# Quantitative Problem 1: Hubbard Industries just paid a common dividend, D0, of $1.80. It expects... ## Question: Quantitative Problem 1: Hubbard Industries just paid a common dividend, D0, of$1.80. It expects to grow at a constant rate of 3% per year. If investors require a 9% return on equity, what is the current price of Hubbard's common stock? Round your answer to the nearest cent. Do not round intermediate calculations. = per share

Quantitative Problem 2: Carlisle Corporation has perpetual preferred stock outstanding that pays a constant annual dividend of $1.00 at the end of each year. If investors require an 8% return on the preferred stock, what is the price of the firm's perpetual preferred stock? Round your answer to the nearest cent. Do not round intermediate calculations. = per share Quantitative Problem 3: Assume today is December 31, 2013. Imagine Works Inc. just paid a dividend of$1.15 per share at the end of 2013. The dividend is expected to grow at 15% per year for 3 years, after which time it is expected to grow at a constant rate of 5.5% annually. The company's cost of equity (rs) is 9%. Using the dividend growth model (allowing for non constant growth), what should be the price of the company's stock today (December 31, 2013)? Round your answer to the nearest cent. Do not round intermediate calculations. = per share

## Dividend Discount Model:

The dividend discount model is used to determine the intrinsic value of a stock. All the different generators from the stock are discounted using the required rate of return. The formula is: Share price = Expected dividend / (Required rate - Dividend growth rate)

Problem 1:

Info:

Current dividend = $1.80 Growth rate = 3% Discount rate = 9% Computing: {eq}Current \ stock \ value \ = \ \dfrac{Current \ Dividend \ \times \ \left ( 1 \ + \ Growth \ rate \right )}{Discount \ rate \ - \ Growth \ rate} \\ Current \ stock \ value \ = \ \dfrac{1.80 \ \times \ \left ( 1 \ + \ 0.03 \right )}{0.09 \ - \ 0.03} \\ Current \ stock \ value \ = \ \$30.9 {/eq}

Problem 2:

Info:

Annual dividend = $1 Return on preferred stock = 8% Computing: {eq}Preferred \ stock \ price \ = \ \dfrac{Annual \ dividend}{Return \ on \ preferred \ stock} \\ Preferred \ stock \ price \ = \ \dfrac{1}{0.08} \\ Preferred \ stock \ price \ = \ \$12.5 {/eq}

Problem 3:

Formula:

{eq}Present \ value \ discount \ factor \ at \ 9\% \ = \ \left [ \dfrac{1}{\left ( 1 \ + \ Discount \ factor \right )^{Year}} \right ] {/eq}

Present Value of dividends for 3 years is calculated below:

Year Dividend = (Increasing by 15% * (1.15)) (A) Present value discount factor at 9% (B) Present value ((C) = (A) * (B))
1 $1.3225 0.9174$1.2133
2 $1.5209 0.8417$1.2801
3 $1.7490 0.7722$1.3506
Total = $3.8439 Dividend for the perpetuity can be calculated as follow: Info: Dividend for year 3 =$1.7490

Growth rate = 5.5%

Expected return = 9%

Present value factor for 12% at year 3 = 0.7722

Computing:

{eq}Dividend \ = \ \dfrac{Dividend \ for \ year \ 3 \ \times \ \left ( 1 \ + \ Growth \ rate \right )}{\left ( Expected \ return \ - \ Growth \ rate \right )} \ \times \ Present \ value \ factor \ for \ 12\% \ at \ year \ 3 \\ Dividend \ = \ \dfrac{1.7490 \ \times \ \left ( 1 \ + \ 0.055 \right )}{\left ( 0.09 \ - \ 0.055 \right )} \ \times \ 0.7722 \\ Dividend \ = \ 52.7199 \ \times \ 0.7722 \\ Dividend \ = \ \$40.7103 {/eq} Value of stock can be calculated as follow: Value of stock = Present value of dividend + Present value of dividends for perpetuity Value of stock = 3.8439 + 40.7103 Value of stock =$44.55