Forecasting Revenue Growth Rates) a. Forecast Period (AKA near-term, forecast horizon, horizon period) i. Next 3-5 years (or longer for startups) ii. Period between current year and preselected horizon date (when the company reaches a mature phase) iii. After horizon, growth is expected to reach long-term sustainable equilibrium iv. Can predict revenue growth in this period with relatively more accuracy b. Terminal Period (AKA long-term) i. Period after the horizon date – more of a guess  ii. Assuming company will grow at a constant perpetuity growth rate (AKA terminal period growth rate, terminal growth rate, long-term growth rate) iii. Terminal period growth rate often assumed to be between historical inflation rate of 2-3% and historical GDP growth rate of 4-5% (do not assume a negative here, but if they’re on low end use inflation, on high end use GDP rate) 1. Sensitivity analysis 2. Market implied growth rate 4. Forecasting growth rate for next year a. Revenue t+1 = Revenue t * (1+ Revenue growth rate) i. Will be given this on exam b. Sources of information about revenue growth rate for the next year i. Company investor relation website “Investor Relations company name → Presentations and Events → Earnings Presentation → FY 2025 Guidance Sales): will see predictions 1. Management guidance and forecast (in presentation slides) 2. Audios or scripts/conference calls with analysts 3. Press releases ii. Analysts revenue forecasts (Yahoo Finance Analysis tab) iii. Your own analysis 1. Trend of past revenue growth (3-5 years) 2. Industry growth trend and your firm’s competitive position within industry 3. Major issues limiting/propelling revenue growth 5. Finding Growth Rate a. Ex. P&G i. Net Sales Growth (GAAP #, reported on Income Statement) ii. Forecasting use Organic Sales Growth (if a range, use the midpoint of the range - common practice) 6. Organic growth a. Represents growth of company’s existing core businesses, excluding effects of acquisitions and divestitures (and often currency exchange effects) b. Organic growth rate is value relevant – what we should use for forecasting purpose i. We exclude acquisition because growth by acquisition is not value relevant ii. Read footnote disclosure, and what sales would have been for other years 7. Forecasting Growth Rates for other years a. To forecast growth rates for other years in the forecast period, consider historical trends, industry, and macro environment, etc. b. Practical (lazy) approach (as last resort) – if you have no clue: i. Use forecasted organic growth rate for the next year as the starting point; use the assumed terminal period growth rate as the ending point. ii. Determine the length of the forecast horizon, that is, how many years it will take for the firm growth to reach sustainable equilibrium.  iii. “Fade” the growth rate evenly from the starting point to the ending point over the length of the forecast horizon. iv. Ex. Forecasted organic growth rate for next year is 9%, and terminal period growth rate is 5%: 1. Fade by 0.5% per year (straight line allocation) 8. Parsimonious Method *most important slide for today a. Assume NOPM and NOAT remain unchanged i. (Sometimes analysts relax this assumption to allow NOPM to change) ii. Research shows that NOATis more persistent, but NOPM tends to revert b. Inputs i. Sales ii. NOPM iii. NOAT = Sales / ending NOA 1. Use ending NOA instead of average to forecast year-end values iv. Forecasted sales growth rates for forecast and terminal periods c. Forecasts: d. Ex. P&G - Can start - To spot non-recurring items easily: if an item is included in one year, but missing in working on others  Individual - Assignment 2: Assignment #2 - Need NOPAT and NOA as starting metrics – very important that these are - correct from Assignment #1 - What do you think is best case scenario (terminal), what is worse, look at range and justify guesses - When predicting growth rates, g should change per year if you use your own analysis based on historical trends (unless company is incredibly stable) - Most reliable source for growth projections is from managers forecast number (ideally not analysts, but only if you can’t find anywhere else) - Does not recommend parsimonious approach for assignment - Ex. Company in its terminal period: P&G - Organic growth AKA same store growth, existing store growth 10/14 Cost of Capital and Valuation Basics 1. F Lecture 18 1. Review: Module 11 a. Adjustments before forecasting i. Remove non-recurring items from income statement ii. Convert from LIFO to FIFO iii. Pro-forma consolidation of equity-method investments (sometimes) Ref: Pro-forma capitalization of R&D expenditures - Costco b. Forecasting Revenue i. Forecasting sales growth rate t+1: 1. Organic Growth Rate ii. Forecasting sales growth rates for Terminal Period and Horizon Period c. Parsimonious Method of forecasting i. Assume NOPM and NOAT remain unchanged ii. NOPM = adjusted NOPATt / Sales t ; NOAT = Sales t / adjusted Ending NOAt iii. Sales t+1 = Sales t *(1+ gt+1) where gt+1 is the sales growth rate for period t+1 iv. NOPATt+1= NOPM x Salest+1 NOAt+1 = Sales t+1 / NOAT 2. Example: Costco Wholesale Corp a. Press release not on 10-K, but can contain same information b. Excluding impacts from changes in gasoline prices and foreign exchange i. Factors out of their control 3. Valuation Basics 4. Cost of Capital 5. Weighted Average Cost of Capital 6. Present Value Review 7. Present Value of a Perpetuity 8. Present Value of a Growing Perpetuity 9. General Structure of Valuation Models 