Sustainable Growth Rate [LO3] In the chapter, we discussed the two versions of the sustainable growth rate formula. Derive the formula
To determine: The internal growth rate is
Introduction:
ROA (return on assets) indicates the operating efficiency of the firm and using ROA the internal growth of firm can be determined. ROE (return on equity) measures the amount of profit, which can be derived from the shareholder’s equity and using ROE the sustainable growth rate of the firm can be determined.
Explanation of Solution
Given information:
ROE is based on the beginning of period equity.
Assumption: The beginning of period equity as x, which represents (ROEx) and the end of period equity as y, which represents (ROEy)
Formulae:
The formula to compute the sustainable growth rate:
Where,
b refers to the retention ratio
The formula to compute the internal growth rate:
Derive
Here, NI is net income and TE is total equity.
Substitute
Multiply
Where, the beginning of period equity is
The below equation is arrived by substituting equation 3 in equation 2.
Rewrite it as
Therefore,
Hence, the sustainable growth rate equation is
Compute
Where, TA is total assets
Multiply, internal growth rate with
Where,
The beginning of period equity is
Therefore,
Substitute,
Hence, the equation of internal growth rate is
Want to see more full solutions like this?
Chapter 4 Solutions
Fundamentals of Corporate Finance
- Start with the partial model in the file Ch15 P13 Build a Model.xlsx on the textbook’s Web site. Reacher Technology has consulted with investment bankers and determined the interest rate it would pay for different capital structures, as shown in the following table. Data for the risk-free rate, the market risk premium, an estimate of Reacher’s unlevered beta, and the tax rate are also shown. Reacher expects zero growth. Based on this information, what is the firm’s optimal capital structure, and what is the weighted average cost of capital at the optimal structure?arrow_forward1.What is the project’s net present value? 2. What is the project’s internal rate of return to the nearest whole percent? 3. What is the project’s simple rate of return? 4-a. Would the company want Casey to pursue this investment opportunity? 4-b. Would Casey be inclined to pursue this investment opportunity?arrow_forwardAnswer the following question (Q#4) Consider a poor country with an under-developed economy which could invest trillions into its current capital stock – either moving “up” its current productivity “curve” (PC) or shifting to a new and higher productivity (PC) curve. Which approach is likely best for increasing the country’s living standards (Real GDP Per Person) through time? (a) A continuous build-up of the current capital stock with established technology will achieve more – capital “deepening” with more capital for each worker. (b) R&D that supports “cutting edge” invention and innovation will propel labor (Q#8) Until recently, the economy in China has grown steadily due to the deliberate emphasis on low skill – low wage factory labor methods. However, China’s economic standard of living is still comparatively low. To achieve a U.S. or German standard of living what should be done? a) China should…arrow_forward
- H2. Do all firms have the potential to be aggressive rapid-growth firms? Why or why not?arrow_forwardWhat is meant by the term “self-supporting growth rate”? How is this raterelated to the AFN equation, and how can that equation be used to calculatethe self-supporting growth rate?arrow_forwardThe payoffs of an investment are dependent on the state of the economy. The economy can have two states, recession or growth, with equal probability. If the payoff in the event of growth is $140 and in the event of recession is $80, what is the expected payoff for the investment? a.$100 b.$130 c.$120 d.$110arrow_forward
- H5. Discuss the following statement: If a firm has only independent projects, a constant WACC, and projects with normal cash flows, the NPV and IRR methods will always lead to identical capital budgeting decisions. What does this imply about the choice between IRR and NPV? If each of the assumptions were changed (one by one), how would your answer change? Explain with detailsarrow_forward4) A project is predicted to have a return of -£16m in a recession, and the probability of a recession is estimated to be 0.25. In a growth period the return would be 16m (with probability 0.50) and in a boom the return would be £24m (with probability 0.25). What is the expected return? A) £24m B) £50m C) £10m D) £80marrow_forwardHow could I estimate the Sustainable Growth Rate considering the ROE?arrow_forward
- For most firms, there is some sales growth rate atwhich they could grow without needing any external financing, that is, where AFN = $0. How couldyou determine that growth rate? What variablesunder management’s control would affect thissustainable growth rate?arrow_forwardIn 100 words or less, discuss market efficiency. How does this affect investors?arrow_forwardQ25 Following are three economic states, their likelihoods, and the potential returns: Economic State Probability Return Fast growth 0.3 40 % Slow growth 0.4 10 Recession 0.3 –25 Determine the standard deviation of the expected return. (Do not round intermediate calculations and round your answer to 2 decimal places.) STANDARD DEVIATION. %arrow_forward
- Intermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning