Problem 1 If a stock's P/E ratio is 12 at a time when earnings are $3 per year, what is the stock's current price? Problem 2 What should be the price for a common stock paying $6.00 annually in dividends if the growth rate is zero and the discount rate is 8%? er e Problem 3 What price was quoted to an investor who paid $982.50 for a $1,000 par value bond? as quoted to Problem 4 What is the goal of the firm? Problem 5 If the dividend yield for year one is expected to be 8% based on the current price of $25, what will the year four dividend be if dividends grow at a constant 6%?

Explanation:

1)

Stock’s current price:

= P/E Ratio×EPS   = 12×$3

= $36

2)

Price of Stock = Annual Dividend / Discount Rate

Price of Stock = $6.00 / 0.08

Price of Stock = $75.00

3)

Price of Bond = Quoted price * Par Value

$982.50 = Quoted price * $1,000

Quoted price = 98.25

5)

D1 = Dividend yield *price  = 0.08 *25 = $ 2

D4 = D1(1+G)^N

D4 = 2(1+.06)^3

D4 = 2* 1.19102

D4 = $ 2.38 per share

1. The stock's current price is $36.

2. Price of the common stock is $75.

3. The quoted price of bond to the investor is 98.25.

4. Wealth maximization and cost of capital minimization.

5. Year four dividend will be $2.38 per share.

Explanation:

Problem 1: If a stock's P/E ratio is 12 at a time when earnings are $3 per year, what is the stock's current price?  

P/E = Stock price (P) ÷ Earning per share (E) = 12

From the question, earning per share (E) is $3. We therefore substitute and have:

Stock price (P) ÷ $3 =12

Stock price (P) = 12 × $3 = $36

Therefore, the stock's current price is $36.

Problem 2 What should be the price for a common stock paying $6.00 annually in dividends if the growth rate is zero and the discount rate is 8%?  

When the growth rate of dividend of stock is zero, the price of the of the stock can be obtained by simply dividing the dividend by the discount rate as follows:

Price of the common stock = Dividend/discount rate = $6/0.8 = $75.

Problem 3 What price was quoted to an investor who paid $982.50 for a $1,000 par value bond? as quoted to  

Quotation of bonds is not stated in dollars and cents like stocks and other securities, but rather it quoted as a percentage of its own par value without adding a percentage sign after it. For this question, it can be calculated as follows:

Bond price = Quoted price to an investor × Bond par value

Quoted price to an investor = Bond price ÷ Bond par value = $982.50 ÷ $1,000 = 0.9825, or 98.25

Therefore, the quoted price of bond to the investor is 98.25.

Problem 4 What is the goal of the firm?  

The goal of the firm is to maximize the wealth of shareholders while the cost of capital is being simultaneously minimized.

Problem 5 If the dividend yield for year one is expected to be 8% based on the current price of $25, what will the year four dividend be if dividends grow at a constant 6%?

Year 1 dividend = 0.08 × 25 = $ 2

Using the Forward value formula, Year 4 dividend can be calculated as follows:

Year 4 dividend = Year 1 dividend × (1 + growth rate)^number of years remaining

                           = 2 × (1 + 0.06)^3

                           = 2* 1.191016

Year 4 dividend = $2.382032, or $2.38 approximately.

Therefore, year four dividend will be $2.38 per share.

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