10. Dividend Discount Model 11. Example: DDM with Constant Perpetuity  12. Action Items - On quizzes/exams unless he specifies, the NOPM and Ending NOA are assumed - to be adjusted already - Comparable sales = organic sales = same store growth - Risk free rate = federal funds rate - Rm = market rate of return Lecture 18 Transcript Many times, we make pro-forma consolidations and adjustments to ensure that the balance sheet accurately reflects economic resources. A key task in forecasting is predicting revenue, starting with a sales growth forecast. Regardless of the approach, forecasting revenue is essential. We often focus on "organic growth," meaning growth based on the core business, not on expansion or new business ventures. If we have, for example, state funding, it would adjust our forecast. Next, we consider growth rates for the terminal period and the horizon period. The horizon period typically spans 3–5 years, often longer for startups, while the terminal period assumes a stable growth rate into perpetuity. For revenue forecasting, we use the "parsimonious method," assuming that both NOPM (Net Operating Profit Margin) and NOAT (Net Operating Asset Turnover) remain unchanged. Adjusted NOPAT (Net Operating Profit After Tax) is calculated using NOPM, with NOAT calculated by dividing sales by the ending balance of NOA (Net Operating Assets). For your assignment, any adjustments to NOPAT are optional. Forecast numbers, unless otherwise noted, will be provided already adjusted. Now, sales for the next period can be forecasted by multiplying current sales by (1 + sales growth rate). NOPAT is calculated by multiplying NOPM by forecasted sales, while forecasted NOA equals forecasted sales divided by NOAT. Looking at an example from Costco, they report comparable sales, which reflect "same-store growth." In retail, this metric shows organic growth, often excluding gasoline price fluctuations and foreign exchange impacts, as these factors are outside their control. Today's discussion includes the cost of capital and valuation models. The "cost of capital" is the rate of return required by investors. There are two components: 1. Cost of Debt: Calculated as the pretax borrowing rate multiplied by (1 - tax rate). The pretax borrowing rate often appears in long-term debt footnotes. If unavailable, we can estimate it by dividing interest expense by average total debt. 2. Cost of Equity: Using the Capital Asset Pricing Model (CAPM), this is calculated as rf+β×(rm−rf)r_f + \beta \times (r_m - r_f)rf​+β×(rm​−rf​), where:  ○ rfr_frf​is the risk-free rate, typically the 10-year Treasury rate, ○ β\betaβ measures stock sensitivity to the market, ○ rm−rfr_m - r_frm​−rf​is the market risk premium. For instance, if the risk-free rate is 3%, the market risk premium is 6%, and β\betaβ is 1.5, then the cost of equity is 12%. The Weighted Average Cost of Capital (WACC) combines debt and equity costs, weighted by their proportions in the firm's capital structure. WACC reflects the required return for both debt and equity holders, calculated as follows: WACC=VEVE+VD×re+VDVE+VD×rdWACC = \frac{V_E}{V_E + V_D} \times r_e + \frac{V_D}{V_E + V_D} \times r_dWACC=VE​+VD​VE​​×re​+VE​+VD​VD​​×rd​ For present value calculations, if we receive $100 in three years with a 12% discount rate, the present value is calculated by discounting it back to today. Perpetuities provide a series of payments that continue indefinitely. The present value of a perpetuity (e.g., $100 received annually at a 12% discount rate) simplifies to Cash FlowDiscount Rate\frac{\text{Cash Flow}}{\text{Discount Rate}}Discount RateCash Flow​. For a growing perpetuity, if each payment grows by a constant rate (e.g., 10% per year), the present value is adjusted to account for growth, given by Cash FlowDiscount Rate - Growth Rate\frac{\text{Cash Flow}}{\text{Discount Rate - Growth Rate}}Discount Rate - Growth RateCash Flow​, assuming the growth rate is less than the discount rate. When valuing companies, we identify relevant cash flows (e.g., dividends or free cash flows) and apply appropriate discount rates based on claimants (equity or both debt and equity holders). In the Dividend Discount Model (DDM), the value is the present value of expected dividends, with the cost of equity capital as the discount rate. For example, if dividends are $1.50 in the first two years, $2.25 in year three, and $2.75 perpetually afterward with a 7.6% cost of equity, we calculate the present value of each dividend and apply perpetuity formulas for the terminal value. Growing perpetuity models further adjust for growth, where dividends increase by a fixed rate in perpetuity. Let’s look at the first three years, then move to the fourth year and beyond, where we use a growing perpetuity formula. After calculating this, we discount it back to today using the appropriate discount factor. Remember, for a growing perpetuity, the formula is XI−G\frac{X}{I - G}I−GX​. Here, XXX is $2.75 (the dividend), III is 7.6% (the discount rate), and GGG is 2% (the growth rate). This step is essential for finding the present value of dividends that grow indefinitely. Many people forget to divide by this factor when discounting, so keep it in mind. If the current stock price is $52.71, and everything else in our model is correct, but we’re uncertain about the 2% dividend growth rate, we could back-solve for the growth rate the  market is using. Assuming the market price reflects the intrinsic value, we set the market price equal to the model's valuation and solve for GGG. In this case, we’ll use the formula to isolate GGG. By solving, we find that the implied dividend growth rate the market is using here is 3%. In your assignment, you’ll calculate a similar market-implied growth rate. Excel can simplify this calculation, but it’s good to understand the logic behind it. As for the cost of capital calculations: 1. Cost of Debt: Use the pretax borrowing rate multiplied by (1 - tax rate). In this case, that results in 8.69%. 