UNIT3 4 Following are projections for required rates of retu

UNIT3 4. Following are projections for required rates of return: SECURITY Constant-Growth Stock Low-growth Common Stock High-growth Common Stock 10% 12% 1796 For the common stock Constant-growth-growth rate of 5% Do-$2.00 Low-growth-D $4.00, growth at 6% per year for 3 years, followed by a rate of 4% forever High-growth-Do-$1.00, growth at 30% for next 4 years, followed by a rate of 7% forever a. What will be the value per share for the constant growth stock? b. What will be the value per share for the low-growth stock? c. What will be the value per share for the high-growth stock? 5. Scott Manufacturing is a firm in the machine-tool-component industry. The firm\'s most recent common-stock dividend was $2.10 per share. Due to its stable sales and earnings, the firms management feels that the dividends will remain at the current level for the foreseeable future

Solution

a)

Value per share for constant growth stock = D1/ required rate of return - growth rate

Value per share for constant growth stock = [ 2 ( 1 + 0.05) / 0.1 - 0.05]

Value per share for constant growth stock = [ 2.1 / 0.05 ]

Value per share for constant growth stock = $42

b)

Year 1 dividend = 4 * 1.06 = 4.24

Yaer 2 dividend = 4.24 * 1.06 = 4.4944

year 3 dividend = 4.4944 * 1.06 = 4.764064

year 4 dividend = 4.764064 * 1.04 = 4.954627

Present value at year 3 = D1 / required rate - growth rate

Present value at year 3 = 4.954627 / 0.12 - 0.04

Present value at year 3 = 61.932832

Present value of 61.932832 = 61.932832 / ( 1 + 0.12)³

Present value = 44.082567

Present value of year 3 dividend = 4.764064 / ( 1 + 0.12)³ = 3.390967

Present value of year 2 dividend = 4.4944/ ( 1 + 0.12)² = 3.582908

Present value of year 1 dividend = 4.24 / ( 1 + 0.12) = 3.785714

Value per share for low growth stock = 3.785714 + 3.582908 + 3.390967 + 44.082567

Value per share for low growth stock = $54.842

c)

Year 1 dividend = 1 * 1.3 = 1.3

Yaer 2 dividend = 1.3 * 1.3 = 1.69

year 3 dividend = 1.69 * 1.3 = 2.197

year 4 dividend = 2.197 * 1.3 = 2.8561

Year 5 dividend = 2.8561 * 1.07 = 3.056027

Present value at year 4 = D1 / required rate - growth rate

Present value at year 4 = 3.056027 / 0.17 - 0.07

Present value at year 4 = 30.56027

Present value of 30.56027 = 30.56027 / ( 1 + 0.17)⁴

Present value = 16.30849

Present value of year 4 dividend = 2.8561 / ( 1 + 0.17)⁴ = 1.524158

Present value of year 3 dividend = 2.197 / ( 1 + 0.17)³ = 1.371742

Present value of year 2 dividend = 1.69 / ( 1 + 0.17)² = 1.234568

Present value of year 1 dividend = 1.3 / ( 1 + 0.17) = 1.1111

Value per share for low growth stock = 1.1111 + 1.234568 + 1.371742 + 1.524158 + 16.30849

Value per share for high growth stock = $21.55