# Finance

posted by .

A common stock is just paid an annual dividend of \$2 yesterday. The dividend is expeccted to grow at 8% annually for the next 3 years, after which is will grow at 4% in perpetuity. The appropriate discount rate is 12%. What is the priceof the stock?

What I know:
Differential growth
DIV=2
g1=.08
g2=.04
r=.12
yr.end 5=Div4(1+g2)=2.52(1.04)=2.6208
p4=DIV5/r-g2=2.6208/.12-.04=32.76 FV
p4/(1+r)^4=32.76/1.12^4=20.82
Present Value of all Div as of yr end 0 is 20.82 + 32.76 =

• Finance -

Perhaps my reply to your previous question would help. On the other hand perhaps I am way off base not being a financial type at all.
by the way, my g for geometric series is starting value.
my r is ratio of value at year (n+1) to value at year n.
in that case sum of infinite series is g/(1-r)

by the way, for just n terms
sum = g + g r + g r^2 +...+ g r^(n-1)
= g (1-r^n)/(1-r)

• Finance -

let's see what the dividends are worth after 3 years (n = 4 because we start at the beginning of year one and the end of the other years)
V3 = 2 + 2(1.08/1.12) + 2(1.08/1.12)^2...
g = 2
r = 1.08/1.12 = .9463
so
sum after three years = 2(1-.9463^3)/(1-.9463) = 2(.1526/.0537) = 5.683
now we go on forever at 4%
g = 5.683
r = 1.04/1.12 = .9286
sum to infinity = 5.683/(1-.9286) = 79.56

• Finance -

wait a minute, we have to subtract the first three years at 4% off the infinite 4% years because we did those years separately with 8%
sum at 4% after three = 2(1-.9286^3)/(1-.9286)
= 2*(.1993/.0714) = 5.583
so it is
79.56 - 5.58 = 73.98

## Similar Questions

1. ### Finance

Faulkner Corporation expects to pay an end-of-year dividend, D1, of \$1.50 per share. For the next two years the dividend is expected to grow by 25 percent per year, after which time the dividend is expected to grow at a constant rate …
2. ### investing

(Dividend discount Model) Assume RHM is expected to pay a total cash dividend of \$56.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market …
3. ### Finance

This morning you purchased a stock that will pay an annual dividend of 1.90 per share next year. You require a 12 percent rate of return and annual dividend increases as 3.5 percent annually. What will be your capital gain be on this …
4. ### Finance

Colgate-Palmolive Company has just paid an annual dividend of \$0.85. Analysts are predicting a 10% per year growth rate in earnings over the next five years. After that, Colgate’s earnings are expected to grow at the current industry …
5. ### Finance

The Isberg Company just paid a dividend of \$0.75 per share, and that dividend is expected to grow at a constant rate of 5.50% per year in the future. The company's beta is 1.25, the market risk premium is 5.00%, and the risk-free rate …
6. ### Finance

MMK Cos. normally pays an annual dividend. The last such dividend paid was \$2.3, all future dividends are expect to grow at a rate of 6 percent per year, and the firm faces a required rate of return on equity of 18 percent. If the …
7. ### Finance

Teddy Company paid a \$3.50 dividend this year (D0 = \$3.50). Next year the company expects to pay a \$4.00 dividend (D1 = \$4.00). The stock's dividend is expected to grow at a rate of 15 percent a year until three years from now (t = …
8. ### finance

This morning, you purchased a stock that will pay an annual dividend of \$1.90 per share next year. You require a 12 percent rate of return and the annual dividend increases at 3.5 percent annually. What will your capital gain be on …
9. ### Finance

This morning, you purchased a stock that will pay an annual dividend of \$1.90 per share next year. You require a 12 percent rate of return and the annual dividend increases at 3.5 percent annually. What will your capital gain be on …
10. ### finance

Stock A is expected to provide a dividend of \$10 per share forever. Stock B is expected to pay a dividend of \$5 next year, after which dividends are expected to grow forever at 5.4%. finally, stock C is expected to pay a dividend of …

More Similar Questions