Part B: The Crescent Corporation just paid a dividend of $2 per share and is expected to continue paying the same amount each year for the next 4 years. If you have a required rate of return of 13%, plan to hold the stock for 4 years, and are confident that it will sell for $30 at the end of 4 years, how much should you offer to buy it at today?
Part C: Use the information in the following table to answer the questions below.
State of Economy Probability of State Return on A in State Return on B in State Return on C in State
Boom .35 0.040 0.210 0.300
Normal .50 0.040 0.080 0.200
Recession .15 0.040 -0.010 -0.260
Part B: To calculate the present value of the dividends and the future selling price, you can use the formula for the present value of a future cash flow.
PV = Div1/(1+r) + Div2/(1+r)^2 + Div3/(1+r)^3 + Div4/(1+r)^4 + Pn/(1+r)^n
Where:
PV = Present value
Div = Dividend amount per year
r = Required rate of return
Pn = Future selling price
n = Number of years
In this case, the dividends are $2 per share for each of the next 4 years, and the future selling price is $30 at the end of 4 years. The required rate of return is 13% and the holding period is also 4 years.
Using the formula, you can calculate:
PV = 2/(1+0.13) + 2/(1+0.13)^2 + 2/(1+0.13)^3 + 2/(1+0.13)^4 + 30/(1+0.13)^4
Simplifying this expression will give you the present value of the stock today.
Part C: To answer questions using the table, you need to calculate the expected returns for each investment option by multiplying the return in each state by its corresponding probability. Then, you can add up the weighted returns to find the expected return for each investment option.
For example, to calculate the expected return for investment A:
Expected Return A = (Return in Boom State) * (Probability of Boom) + (Return in Normal State) * (Probability of Normal) + (Return in Recession State) * (Probability of Recession)
Expected Return A = (0.040 * 0.35) + (0.040 * 0.50) + (0.040 * 0.15)
Similarly, you can calculate the expected returns for investments B and C using the same formula.
Once you have the expected returns for each investment option, you can compare them to make a decision based on the risk and return trade-off.