Exam 4: Security Analysis and Portfolio Theory

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Based on the industry data,cost of equity for each division in the company can be calculated using CAPM $R _ { f } + \left( R _ { m } - R _ { f } \right) \beta$ _{.
The ROE for each division can be calculated using the price-to-earnings relationship}

$\frac { P _ { 0 } } { E _ { 1 } } = \frac { 1 - b } { k - b r }$ $$\begin{array} { c c c } \text { Divizion } & \text { Cost of equity } & \text { ROE } \\\hline \text { A } & 16.75 \% & 19.58 \% \\\text { B } & 18.50 \% & 21.33 \% \\\text { C } & 15.00 \% & 10.00 \%\end{array}$$ ROE of the firm is the weighted average of ROE's for different divisions of the firm,with earnings being the weights.
ROE of the firm = $\left( \frac { 2 } { 11 } \times 19.58 \% \right) + \left( \frac { 5 } { 11 } \times 21.33 \% \right) \left( \frac { 4 } { 11 } \times 10 \% \right)$ = 16.89%
Given the retention ratio of 0.5
The growth rate of the firm can be calculated using $\text { (Retention ratio } \times \mathrm { ROE } \text { ) }$ = 0.5 × 16.89% = 8.45%

Correct Answer:

Verified

a.
Price of the bond is the present value of the cash flows from a bond.
It can be calculated using $$\frac { 115 } { ( 1.11 ) ^ { 1 } } + \frac { 115 } { ( 1.11 ) ^ { 2 } } + \frac { 115 } { ( 1.11 ) ^ { 3 } } \cdots \frac { 115 } { ( 1.11 ) ^ { 19 } } + \frac { 1115 } { ( 1.11 ) ^ { 20 } }$$ = $1039.82
b.
If the coupon is reinvested at 9%,at the end of 20 years it grows to $$115 ( 1.09 ) ^ { 19 } + 115 ( 1.09 ) ^ { 18 } + 115 ( 1.09 ) ^ { 17 } + \ldots + 115 ( 1.09 ) ^ { 2 } + 115 ( 1.09 ) ^ { 1 }$$ = $5,768.414
At the end of 20 years,the investor will have $1115 + $5,768.414 = $6,883.41