Question

HighTech Company is expected to retain all of its earnings for the next two years but start to pay dividends 3 years from today. The first dividend is expected to be $3. Assume that the dividends will grow rapidly at a rate of 10% per year during years 4 to 7. For each year after that it grows at a constant rate of 5%. Assume a discount rate of 12%.

1. What is HighTech’s stock price?
2. Assume that instead of growing at a 5% constant rate starting from year 8, HighTech Company expects, in year 8, to earn an EPS of $8 and reinvest $4 per share to develop new technology. The new technology will generate a 15% return permanently.

What is the constant growth starting from year 8?

What is the stock price today given this constant growth rate?

Answer 1

Retention ratio = 100%; b = 1

D3 = 3

Short-term high growth rate, gS = 10% and gL = 5% (long-term)

a) Price

Using H-DDM formula,

V3 = [ D3 * (1+gL) / (r-gL) ] + [ D3 * H * (gS-gL) / (r-gL)]

where the values given are as:

• D3 = $3
• gL = 5%
• gS = 10%
• H = 4/2 = 2 years
• r = 12%

Substituting values, P3 = [ 3 * ( 1+0.05)/(0.12 - 0.05) ] + [ 3 * 2 * (0.10 - 0.05)/(0.12 - 0.05)]

• P3 = [ 3 *(1.05/0.07) ] + [ 3 * 2 * (0.05/0.07) ]
• P3 = [ 3 * 15 ] + [ 3 * 2 * 0.7143 ] = 45 + 4.29 = 49.29
• Po = 49.29/ (1+0.12)^3 = 35.08

Price = $35.08

b) Given:

Retention ratio,b = $4/$8 = 0.50; ROE = 15%; g = b * ROE = 0.50 * 0.15 = 0.075 (constant growth rate from year 8)

Price:

D3 = 3

Short-term high growth rate, gS = 10% and gL = 7.5% (long-term)

a) Price

Using H-DDM formula,

V3 = [ D3 * (1+gL) / (r-gL) ] + [ D3 * H * (gS-gL) / (r-gL)]

where the values given are as:

• D3 = $3
• gL = 7.5%
• gS = 10%
• H = 4/2 = 2 years
• r = 12%

Substituting values, P3 = [ 3 *( 1+0.075)/(0.12 - 0.075) ] + [ 3 * 2 * (0.10 - 0.075)/(0.12 - 0.075)]

• P3 = [ 3 * (1.075/0.045) ] + [ 3 * 2 * (0.025/0.045) ]
• P3 = [3 * 23.89 ] + 3.33 = 71.67 + 3.33 = 75
• Po = 75/ (1+0.12)^3 = 53.38

growth rate = 7.5%

Price = $53.38