2. Cost of Equity: This uses the market risk premium, with the final cost of equity calculated at 11.65%. Remember, there’s no need to subtract the risk-free rate again here since the market risk premium already accounts for it. 3. WACC: With the equity based on market cap and the debt based on book value, we get a WACC of 11.03%. Now, looking at the Dividend Discount Model (DDM): For a constant dividend of $0.80 paid indefinitely, we use the formula DividendDiscount Rate\frac{\text{Dividend}}{\text{Discount Rate}}Discount RateDividend​, resulting in a valuation of $17.6 per share. If the dividend grows at a constant rate of 5% annually, we adjust to DividendDiscount Rate - Growth Rate\frac{\text{Dividend}}{\text{Discount Rate - Growth Rate}}Discount Rate - Growth RateDividend​, giving us $7.14 per share. In a scenario where the dividend is $0.90 next year, grows at a constant but unknown rate, and the current stock price is $9 per share, we assume the market price is efficient. Solving this will yield the market-implied growth rate, which AJ calculated as 7.6%. 11/6 Cash-Flow Based Valuation 1. Weighted Average Cost of Capital The Weighted Average Cost of Capital (WACC) is essential here, as it represents the (WACC) average cost of financing a company’s assets. WACC is determined by the relative weights - Definition and use as of the market values of equity and debt. We often use the book value of debt as a proxy for the discount rate for market value. A quick recap on perpetuity: the present value of a constant perpetuity is both debt and equity calculated as 𝑃𝑉 = 𝑋/𝑟​, while for a growing perpetuity, it's 𝑃𝑉 = 𝑋/(𝑟 − 𝑔). financing. - Calculation based on I've posted the Exam 3 formulas for reference, and feel free to use them for practice. market values of equity Moving forward, we discussed the Dividend Discount Model (DDM), where dividends serve and debt. as the primary cash flow. The discount rate in this model is the cost of equity capital, which  reflects the claim by equity holders. There are both constant and growing perpetuity 2. Present Value versions of the DDM. Calculations - Constant perpetuity In today's lecture, we began covering the Discounted Cash Flow (DCF) model. Some of - Growing perpetuity you may be familiar with this from finance, but accounting uses a slightly different approach. In the DCF model, the primary attribute is free cash flow to the firm (FCFF), 3. Dividend Discount which is discounted using WACC. The rationale is that FCFF represents cash available to Model (DDM) both debt and equity holders—covering interest and principal payments for debt and - Use of dividends as returns (like dividends) to shareholders. cash flows for equity valuation. In the finance perspective, FCFF is often calculated as cash flow from operations minus - Cost of equity capital capital expenditures (CapEx). However, in accounting, we often derive it using Net as the discount rate. Operating Profit After Taxes (NOPAT) minus the increase in Net Operating Assets (NOA), - Application to both as this approach aligns with key metrics in accounting. constant and growing perpetuities. A note about CapEx: in some statements, it may be listed under different names, such as "additions to PP&E." This is effectively investment in fixed assets like property, plant, and 4. Discounted Cash equipment, which increase net operating assets. Flow (DCF) Model - Focus on Free Cash Once we've defined FCFF, calculating firm value is straightforward: it’s the present value of Flow to the Firm expected future FCFFs. We follow a five-step process in DCF valuation: (FCFF) as the relevant attribute. 1. Forecast and discount FCFF for the horizon period. - Discount rate is 2. Forecast and discount FCFF for the terminal period. WACC due to the claim 3. Sum the present values of both periods to get firm value (or enterprise value). on cash flows by both 4. Subtract net non-operating obligations (NNO) from firm value, as well as debt and equity non-controlling interests and preferred stock, to get equity value. holders. 5. Divide equity value by shares outstanding to get intrinsic value per share. 5. Calculation of Free An example we discussed was Procter & Gamble. For fiscal year-end 2022, we had Cash Flow to the forecasted growth rates and sales, using prior analyses as a basis for estimating intrinsic Firm (FCFF) value per share. - Derived as NOPAT (Net Operating Profit Calculations then move to the present value factor and free cash flow for each forecasted After Taxes) minus year. Discount factors are applied using 𝐷𝐹 = 1 / (1 + 𝑊𝐴𝐶𝐶)^𝑡​for each respective increases in Net period. Present values of free cash flows are then summed to get the cumulative present Operating Assets value for the horizon period. (NOA). - Differences between A particularly important calculation is for the terminal period’s FCFF, as it often has a finance and accounting significant impact on firm value. This involves using the growing perpetuity formula PV = X approaches to / (r - g), where X is the terminal year’s FCFF, r is WACC, and g is the long-term growth calculating FCFF. rate. This value is then discounted back to the present using the last period’s discount factor. 