A company has the following balance sheet, $mm:
Equipment 500 Equity 450
Cash 50 Debt 100
Actual and accounting depreciation are both 10%, which the company replaces. Taxes are 0%. ROE is 12% and there are 10 million shares outstanding.
The company is expected to exist for three years, during which it pays out all earnings as dividends at the end of each year. Then it sells its assets, pays its debts and returns whatever funds it has to shareholders. Using 3% as the risk-free rate and 2% as the risk premium, what is the price per share?
V Same as IV, but assume actual depreciation is 20%. What is the price per share.
VI Again as IV (not V), but the company's financial managers pay out only half of earnings as dividends. The reminder is invested in new equipment which maintains the 12% ROE. What is the price per share?
VII Again as IV (not V or VI). Inflation is 5% per year, which affects earnings (including the first year; i.e., the ROE assumption is before inflation) and the value of the equipment (depreciation is replaced, so can be ignored again) when it is sold. What is the price per share, recognizing the inflation premium in the discounting?
VIII A company is not expected to close, not ever, never!!! It earns $5/share which is expected ad infinitum, and it pays it all out in dividends. The riskless interest rate, risk premium and expected inflation rate are as above. What is the price per share?
IX Now assume the same company as in VIII but only pays out half its earnings as dividends. The remaining allows earnings to grow at 6% per year. The riskless in interest rate, risk premium and expected inflation rate are as above. What is the price per share?
X Same as IX, but price per share is 60. Assuming a constant expected growth rate, what must that be to justify the stock price?
XI Rate-of-Return (ROR) is your dividend plus price change, if any, divided by your investment, in this case the original price of the stock.
You buy the stock in VIII. One year later, expectations are realized. What is the stock price now? What is your Rate-of-Return?
You buy the stock in IX. One year later, expectations are realized. What is the stock price now? Be careful: the original stock price used the first year's earnings in the price equation. The stock price at the end of the year must use the next year's earnings. What is your Rate-of-Return?