Question

13) The chairman of Ronco Industries told a meeting of financial analysts that he expects the firm’s earnings and dividends to double over the next six years. The current dividend is $4.00 per share.

a. Estimate the annual dividend growth rate over the 6-year period.

b. Forecast the dividends per share for each of the next six years at the growth rate determined in Part A.

c. Determine the value of the common stock, assuming dividends are expected to grow at this rate for the foreseeable future, if your required rate of return is 18 percent.

d. Determine the current value of a share of this common stock to an investor (with an 18 percent required rate of return) who plans to hold it for 6 years, assuming that dividends grow at the rate determined in Part A for the next six years and then at six percent thereafter.

Answer 1

a	Growth rate	12.25%
b	Year	Dividend
	1	4.49
	2	5.04
	3	5.66
	4	6.35
	5	7.13
	6	8.00

c: Horizon value = P6=D7/(k-g) = 8*112.25%/(18%-12.25%)

= 156.17

Current share price = D1/(1+k)+ D2/(1+k)^2 +... (Dn+Pn) /(1+k)^n

= 4.49/1.18^1+5.04/1.18^2+5.66/1.18^3+6.35/1.18^4+7.13/1.18^5+(8+156.17)/1.18^6

= 78.08

d:

Horizon value = P6=D7/(k-g) = 8*106%/(18%-6%)

= 70.67

Current share price = D1/(1+k)+ D2/(1+k)^2 +... (Dn+Pn) /(1+k)^n

= 4.49/1.18^1+5.04/1.18^2+5.66/1.18^3+6.35/1.18^4+7.13/1.18^5+(8+70.67)/1.18^6

=$46.40

Workings