6. Steps in DCF Valuation Finally, sensitivity analysis is crucial here. Given the assumptions required to derive - Forecasting FCFF for intrinsic value, we check how sensitive our valuation is to changes in growth rate the horizon period. assumptions. Using tools like Excel's "Goal Seek" helps evaluate how intrinsic value might - Forecasting terminal shift within a realistic growth range based on market research. value for the terminal period. - Summing present When forecasting for long periods, particularly when moving into the terminal period, our values to get firm (or confidence in the estimates naturally decreases. The horizon period, which covers enterprise) value. near-term projections, has a higher certainty than estimates for the terminal period, which - Subtracting net may span five to ten years into the future. This is why we conduct a sensitivity analysis, non-operating adjusting the terminal growth rate to see how changes affect our valuation. obligations (NNO) to get equity value. For your individual assignment, I ask that you justify your chosen terminal growth rate, - Dividing equity value detailing why you think this rate is reasonable. Additionally, provide a range, showing both by shares outstanding a best-case and worst-case scenario based on your judgment. There’s no single correct to calculate intrinsic answer here; it’s about using sound reasoning to defend your choices. This way, you can value per share. see how sensitive the valuation is to different growth rate assumptions. 7. Sensitivity An alternative approach, especially when confidence is low, is to calculate the Analysis market-implied terminal growth rate. This method assumes the market price is accurate, so - Examining how by setting the valuation model to the current market price, we can let the computer changes in the terminal back-solve for the growth rate the market is implicitly using. This “reverse engineering” is growth rate affect the done using Excel's Goal Seek function, which iteratively adjusts the terminal growth rate intrinsic value estimate. until the valuation matches the market price. This value can then be compared to your own - Justifying growth rate growth rate range to see if it falls within your assumptions. assumptions with best-case and For example, I used this approach in a past analysis where the market price was $68.185 worst-case scenarios. per share. Setting the terminal growth rate at 2% in the model yielded a value per share of $65.147. Running a sensitivity analysis by adjusting the terminal growth rate from 0.5% to 8. Market-Implied 4% demonstrated the impact on value estimates. Goal Seek allows you to set the Terminal Growth Rate estimated value to the market price and adjust the terminal growth rate accordingly, - Use of Excel's Goal yielding a growth rate that aligns with the market’s valuation. Seek function to calculate the terminal This process provides a confidence check; if the market-implied growth rate significantly growth rate that aligns diverges from your best-case or worst-case assumptions, you might infer that the market is with the current market either overly optimistic or conservative compared to your analysis. Ultimately, this price. comparison can guide your investment recommendations. - "Reverse engineering" the For practice, let's turn to the spreadsheet example on D2L. It outlines how to perform market price to infer these calculations, with steps to follow in the Goal Seek function. the market's growth rate assumption. Example Walkthrough: 9. Practical Example 1. Set the cell containing the estimated value equal to the market price. and Handouts 2. Select the terminal growth rate cell to be adjusted. - Detailed walkthrough 3. Goal Seek will quickly determine the market-implied growth rate. using Procter & Gamble (P&G) as an This process will assist with ensuring accurate valuations, and we’ll see later that the DCF example. and residual operating income models should yield the same value estimate, providing an - Step-by-step additional accuracy check. calculations for Module 13 Handout: cumulative present values, terminal value, Moving to the handout exercises, we calculated the cumulative present value of the and sensitivity horizon period by summing the discounted cash flows. This provided a cumulative present analysis. value of 10,084. To find the present value of the terminal period’s free cash flow, we used 10. Formula the growing perpetuity formula PV = X / (r - g)​, with X being the terminal year’s free cash Reminders flow, r the WACC, and g the growth rate. This value was then discounted back to the end - NOPM (Net of the horizon period using the discount factor for the final year. Operating Profit Margin) formula and its In calculating total firm value, we summed the horizon and terminal present values. From relation to NOPAT. this, we subtracted net non-operating obligations (NNO) and any preferred stock to get - Accounting formulas equity value. To find the intrinsic value per share, we divided the equity value by the for deriving NOA and number of outstanding shares. NNO as part of valuation. When completing exercises, remember to carefully check units (e.g., thousands vs. millions) to avoid miscalculations. In this exercise, NNO was given in millions and required conversion for consistency. For the final exercise on the handout, we calculated forecasted revenue and derived NOPAT