Question

The risk-free rate is 1.25% and the market risk premium is 5.78%. A stock with a β of 0.84 just paid a dividend of $2.17. The dividend is expected to grow at 20.45% for three years and then grow at 4.90% forever. What is the value of the stock?

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#2

The risk-free rate is 1.04% and the market risk premium is 8.82%. A stock with a β of 0.98 just paid a dividend of $2.43. The dividend is expected to grow at 24.37% for five years and then grow at 3.63% forever. What is the value of the stock?

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#3

Caspian Sea Drinks needs to raise $33.00 million by issuing additional shares of stock. If the market estimates CSD will pay a dividend of $1.12 next year, which will grow at 3.76% forever and the cost of equity to be 13.40%, then how many shares of stock must CSD sell?

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Answer 1

1). Given that,

Risk free rate Rf = 1.25%

market risk premium MRP = 5.78%

The risk-free rate is 1.25% and the market risk premium is 5.78%. A stock with a β of 0.84 just paid a dividend of $2.17. The dividend is expected to grow at 20.45% for three years and then grow at 4.90% forever.

=> D0 = $2.17

Beta = 0.84

growth rate of 3 year = 20.45%

=> D1 = 2.17*1.2045 = $2.6138

D2 = 2.6138*1.2045 = $3.1483

D3 = 3.1483*1.2045 = $3.7921

thereafter growth rate g = 4.90%

So, cost of equity using CAPM = Rf + beta*MRP

=> Firm's Ke = 1.25 + 0.84*5.78 = 6.11%

So, value of stock at year 3 using constant dividend growth rate is

P3 = D3*(1+g)/(Ke -g) = 3.7921*1.049/(0.611 - 0.049) = $330.06

Stock price today is sum of PV of future dividend and P3 discounted at Ke

=> P0 = D1/(1+Ke) + D2/(1+Ke)^2 + D3/(1+Ke)^3 + P3/(1+Ke)^3

=> P0 = 2.6138/1.0611 + 3.1483/1.0611^2 + 3.7921/1.0611^3 + 330.06/1.0611^3 = 284.70

So, Value of stock= $284.70

2).

Given that,

Risk free rate Rf = 1.04%

market risk premium MRP = 8.82%

A stock with a β of 0.98 just paid a dividend of $2.43. The dividend is expected to grow at 24.37% for five years and then grow at 3.63% forever.

=> D0 = $2.43

Beta = 0.84

growth rate of 5 year = 24.37%

=> D1 = 2.43*1.2437 = $3.0222

D2 = 3.0222*1.2437 = $3.7587

D3 = 3.7587*1.2437 = $4.6747

D4 = 4.6747*1.2437 = $5.8139

D5 = 5.8139*1.2437 = $7.2308

thereafter growth rate g = 3.63%

So, cost of equity using CAPM = Rf + beta*MRP

=> Firm A's Ke = 1.04 + 0.98*8.82 = 9.68%

So, value of stock at year 5 using constant dividend growth rate is

P3 = D3*(1+g)/(Ke -g) = 7.2308*1.0363/(0.0968 - 0.0363) = $123.86

Stock price today is sum of PV of future dividend and P3 discounted at Ke

=> P0 = D1/(1+Ke) + D2/(1+Ke)^2 + D3/(1+Ke)^3 + D4/(1+Ke)^3 + D5/(1+Ke)^5 + P5/(1+Ke)^5

=> P0 = 3.0222/1.0968 + 3.7587/1.0968^2 + 4.6747/1.0968^3 + 5.8139/1.0968^4 + 7.2308/1.0968^5 + 123.86/1.0968^5 = 96.03

So, Value of stock = $96.03

3).

Given that Caspian Sea Drinks needs to raise $33.00 million by issuing additional shares of stock. If the market estimates CSD will pay a dividend of $1.12 next year, which will grow at 3.76% forever and the cost of equity to be 13.40%,

=> D1 = $1.12

growth rate g = 3.76%

Ke = 13.40%

So, value of stock today using constant dividend growth rate is

P0 = D1/(Ke -g) = 1.12/(0.1340 - 0.0376) = $11.62

So, Value of stock = $11.62

total number of share = 33000000/11.62 = 2840357 shares