gray cave furniture stock is expected to pay a dividend of $5.52 in 1 year, $9.33 in 2 years, $x in 3 years…

gray cave furniture stock is expected to pay a dividend of $5.52 in 1 year, $9.33 in 2 years, $x in 3 years, and $5.33 in 4 years. the stock is currently priced at $219.48 and is expected to be priced at $263.26 in 3 years. the expected return for the stock is 9.34 percent per year. the stocks dividends are paid annually and the next dividend is expected in 1 year. what is x? input instructions: round your answer to the nearest cent (so 2 decimal places).

gray cave furniture stock is expected to pay a dividend of $5.52 in 1 year, $9.33 in 2 years, $x in 3 years, and $5.33 in 4 years. the stock is currently priced at $219.48 and is expected to be priced at $263.26 in 3 years. the expected return for the stock is 9.34 percent per year. the stocks dividends are paid annually and the next dividend is expected in 1 year. what is x? input instructions: round your answer to the nearest cent (so 2 decimal places).

Answer

Answer:

$10.47$

Explanation:

Step1: Present - value formula

The present - value of the stock is the sum of the present - values of future dividends and the present - value of the stock price in 3 years. The present - value formula is $PV=\frac{CF_1}{(1 + r)^1}+\frac{CF_2}{(1 + r)^2}+\frac{CF_3+P_3}{(1 + r)^3}$, where $PV$ is the present value of the stock, $CF_i$ is the cash - flow (dividend) in year $i$, $r$ is the discount rate, and $P_3$ is the stock price in year 3. We know that $PV = 219.48$, $CF_1=5.52$, $CF_2 = 9.33$, $CF_4 = 5.33$, $P_3=263.26$, and $r=0.0934$.

Step2: Substitute values into the formula

$219.48=\frac{5.52}{1 + 0.0934}+\frac{9.33}{(1 + 0.0934)^2}+\frac{X + 263.26}{(1 + 0.0934)^3}$ First, calculate $\frac{5.52}{1 + 0.0934}=\frac{5.52}{1.0934}\approx5.05$. Second, calculate $\frac{9.33}{(1 + 0.0934)^2}=\frac{9.33}{1.0934^2}=\frac{9.33}{1.1956}\approx7.80$. Let $y=\frac{X + 263.26}{(1 + 0.0934)^3}=\frac{X + 263.26}{1.0934^3}=\frac{X + 263.26}{1.3069}$. Then the equation becomes $219.48=5.05 + 7.80+y$. $y=219.48-(5.05 + 7.80)=219.48 - 12.85=206.63$.

Step3: Solve for $X$

Since $y=\frac{X + 263.26}{1.3069}=206.63$, we can solve for $X$. Multiply both sides by $1.3069$: $X + 263.26=206.63\times1.3069$. $206.63\times1.3069 = 206.63\times(1+0.3069)=206.63+206.63\times0.3069=206.63 + 63.39=269.92$. $X=269.92 - 263.26=10.47$.