Question

Vinca Inc. has paid a dividend of $1.2 a share last year. Yesterday, the firm announced that the dividend will increase by 10 percent each year for the next three years, after which time the dividends will increase by 4 percent annually. The required return on this stock is 12 percent. What is the current value per share?

a. $16.31
b. $14.70
c. $20.76
d. $18.24

Answer 1

option (d) $18.24

Step-by-step explanation:

Data provided in the question:

Dividend paid last year = $1.2

Dividend growth rate for 3 years, g = 10%

After 3 years Dividend growth rate, g' = 4%

Required return, r = 12%

Now,

Present vale factor, PVF =
`(1)/((1+i)^n))`

Year Dividend PVF @12% Dividend × PVF

1 1.2(1+.10)= 1.32 0.89286 1.1786

2 1.32(1+.10)= 1.452 0.79719 1.1575

3 1.452(1+.10)= 1.5972 0.71178 1.1369

3(Terminal value) 20.7636 0.71178 14.7791

=====================================================

Current share price ∑(Dividend × PVF ) ≈ $18.24

Note:

Terminal value at year 3 =
`(D3(1+g'))/((r-g'))`

=
`(\$1.5972(1+0.04))/((0.12-0.04))`

= $20.7636

Hence,

The correct answer is option (d) $18.24