by multiplying sales by NOPM (Net Operating Profit Margin). Free cash flow to the firm (FCFF) was then calculated using NOPAT minus the increase in NOA, following the same steps as above. In summary, each of these exercises reinforces the core valuation principles and provides a practical application of DCF valuation. These methods, including sensitivity analysis and market-implied terminal growth rate, offer robust insights for making informed investment decisions. Equations: 1. Constant Perpetuity (Present Value): PV = X / r 2. Growing Perpetuity (Present Value): PV = X / (r - g) 3. Weighted Average Cost of Capital (WACC): WACC = (E / (E + D)) * re + (D / (E + D)) * rd * (1 - t) Where: E = Market value of equity D = Market value of debt re = Cost of equity rd = Cost of debt t = Tax rate  4. Free Cash Flow to the Firm (FCFF): FCFF = NOPAT - Δ NOA Where: NOPAT = Net Operating Profit After Taxes Δ NOA = Change in Net Operating Assets 5. Terminal Value (Growing Perpetuity at Terminal Period): TV = FCFF_terminal / (WACC - g) Where: FCFF_terminal = Free Cash Flow to the Firm at terminal period WACC = Weighted Average Cost of Capital g = Terminal growth rate 6. Discount Factor: DF = 1 / (1 + WACC)^t Where: WACC = Weighted Average Cost of Capital t = Time period (years) 7. Intrinsic Value per Share: Intrinsic Value per Share = Equity Value / Shares Outstanding 8. Net Operating Profit Margin (NOPM): NOPM = NOPAT / Sales - Homework 6/7 - CAPEX in cash flow statements = Investments in PPE/Additions to PPE - Individual - Individual assignment 2 assignment 2 - Explain (sensitivity analysis) 10:05 (11/18) - Remember formula for NOPM = NOPAT/Sales - Assurance learning exit assessment (11/20) 11/13 Operating Income Based Valuation Lecture 20 Slides Module 14 Handout Review: Discounted Cash Flow (DCF) Valuation Model 1. Discount Rate: Weighted Average Cost of Capital (WACC) ○ Explanation: WACC, as the discount rate here, represents the blended cost of financing from both debt and equity sources. “Remember, this rate is not the same as the Dividend Discount Model (DDM).” In the DDM, we use re, or the cost of equity, while here in DCF, we’re working with WACC. “You’ll want to be clear on this for Exam 3” 2. Firm Value Calculation ○ Formula: Firm Value = PV of Free Cash Flows (FCFF) for both the horizon period and the terminal period. ○ Steps to Calculate Firm Value: FCFF Calculation: Defined as Net Operating Profit After Taxes (NOPAT) minus increases in Net Operating Assets (NOA). Present Value for the Terminal Period: “It’s critical to get comfortable with how to calculate the present value of FCFF in the terminal period. I can guarantee this will be on the exam, and maybe in more than one problem.” Firm Equity Value: Calculated as Firm Value minus NNO (Net Non-Operating Obligations) and non-controlling interest (if applicable). ○ Intrinsic Value per Share Calculation: “The intrinsic value per share is simple once you have the firm equity value; it’s just firm equity value divided by shares outstanding.” 3. Terminal Growth Rate & Sensitivity Analysis ○ Terminal Growth Rate This rate is ultimately an “educated guess” about the future. He noted that students often ask, “How can we forecast something so far off?” The answer is, it’s about setting a reasonable range. ○ Sensitivity Analysis: “With sensitivity analysis, we can put in different terminal growth rates to see how the intrinsic value changes,” he said, allowing us to test a “bull case” (best-case scenario) or a “bear case” (worst-case scenario) to gauge how realistic the model assumptions are. Goal Seek Steps to Use Excel’s Goal Seek Reverse Engineering with Goal Seek (Excel): This method lets us “start with the current share price and work backwards to figure out the implied assumptions.” Using Excel’s Goal Seek, we can input the current market price to have Excel back-solve the terminal growth rate, helping confirm whether it falls within our specified reasonable range. “If it’s outside the range, this could be a signal that the market is under- or overvaluing the stock”. 1. Set up your model in Excel: ○ Ensure your Excel sheet calculates intrinsic value per share based on all your model inputs (e.g., growth rate assumptions, WACC, and cash flows). ○ Make sure all cells in the model are properly linked so that any changes to inputs automatically update the intrinsic value per share. Prof. Yu emphasized this: "If any cells aren’t linked, Goal Seek won’t work because it needs to adjust values dynamically across the entire model." 2. Access the Goal Seek tool: ○ Go to the Data tab. ○ Select What-If Analysis in the Forecast group, then choose Goal Seek from the dropdown menu. 3. Configure Goal Seek with your target values: ○ In the Goal Seek dialog box, you’ll see three fields: Set cell: Enter the cell containing your calculated intrinsic value per share (e.g., D10). This cell should dynamically update based on all other model inputs. To value: Enter the target value you want this cell to reach, which is usually the current market price per share (e.g., $100). By changing cell: Enter the cell for the assumption you want to adjust to reach the market price—in this case, the terminal growth rate (e.g., B5). 4. Run Goal Seek: ○ Click OK to start Goal Seek. Excel will adjust the terminal growth rate to match the calculated intrinsic value with the market price. ○ Goal Seek will display a message once it finds a solution. If Goal Seek doesn’t converge, Prof. Yu noted that the issue may lie in “incorrect cell references or cells not being linked correctly.” Always double-check that you’re referencing active cells and that all necessary values are updated. 