FINA 303 Chapter 6 (Stocks - Characteristics and Valuation)

Average dividend multiple for comparable

(PE ratios added together) / amount of PE ratios = Average dividend multiple for comparable

Estimating per share-value

(average dividend multiple for comparable) x company's current EPS = Estimating per share-value

A share of common stock has a current price of $82.50 and is expected to grow at a constant rate of 10%. If you require a 14% rate of return, what is the current dividend (D0) on this stock?

P = $82.50; g = 10%; r = 14% => D0 = ? P=D0(1+g)r−g=>$82.50=D0(1+10%)14%−10%=>D0=$3

MSFT current dividend is $0.28/share each quarter. On average, dividends grow at a rate of 1%/quarter. Assuming expected return for MSFT is 2%/quarter, what is its price today?

D0 = $0.28; g = 1%; r = 2% => P = ? P=D0(1+g) / r−g= $0.28(1+1%) / 2%−1%=$28.28

A stock's current annual dividend is $1/share and its expected return is a constant 9%. It currently trades for $55/share. Future expected returns and expected dividend growth are both constant forever into the future. What must the market expect the average dividend growth rate to be?

D0 = $1; P = $55; r = 9% => g = ? P=D0(1+g) / r−g=>$55 = $1(1+g) / 9%−g=>g=7.05%

Coca Cola's dividend is $1/share per quarter. On average, the dividends are expected to grow by 2% per quarter. Assuming the expected return of the stock is 5% per quarter. What is the share price today?

D0 = $1; g = 2%; r = 5% => P = ? P=D0(1+g) / r−g = $1(1+2%) / 5%−2%=$34

For the Dividend Discount Model to work in the long run, which of this following statement needs to hold? Explain why a. The dividend growth rate has to be strictly less than the required rate of return (g < r) b. The dividend growth rate has to be exactly the same as the required rate of return (g = r) c. The dividend growth rate has to be strictly more than the required rate of return (g > r) d. There is no necessary restriction on g and r.

DDM model formula P=D0(1+g) / r−g If r < g => negative price If r = g => cannot solve for price => A. The dividend growth rate has to be strictly less than the required rate of return (g < r)

A firm expects to pay dividends at the end of each of the next four years of $2.00, $1.50, $2.50, and $3.50. If growth is then expected to level off at 8 percent, and if you require a 14 percent rate of return, how much should you be willing to pay for this stock? (Round intermediate calculations to two decimal places).

First, we need to calculate the PV of each dividend in the first stage: D1=$2.00=>PVD1=$2.00(1+14%)=$1.75 D2=$1.50=>PVD2=$1.50(1+14%)2=$1.15 D3=$2.50=>PVD3=$2.50(1+14%)3=$1.69 D4=$3.50=>PVD4=$3.50(1+14%)4=$2.07 Second, we need to calculate the PV of the dividend stream when it enter the constant growth stage. Here, n = 4 PVconstantgrowth=D4(1+g) / r−g×1 / (1+r)4=$3.5(1+8%) / 14%−8%×1 / (1+14%)4=$37.30 The last step is to sum up all PVs to find the stock price P=$1.75+$1.15+$1.69+$2.07+$37.30=$43.96

For the past 15 years, the PE ratio of North/South Travel has been between 28 and 30. If North/South's earnings per share is $4, in what price range would you estimate its stock should be selling?

Maximum price = 30 x $4 = $120 Minimum price = 28 x $4 = $112

2 companies have the same PE ratios. Company A has a per-share price of $10 and an EPS of $0.50. Company B has a current EPS of $1.25, what is Company B's current per-share price?

PEA=PEB=>PAEPSA=PBEPSB=> $10/$0.5=PB$1.25=>PB=$25

PE Ratio

Share price / Earnings per share =PE Ratio

Sparkle Jewelers expects to pay dividends (per shares) of $0.60, $0.90, $2.40 and $3.50 during the next 4 years. Beginning in the 5th year, the dividend is expected to grow at a 4% rate indefinitely. If investors require a 20% return to purchase Sparkle's stock, what is the current value of the company's stock?

There are 2 stages of dividend stream: (1) when dividends are uneven without any pattern (first 4 years) and (2) when dividends grow at a constant rate every year (starting from year 5) First, we need to calculate the PV of each dividend in the first stage: D1=$0.6=>PVD1=$0.6(1+20%)=$0.5 D2=$0.9=>PVD2=$0.9(1+20%)2=$0.625 D3=$2.4=>PVD3=$2.4(1+20%)3=$1.39 D4=$3.5=>PVD4=$3.5(1+20%)4=$1.69 Second, we need to calculate the PV of the dividend stream when it enter the constant growth stage. Here, n = 4 PV constant growth=D4(1+g)r−g×1(1+r)4=$3.5(1+4%)20%−4%×1(1+20%)4=$10.97 The last step is to sum up all PVs to find the stock price P=$0.6+$0.625+$1.39+$1.69+$10.97=$15.275