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  1. 003A company earns a 20% after-tax return on the capital it invests and wants operating profit to grow 15% a year. What share of operating profit must it reinvest each year? What changes if the return on capital is 10%?Ratio and margin riddlesHardEquity researchCorporate finance

    Try it first

    At a 20% return on capital, how much of each year's operating profit has to go back into the business to grow 15%?

    Show the worked solution

    It must reinvest 75% of operating profit at a 20% return, and 150% at a 10% return. Growth equals return on capital times the share of profit reinvested, so the reinvestment rate is 15% divided by the return. At 20% that leaves Rs 25 of every Rs 100 free. At 10% the company must invest Rs 150 for every Rs 100 it earns, raising Rs 50 from lenders or shareholders to keep growing.

    Where does growth in operating profit come from?

    Picture a tailor who earns 20% a year on every rupee of sewing machines she owns. If she wants next year's profit 15% higher, she needs 15% more machines' worth of profit, and each rupee of machines earns only 20 paise. Growth equals the return on new capital multiplied by the share of profit put back in. That share is the reinvestment rate, and it is the price the company pays today for tomorrow's growth.

    The relationship
    g=ROC×b⇒b=gROC=15%20%=75%g = \text{ROC} \times b \quad\Rightarrow\quad b = \frac{g}{\text{ROC}} = \frac{15\%}{20\%} = 75\%
    ggrowth in operating profit, 15% a year
    ROCafter-tax return on the new capital invested
    bthe share of after-tax operating profit reinvested
    What it says in wordsDivide the growth you want by the return you earn, and that is the share of profit you must plough back.
    Reinvestment needed for 15% growth, by return on capital50%100%150%200%0%10%15%20%25%30%Return on capitalShare of operating profit reinvestedShaded zone, above 100%: profit is notenough, so outside money is needed10% return: 150%15%: exactly 100%20% return: 75%30%: 50%
    To grow operating profit 15% a year, a company earning 30% on capital reinvests 50% of its profit, one earning 20% reinvests 75%, one earning 15% reinvests all of it, and one earning 10% must invest 150%, raising the gap from outside.

    What does the 10% case tell an analyst?

    Below a 15% return, 15% growth cannot be paid for out of profit at all. At 10%, for every Rs 100 earned the company must invest Rs 150, so Rs 50 comes from new debt or new shares every year and free cash flow is negative. The table shows how the free cash left for owners changes with the return on capital.

    Return on capitalReinvestment rateFree cash per Rs 100 of profit
    30%50%50
    20%75%25
    15%100%0
    10%150%(50)
    Same 15% growth in every row. Free cash is operating profit less reinvestment; a bracket means cash must be raised from outside.

    Growth at a low return can still be worth having if the return beats the cost of capital, and it destroys value if it does not. Say the limitation: the formula assumes new capital earns what old capital earns. Price increases and efficiency gains are growth that needs no reinvestment, so real companies sometimes beat it.

    Where candidates lose it

    The quick wrong answer is 15%, treating the growth rate as the share you reinvest. That ignores the return: the same growth costs very different amounts of capital at 10% and at 30%.

    The second loss is stopping at 150% without saying what it means. A reinvestment rate above 100% is a funding need, and the interviewer wants to hear that growth at a low return on capital burns cash.

    What the interviewer asks next

    • At a 12% cost of capital, is 15% growth at a 10% return good or bad for shareholders?
    • How would you estimate return on capital for a company from its annual report?
    • What happens to the valuation if growth falls to 5% with the return held at 20%?