5. Interpret the Result: ○ The resulting value in the growth rate cell is the market-implied terminal growth rate. Prof. Yu emphasized that this growth rate is a confidence check: if the market-implied rate falls outside your reasonable range, it could indicate that the market is undervaluing or overvaluing the stock. “This gives us a confidence check on our own assumptions, highlighting areas where the market might be more optimistic or conservative than we are.” Residual Operating Income (ROPI) Valuation Model ○ X = Residual Operating Income ○ Discount rate r is WACC (𝑟𝑤) Definition of ROPI ○ Formula for ROPI: ROPI = NOPAT - (Beginning NOA × WACC) ○ Explanation of Terms: Beginning NOA: Represents net operating assets at the start of the period, a measure of capital provided by stakeholders. Hurdle Profit: This is the minimum return expected by capital providers, covering their opportunity cost. If the firm earns more than this, it’s adding value. Firm Value in ROPI: Economic Value Added (EVA) ○ EVA is the portion of operating profit above the required hurdle and represents real value created for shareholders. ○ Firm Value Calculation Steps: Firm Value = Current NOA + PV of Expected ROPI Subtract NNO for Firm Equity Value: After calculating firm value, subtract NNO, non-controlling interests, and any preferred stocks to get firm equity value. Intrinsic Value per Share: Divide firm equity value by shares outstanding for the intrinsic value. ○ Advantages of ROPI Model: One key advantage of the ROPI model is that it relies less on future projections and more on current, audited NOA, which can make it a stronger model in certain cases. Implementation of the ROPI Model 5-Step Process (similar to DCF): 1. Forecast and discount ROPI for the horizon period. 2. Forecast and discount ROPI for the terminal period. 3. Sum the PVs of horizon and terminal periods and add the current NOA. 4. Subtract NNO and any non-controlling interest to get firm equity value. 5. Divide by shares outstanding for intrinsic value per share. Example - Procter & Gamble: Using forecasts for sales, NOPAT, and NOA, calculate ROPI using NOPAT - (Beginning NOA × WACC) and add up these values over the horizon and terminal periods. Comparison of Valuation Models: DDM, DCF, and ROPI  Key Differences: ○ DDM: Cash flow = Dividends; Discount Rate = re (cost of equity). ○ DCF: Cash flow = FCFF; Discount Rate = WACC. ○ ROPI: Cash flow = ROPI; Discount Rate = WACC. Weight on Terminal Period: ○ The ROPI model places less weight on terminal value than DCF or DDM, where terminal value often constitutes 80% or more of firm value. In the ROPI model, this proportion is typically lower, making ROPI more precise since it depends less on long-term projections. Steady State Condition Definition: ○ Steady state is achieved when sales, NOPAT, and NOA all grow at the same constant rate. Implications for DCF and ROPI Models: ○ When steady state is achieved in the terminal period, both DCF and ROPI should yield identical values. This is why the terminal growth rate is so crucial—it connects our models to long-term reality by assuming a constant growth rate for the terminal period. Sensitivity Analysis & Reverse Engineering in Valuation Purpose of Sensitivity Analysis: ○ Sensitivity analysis allows us to test the robustness of our assumptions, especially around the terminal growth rate. By observing how intrinsic value changes with different rates, we can assess the reliability of our estimates. Reverse Engineering with Goal Seek: ○ Goal Seek in Excel automates the guessing process, allowing us to set the intrinsic value per share to the market price and determine the growth rate the market implicitly assumes. This gives us a confidence check—if the market-implied growth rate diverges significantly from our own assumptions, it might suggest that the market is either overly optimistic or conservative. Slide 8: Practical Exercise & Key Equations Example Walkthrough: ○ Using Procter & Gamble as an example, Prof. Yu guided through cumulative present values and final valuation calculations with key formulas. Students are encouraged to check their calculations carefully for accuracy. Key Equations for Reference: 1. Constant Perpetuity (Present Value): PV = X / r 2. Growing Perpetuity (Present Value): PV = X / (r - g)  3. Weighted Average Cost of Capital (WACC): WACC = (E / (E + D)) * re + (D / (E + D)) * rd * (1 - t) where: ○ E = Market value of equity ○ D = Market value of debt ○ re = Cost of equity ○ rd = Cost of debt ○ t = Tax rate 4. Free Cash Flow to the Firm (FCFF): FCFF = NOPAT - ΔNOA where: ○ NOPAT = Net Operating Profit After Taxes ○ ΔNOA = Change in Net Operating Assets 5. Terminal Value (Growing Perpetuity at Terminal Period): TV = FCFF_terminal / (WACC - g) where: ○ FCFF_terminal = Free Cash Flow to the Firm at the terminal period ○ WACC = Weighted Average Cost of Capital ○ g = Terminal growth rate 6. Discount Factor (DF): DF = 1 / (1 + WACC)^t where: ○ WACC = Weighted Average Cost of Capital ○ t = Time period (years) 7. Intrinsic Value per Share: Intrinsic Value per Share = Equity Value / Shares Outstanding 8. Net Operating Profit Margin (NOPM): NOPM = NOPAT / Sales - Do Individual - Exam 3 (more than 1 problem) Assignment 2 - Calculating present cash flows of terminal year sooner than - Final Note: Prof. Yu wrapped up with a reminder that these models are only as later (11/18) effective as the assumptions we feed into them. Reverse engineering and - HW due today sensitivity analysis are not just validation tools—they also reveal the market’s - HW 7 due 11/25 perspective and help us assess the reliability of our own estimates. 