The common stock of PQR Inc. is expected to pay a dividend of $15 for each share exactly one year from now. Given the risk of the stock, the market requires a rate of return of 22%. The dividends are expected to grow in perpetuity at a constant rate of 10%.

(i) What is the “constant”-growth Gordon Growth Model intrinsic value of stock of the firm?

(ii) Assume that the firm has a stable plowback ratio of 39.5%. Assume that the retained earnings are used entirely for new investments and that assets in place are replaced in perpetuity by accumulated depreciation. The implied reinvestment return from plowback is 25.32%. What is the present value of earnings per share from the assets in place (value if there is no growth)? Using these figures, what is the Present Value of Growth Opportunities?

(iii) Prove using a forecast of future earnings, calculation of year-by-year NPV of plowback, and the standard PV arguments that this PVGO is correct.

(iv) Work out how the firm’s P/E ratio will change if from t=0 onwards the firm chooses to retain 5% instead of the current 39.5%, in the business.(v): Suppose appropriate discount rate for the firm’s stock rises to 30% (from 22% that we had earlier assumed). Explain qualitatively why the P/E does not rise when the firm increases the retention ratio.

(v) Suppose appropriate discount rate for the firm’s stock rises to 30% (from 22% that we had earlier assumed). Explain qualitatively why the P/E does not rise when the firm increases the retention ratio.