Question

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next 10 years because the firm needs to plow back its earnings to fuel growth. The company will pay a dividend of $10 per share 11 years from today and will increase the dividend by 7 percent per year thereafter.

If the required return on this stock is 14 percent, what is the current share price?

Lohn Corporation is expected to pay the following dividends over the next four years: $10, $7, $6, and $2. Afterward, the company pledges to maintain a constant 6 percent growth rate in dividends forever.

If the required return on the stock is 12 percent, what is the current share price?

Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 23 percent for the next 3 years, with the growth rate falling off to a constant 6 percent thereafter.

If the required return is 11 percent and the company just paid a $1.30 dividend. what is the current share price?

Answer 1

Let the dividend for year n be denoted by Dn

Let required rate of return be r

Let Growth rate be g

(1) Given, D11 = 10, g = 7% and r = 14%

According to Gordon's Growth Formula,

P10 = D11/(r - g) = 10/(0.14 - 0.07) = $142.86

Hence, P0 = P10/(1+r)¹⁰ = 142.86/(1+0.14)¹⁰ = $38.54

Hence, Price of stock now = $38.54

(2) Given, D1 = 10, D2 = 7, D3 = 6, D4 = 2, g = 6%, r = 12%

According to Gordon's Growth Formula, P3 = D4/(r - g) = 2/(0.12 - 0.06) = $33.33

Hence, Price of stock now = D1/(1+r) + D2/(1+r)² + D3/(1+r)³ + P3/(1+r)³ = 10/(1+0.12) + 7/(1+0.12)² + 6/(1+0.12)³ + 33.33/(1+0.12)³ = $42.50

(3) Given, D0 = $1.30, g1 = 23%, r = 11% and g2 = 6%

D1 = D0(1+g1) = 1.30(1+0.23) = $1.599

D2 = D1(1+g1) = 1.599(1+0.23) = $1.967

D3 = D2(1+g1) = 1.967(1+0.23) = $2.419

D4 = D3(1+g2) = 2.419(1+0.06) = $2.564

According to Gordon's Growth Formula, P3 = D4/(r - g) = 2.564/(0.11 - 0.06) = $51.28

Hence, Price of stock now = D1/(1+r) + D2/(1+r)² + D3/(1+r)³ + P3/(1+r)³ = 1.599/(1+0.11) + 1.967/(1+0.11)² + 2.419/(1+0.11)³ + 51.28/(1+0.11)³ = $42.30