11/18 Market-Based Valuation Lecture 21 Slides 1. Review Module 14 a. Firm Value: i. Formula: Firm Value = Net Operating Assets (NOA) + Present Value (PV) of Residual Operating Income (ROPI) for the horizon and terminal periods. ii. Important: You must know how to calculate the PV of ROPI for the terminal period. Expect questions about this on Exam 3. iii. Example Walkthroughs:  1. Use provided formulas (e.g., ROPI=NOPAT−NOABeginning×WACCROPI = NOPAT - NOA_{Beginning} \times WACCROPI=NOPAT−NOABeginning​×WACC). iv. Pay attention to horizon vs. terminal periods. Terminal value uses the growing perpetuity formula b. Comparison: DCF vs. ROPI: i. DCF Model: 1. Uses Free Cash Flow to the Firm (FCFF). 2. Formula: FCFF = NOPAT − Increase in NOA. ii. ROPI Model: 1. Focuses on Residual Operating Income (ROPI). 2. Formula: ROPI = NOPAT − NOA × WACC. iii. Steady State: 1. Both models yield the same valuation if steady state is achieved: a. Sales, NOPAT, and NOA grow at the same constant rate. 2. Valuation using Market Multiples a. Basic process i. Value = Summary Performance Measure × Market Multiple. ii. Professor’s Tip: Multiples work well for screening or rough estimates but are not as robust for detailed investment decisions. b. Value = Summary performance measure x Market multiple 3. Equity Value or Firm Value a. Use market cap for equity measures (e.g., Net Income, Book Value of Equity). b. Use firm value (Market Cap + NNO) for firm measures (e.g., NOPAT, NOA). 4. Steps to Apply Market Multiples: a. Step 1: Select a performance measure. i. Equity measures: Net Income, Book Value of Equity. ii. Firm measures: NOPAT, NOA. iii. Tip: Check Yahoo Finance for basic metrics like P/E ratios. b. Step 2: Identify comparable companies ("comps"). i. Firms similar in size, industry, or growth. ii. Tip: "Comps" is shorthand for comparables—know this term for interviews. c. Step 3: Compute the Market Multiple. i. Equity multiple: Market Cap÷Performance Measure\text{Market Cap} \div \text{Performance Measure}Market Cap÷Performance Measure. ii. Firm multiple: Firm Value÷Performance Measure\text{Firm Value} \div \text{Performance Measure}Firm Value÷Performance Measure. iii. Average the multiples from your comps.  d. Step 4: Apply the Multiple. i. Equity Value = Target’s Performance Measure × Equity Market Multiple. ii. Firm Value = Target’s Performance Measure × Firm Market Multiple. 1. Subtract NNO to calculate equity value. e. Step 5: Calculate Per-Share Value. i. Equity Value ÷ Shares Outstanding. 5. Weakness of Market Multiple Method a. Guaranteed on Exam 3 b. “Quick and dirty”, good for screening but not investment decisions c. Assumes comparables are accurately valued while the target is mispriced d. Results are sensitive to outliers or poorly chosen comps e. Lacks rigorous theoretical foundation compared to DCF or ROPI f. Best use: i. Quick screening, benchmarking, rough estimates ii. Not suitable for robust investment decisions 6. Detailed Examples a. Valuation Using Net Income (P/E Ratio): i. Example: 1. Net Income = $2,399, P/E Market Multiple = 14.08. 2. Equity Value = $2,399 × 14.08 = $33,778. 3. Per Share Value = $33,778 ÷ 230 = $146.86. b. Valuation Using NOA (Firm Measure): i. Example: 1. NOA = $20,163, NOA Market Multiple = 1.66, NNO = $13,902. 2. Firm Value = $20,163 × 1.66 = $33,471. 3. Equity Value = $33,471 − $13,902 = $19,569. 4. Per Share Value = $19,569 ÷ 230 = $85.08. c. Valuation Using NOPAT: i. Example: 1. NOPAT = $2,524, NOPAT Market Multiple = 20.765, NNO = $13,902. 2. Firm Value = $2,524 × 20.765 = $52,411. 3. Equity Value = $52,411 − $13,902 = $38,509. 4. Per Share Value = $38,509 ÷ 230 = $167.43. 7. Key Ratios a. Price-to-Book Ratio (PB Ratio): i. Formula: Market Value of Equity ÷ Book Value of Equity. ii. Factors: 1. Increases with profitability (e.g., ROPI), growth, and leverage. 2. Decreases with operating risk (higher WACC).  iii. Exam Tip: Focus on the yellow box on Slide 13 for key insights. b. Price-to-Earnings Ratio (P/E Ratio): i. Highly popular (used in 76% of analyst reports). ii. Trailing P/E: Price ÷ Current EPS. iii. Forward P/E: Price ÷ Next Year’s Expected EPS. iv. Factors: 1. Increases with growth; decreases with cost of equity. 2. Example: Tesla and NVIDIA have high P/E ratios due to expected explosive growth. c. PEG Ratio: i. Formula: P/E Ratio ÷ (Growth Rate × 100). ii. PEG < 1: Possible undervaluation. iii. Tip: Rare to see PEG < 1 in today’s market. 8. 9. Price-to-Book Ratio (PB ratio) a. All we need to know is yellow box on this slide (Slide 13) 10. - Evaluation - Market Value of Equity = market cap or equity value Exam on Wednesday - Quiz Guaranteed on Exam 3 Wednesday - Assignment 2 Concepts to Study: due today ○ Valuation using market multiples (both equity and firm measures). - Exam 3 ○ Sensitivity analysis and terminal value calculations. Monday ○ Differences between DCF and ROPI models. - HW 7 Monday ○ Importance of NNO in calculating equity value. Tips for Success: ○ Review handout problems carefully. Many exam questions are direct variations. ○ Practice examples of: Market multiples (e.g., P/E, P/B, NOA multiples). Terminal value calculations using the growing perpetuity formula. ○ Remember: Most questions will combine conceptual understanding with numerical accuracy. Team Presentation Reminders Structure: ○ 12–15 minutes, followed by a 5–10 minute Q&A. ○ Business or business casual attire is required. ○ All members must participate. Content Focus: ○ Growth assumptions, valuation results, sensitivity analysis, and recommendations.  ○ Avoid overloading slides with numbers; focus on summaries and visuals. ○ Include clear comparisons of intrinsic value and current market value. Professor’s Tip: ○ Use concise charts and graphs to summarize performance metrics. ○ Highlight best-case, worst-case, and market-implied scenarios in sensitivity analysis. 11/20 Exam Review; AOL Assessment Lecture 22 Slides 1. Review Slides a. Module 11 i. Organic growth rate: 1. Focuses on growth excluding acquisitions. 2. Exam Tip: Be able to distinguish organic growth from total growth (including acquisitions). ii. Horizon Period vs. Terminal Period: 1. Horizon Period: Can be forecasted with more precision. 2. Terminal Period: Relies on growth assumptions extending indefinitely. iii. Parsimonious method 1. Simplified approach to project key variables without unnecessary complexity. b. Module 12 i. WACC 1. Formula includes pre-tax borrowing rate, tax rate, beta, and market risk premium. 2. On the exam, all necessary inputs will be provided. ii. Market Value of Debt: 1. Required for WACC calculation; know how to calculate it. iii. Discount Rate for Perpetuities: 1. Remember: This is not WACC but typically tied to equity cost or a specific cash flow. c. Module 13 i. Discount Rate for DCF: 1. WACC is used to discount Free Cash Flow to the Firm (FCFF). 2. Different from the dividend discount model, which uses the cost of equity. ii. FCFF Formula: 1. Provided during the exam; focus on applying it correctly. iii. Terminal Value of FCFF: 1. Calculated using the perpetuity growth formula. d. Module 14 i. ROPI Model: 1. Firm Value*** = NOA + PV of ROPI (horizon + terminal periods). 2. Discount Rate: Weighted Average Cost of Capital (WACC).  ii. Terminal Period ROPI: 1. Know how to calculate the present value for terminal period ROPI. 2. ROPI places the lowest weight on terminal period value compared to other models. iii. DCF vs. ROPI: 1. Both yield the same value in a steady state: a. Sales, NOPAT, and NOA grow at the same constant rate. 2. Market Multiples Valuation Process a. Select a Performance Measure: i. Equity Measures: Net Income, Book Value of Equity. ii. Firm Measures: NOPAT, NOA. b. Identify Comparable Companies (Comps): i. Comparable firms should share similar characteristics, such as industry, size, growth potential, and risk. c. Compute Market Multiple (MM): i. Equity MM: Market Value of Equity ÷ Equity PM ii. Firm MM: Market Value of Firm÷Firm PM. iii. Professor’s Tip: Use the correct numerator for consistency (market cap for equity; firm value for firm measures). d. Apply the Multiple: i. Equity Value = Target’s Equity PM × Equity MM. ii. Firm Value = Target’s Firm PM × Firm MM. iii. Subtract NNO to compute equity value if starting with firm value. e. Calculate Equity Value Per Share: i. Equity Value ÷ Shares Outstanding. 3. Key Ratios and Their Drivers a. Price-to-Book Ratio (PB or P/B): i. Formula: Market Value of Equity÷Book Value of Equity\text{Market Value of Equity} \div \text{Book Value of Equity}Market Value of Equity÷Book Value of Equity. ii. Drivers: 1. Increases with profitability (e.g., ROPI), growth, and leverage. 2. Decreases with risk (higher WACC). iii. Tip: Focus on Slide 13 for PB insights. b. Price-to-Earnings Ratio (PE or P/E): i. Formula: Market Value of Equity÷Net Income\text{Market Value of Equity} \div \text{Net Income}Market Value of Equity÷Net Income. ii. Drivers: 1. Increases with growth. 2. Decreases with cost of equity (re). iii. Types: 1. Trailing PE: Based on historical EPS. 2. Forward PE: Based on forecasted EPS. c. PEG Ratio:  i. Formula: PE÷(Growth Rate×100)\text{PE} \div (\text{Growth Rate} \times 100)PE÷(Growth Rate×100). ii. Threshold: PEG = 1 is considered attractive. iii. Professor’s Tip: Rare to find PEG < 1 in today’s market. 4. Weaknesses of Market Multiples a. Assumes comparables are correctly valued while the target is not. b. Results depend heavily on comp selection and market conditions. c. Lacks rigorous theoretical underpinnings like DCF or ROPI models. d. Professor’s Tip: “Quick and dirty—great for screening but not for precise investment decisions.” - Transcribe last - Comps = comparable firms week’s notes - Them more profitable a company is, the higher their price-to-book ratio - Team - Price to book Ratio = market to book ratio Presentation - Increases with leverage - Each team - Decreases with operating risk – the more risky a company is, investors will should spend price protect themselves 12-15 minutes - Affected by WACC on analysis, - P-E ratio 5-10 Q&A - Easiest, fewer determinants - Ask - Should be on average about 20% question - Affected only by cost of equity capital, not by WACC s - Presentation - Spend - Sensitivity Analysis more - Lower and Upper Bound on a scale time not - Summary and hear more of our explanations instead of reading off slides on busines s Guaranteed on Exam 3 environ ment 1. Key Topics: ○ Market multiples process for equity and firm measures. ○ Sensitivity analysis and calculations involving PB, PE, and PEG. ○ Conceptual questions about DCF, ROPI, and their assumptions. 2. Exam Logistics: ○ Closed-book exam with a formula sheet provided. ○ Arrive early and follow the seating chart. ○ Expect questions similar to handout problems. 11/18 11.  - Evalu - 11/18 12. - Evalu -