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stellarik [79]
4 years ago
15

National Advertising just paid a dividend of D 0 = $0.75 per share, and that dividend is expected to grow at a constant rate of

6.50% per year in the future. The company's beta is 1.25, the required return on the market is 10.50%, and the risk-free rate is 4.50%. What is the company's current stock price?
Business
1 answer:
DerKrebs [107]4 years ago
5 0

Answer:

$14.52

Explanation:

The calculations proceed as follows:

Step 1: Calculation of expected return

This is done by using the Capital Asset Pricing Model (CAPM) formula as follows:

ERi = Rf + βi(ERm - Rf) ........................................... (1)

Where:

ERi = expected return of investment = ?

Rf = risk-free rate  = 4.50% = 0.0450

ERm = market rate = 10.50% = 0.1050

βi  = beta of the investment  = 1.25

(ERm  - Rf) = market risk premium  = 0.1050 - 0.0450 = 0.060

​Substituting the values into equation (1), we have:

ERi = 0.0450 + 1.25(0.060) = 0.120 = 12%

Step 2: Calculation of current year dividend

D1 = Do × (1 + g) ........................................ (2)

Where;

D1 = current year dividend = ?

Do = last year dividend = $0.75

g = growth rate = 6.50% = 0.065

Substituting the values into equation (2), we have:

D1 = 0.75 × (1 + 0.065) = $0.79875

Step 3: Calculation of current stock price

The dividend growth model formula for calculating stock price is used as follows:

Stock price = D1 ÷ (ERi - g)

                   = $0.79875 ÷ (0.120 - 0.065)

                   =  14.5227272727273

Stock price = $14.52.

Therefore, the company's current stock price is $14.52.

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1-b. Dollars of gross profit from selling cases = $1,500

1-c. Gross profit percentage from selling tags = 72.86%

1.d. Gross profit percentage from selling cases = 83.33%

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2-b. Tag yields more profit per dollar of sales.

Explanation:

Note: The requirements for this question are two not three as erroneously stated. This is because, the first and the third question are the same. Therefore, the two relevant requirements of the question are:

1. Calculate the dollars of gross profit and the gross profit percentage from selling tags and cases.

2. Which product line yields more dollars of profit? - Which product line yields more profit per dollar of sales?

The explanation of the answers is now given as follows:

1. Calculate the dollars of gross profit and the gross profit percentage from selling tags and cases.

Sales revenue from tags = Sales value of 160 tags mailed to customers on Jan. 8 at a price of $30 per tag + Sales value of 260 tags mailed to customers on Jan. 21 at a price of $30 per tag = (160 * $30) + (260 * $30) = $12,600

Sales revenue from cases = Sales value of 120 cases mailed to customers on Jan. 19 at a price of $15 per case = 120 * $15 = $1,800

Total number of tags sold = 160 tags mailed to customers + 260 tags mailed to customers on Jan. 21 = 420

Total number of cases sold = 120 cases mailed to customers on Jan. 19 at a price of $15 per case = 120

Using FIFO, we have:

Cost of tags sold = Value of 260 tags purchased on Jan.2 from Xioasi Manufacturing (XM) at a cost of $7 per tag + Value of the remaining 160 (i.e. 420 – 260 = 160) tags sold based on the 360 tags purchased on Jan. 11 from XM at a cost of $10 per tag = (260 * $7) + (160 * $10) = $3,420

Cost of cases sold = Value of 60 cases purchased on Jan.4 from Bachittar Products (BP) at a cost of $2 per case + Value of the remaining 60 cases sold based on the 160 cases purchased on Jan. 14 from BP at a cost of $3 per case = (60 * $2) + (60 * $3) = $300

Therefore, we have:

1-a. Dollars of gross profit from selling tags = Sales revenue from tags - Cost of tags sold = $12,600 - $3,420 = $9,180

1-b. Dollars of gross profit from selling cases = Sales revenue from cases - Cost of cases sold = $1,800 - $300 = $1,500

1-c. Gross profit percentage from selling tags = (Dollars of gross profit from selling tags / Sales revenue from tags) * 100 = ($9,180 / $12,600) * 100 = 72.86%

1.d. Gross profit percentage from selling cases = (Dollars of gross profit from selling cases / Sales revenue from cases) * 100 = 83.33%

2. Which product line yields more dollars of profit? - Which product line yields more profit per dollar of sales?

2-a. Which product line yields more dollars of profit?

From part 1 above, we have:

Dollars of gross profit from selling tags = $9,180

Dollars of gross profit from selling cases = $1,500

Since the dollars of gross profit from selling tags of $9,180 is greater than the dollars of gross profit from selling cases of $1,500, this implies that Tag yields more dollars of profit.

2-b. Which product line yields more profit per dollar of sales?

From part 1 above, we have:

Total number of tags sold = 420

Total number of cases sold = 120

Therefore, we have:

Tag's profit per dollar of sales = Dollars of gross profit from selling tags / Total number of tags sold = $9,180 / 420 = $21.86

Case's profit per dollar of sales = Dollars of gross profit from selling cases / Total number of cases sold = $1,500 / 120 = $12.50

Since Tag's profit per dollar of sales of $21.86 is greater than Case's profit per dollar of sales of $12.50, this implies that Tag yields more profit per dollar of sales.

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