California Clinics, an investor-owned chain of ambulatory care clinics, just paid a dividend of $2 per share. The firm’s dividend is expected to grow at a constant rate of 5% per year, and investors require a 15 % rate of return on the stock.
1. What is the stock’s value?
2. Suppose the riskiness of the stock decreases, which causes the required rate of return to fall to 13%. Under these conditions, what is the stock’s value?
3. Return to the original 15% required rate of return and assume a dividend growth rate estimate increase to 7% per year, what is the stock value?
4. Explain how each of the four (4) fundamental factors that affect the supply and demand for investment capital, and hence, interest rates, (namely productive opportunities, time preferences for consumption, risk, and inflation) affects the cost of money.
5. Why is risk aversion so important to financial decision making?
6. Explain the three (3) techniques for solving time value problems.
To answer these questions, we will first need to understand some basic concepts and formulas related to stock valuation and the time value of money.
1. To find the stock's value, we can use the Gordon Growth Model, which calculates the present value of the expected future dividends. The formula is as follows:
Stock Value = Dividend / (Required Rate of Return - Dividend Growth Rate)
In this case, the dividend is $2, the required rate of return is 15%, and the dividend growth rate is 5%. Substituting the values:
Stock Value = $2 / (0.15 - 0.05) = $2 / 0.10 = $20
Therefore, the stock's value is $20 per share.
2. If the required rate of return decreases to 13%, we can use the same formula to calculate the stock's value:
Stock Value = $2 / (0.13 - 0.05) = $2 / 0.08 = $25
So, under these conditions, the stock's value would increase to $25 per share.
3. Returning to the original required rate of return of 15% and assuming a new dividend growth rate of 7%, we can apply the formula again:
Stock Value = $2 / (0.15 - 0.07) = $2 / 0.08 = $25
Therefore, even with the increased dividend growth rate, the stock's value remains $25 per share.
4. The four fundamental factors affecting the supply and demand for investment capital and interest rates are as follows:
- Productive Opportunities: When there are more investment opportunities with higher expected returns, the demand for investment capital increases, leading to higher interest rates. Conversely, when there are limited productive opportunities, the demand for investment capital decreases, resulting in lower interest rates.
- Time Preferences for Consumption: People generally prefer to consume goods and services today rather than in the future. Higher time preferences for consumption lead to a higher demand for current consumption, reducing the supply of savings and increasing interest rates. Lower time preferences for consumption have the opposite effect.
- Risk: Increased risk raises the required return on investments, leading to higher interest rates. If the risk is perceived to be lower, the required return decreases, resulting in lower interest rates.
- Inflation: Inflation erodes the purchasing power of money over time. Higher inflation expectations lead to higher interest rates because lenders require compensation for the expected loss in purchasing power. Lower inflation expectations have the opposite effect.
5. Risk aversion is crucial in financial decision making because it reflects an individual's willingness to accept a lower expected return in exchange for a lower level of risk. Investors tend to avoid risky investments unless they are compensated for taking on additional risk. Without considering risk aversion, investors may make imprudent decisions and expose themselves to excessive risk, potentially leading to financial losses.
6. The three techniques for solving time value problems are as follows:
- Future Value (FV): Calculates the future value of a sum of money invested at an interest rate over a specific period. The formula is FV = PV × (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods.
- Present Value (PV): Determines the present value of a future sum of money discounted at a certain interest rate. The formula is PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of periods.
- Annuities: Deals with a series of equal cash flows or payments made at regular intervals. The formulas for calculating the present value (PV) and future value (FV) of annuities differ depending on whether the cash flows occur at the beginning or end of each period, and whether the interest is compounded once per period or continuously.
By utilizing these techniques, we can accurately determine or evaluate the value of money over time and make informed financial decisions.