# Homework Solutions - Lecture 4

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2 Ideally, we should define ROC as the adjusted after-tax operating income in the current year divided by the adjusted beginning-of-year value of debt plus equity. For simplicity, I will define the ROC using the current year's adjusted debt and equity values. From the lecture 3 homework, we found that the adjusted book values of debt and equity were and Another simple alternative would be to assume that the beginning of year adjustments to debt and equity are the same as the current adjustments. Using my approximation, we get: ROC 12.70% ( ) Assuming ROC does not change over time, fundamental growth in operating income is defined as: g EBIT ( Reinvestment Rate)( ) (. 2835)(.1270) 3.60% ROC Ignoring operating lease and advertising adjustments to EBIT (but removing one-time charges), the historical growth rate from 2009 to 2010 was 0.78%. However, if we correctly incorporate adjustments to operating income in both years, operating income decreases from 2,283 million to 2, million, or -8.66%. Our forecasted fundamental growth rate is slightly higher than the actual (adjusted) historical growth rate. This difference may reflect the decrease in ROC from 14.7% in 2009 to 12.7% in **Note that the analysis above ignores any changes in ROC. To correctly analyze past fundamental growth, we would need to incorporate any changes in ROC over time. To correctly forecast future income based on fundamental growth, we would need to incorporate any future changes in ROC based on our ROC forecast.

4 **Note that the analysis above ignores any changes in ROE. To correctly analyze past fundamental growth, we would need to incorporate any changes in ROE over time. To correctly forecast future income based on fundamental growth, we would need to incorporate any future changes in ROE based on our ROE forecast.

5 3. Consider a simple firm that pays no taxes and pays out all of its earnings as dividends. In the current year, the firm has total revenues of \$500 million and total expenses of \$400 million. The firm's book value of capital at the beginning of the year was \$1 billion. a) Calculate the firm's operating income and its return on capital (ROC) in the current year. Operating Income \$500 - \$400 \$100 million ROC 100/ % b) The current inflation rate is 3% and the firm expects this inflation rate to affect revenues and expenses equally (i.e., both will increase by 3% in the second year). Given these assumptions, calculate the firm's operating income and its return on capital (ROC) in the second year. Operating Income \$500(1.03) - \$400(1.03) \$515 - \$412 \$103 million ROC 103/ % c) Calculate the percentage change (growth rate) in operating income for this firm from the first year to the second. Using the fundamental growth equation we discussed in class, write the firm's growth rate as a function of reinvestment and return on capital (ROC). g EBIT, Actual % g EBIT, Fundametal ( Reinv Rate)( ROC) ROC ( 0) (10.3%) % Note that inflation leads to a 3% increase in ROC, because earnings are affected by inflation while the book value of capital is not. As a result, even though the firm does no reinvestment, inflation leads to a fundamental growth rate of 3%.

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