Question

1. (10 pts) The intrinsic value of a share of stock is equal to today’s value of all expected future cash flows to be received by an investor. The more risk the stock exposes the investor to, the less the investor shall be willing to pay. Support this thought with only two principles of finance.

Please show all work.

Answer 1

The two principles of finance that can be used to support this thought are:

1. The principle of time value of money
2. The principle of risk and return

Principle of time value of money – This principle states that the value of money declines with time and the value of an asset or a stock or a series of cash flow today is the sum of all present values of cash flows that will be received in future from that asset or stock.

Suppose that a company has a stock that is expected to pay $2 as dividends next year. This dividend will grow at the rate of 5% per annum for perpetuity. The company has a required rate of return of 12%.

Thus as per the principle of time value of money value of the share today = dividend/(rate of return – growth rate) = $2/(12%-5%)

= $28.57

Thus the principle of time value of money or the principle of present value of money supports the thought that intrinsic value of a share of stock is equal to today’s value of all expected future cash flows to be received by an investor.

Principle of risk and return – This principle is based on the concept that investors care about both risk as well as returns. Risk and returns are directly related and so the higher the risks the higher should be the quantum of returns and the lower the risks the lower should be the quantum of returns.

Suppose that in the above example the company exposes the investors to more risk due to business diversification. As such the investors will start demanding greater returns form a stock.

We can explain this numerically from the CAPM model. As per CAPM model cost of equity = risk free rate + (beta * market premium). Now suppose that risk free rate is 2%, beta is 1.1 and market premium is 5%. Thus cost of equity = 2%+(1.1*5%) = 7.5%. Now suppose that business diversifies in a new field and hence beta increases to 1.3. Thus new cost of equity = 2%+(1.3*5%) = 8.5%.

Thus cost of equity increases by 100 basis points from 7.5% to 8.5%. This is due to increased level of risks associated with the stock.