Final answer:
The value of a firm with a dividend of $70 and a cost of equity of 10% can be estimated at $700 per share assuming zero dividend growth, but this does not account for changes over time. For Big Drug, the optimal investment considering only private benefits is $30 million, while including social benefits it increases to $52 million.
Step-by-step explanation:
The value of a firm when the cost of equity (rE) is 10% and the dividend is $70 can be calculated using the dividend discount model (DDM), which states that the value of a stock is the present value of all its future dividends. However, without the growth rate of the dividends, we cannot provide a complete answer. If we were to assume a zero growth rate, the value of the firm could be found by dividing the dividend by the required rate of return, which would be $70 / 0.10, resulting in a value of $700 per share. Nevertheless, this is an oversimplification, as it does not take into account any growth in dividends or changes in the required rate of return over time.
Regarding the scenario described for Big Drug, the firm faces an 8% cost of borrowing. If it accounts only for private benefits, as seen in its Dprivate curve, its optimal investment would be $30 million. However, considering the spillover benefits to society (Dsocial), the optimal investment level would be $52 million, which would be realized if the firm could internalize the social benefits of its R&D investments.