Question

5. (a) Plantfood paid an annual dividend of $3 on its common stock and promises that the dividend will grow by 3% per year. If the stock’s market price is $30, what is required rate of return for this stock?
(b) Datasoft is currently paying dividends of $0.70 a share. These dividends are expected to grow at a rate of 20% for the next two years and at a constant growth rate of 3.5% thereafter. What would be the current price of Datasoft shares given a required return of 15%?
(c) Compare and contrast the risk and return for debt and equity securities from the perspective of both lenders/investors and issuers.
(d) Formally derive and discuss the dividend discount model used for the valuation of common stocks.

Answer 1

Q5) a) Required rate of return or equity= dividend paid (1+growth rate) / Price + growth rate

= 3 (1+0.03) / 30 + 0.03

= 3 (1.03) / 30 + 0.03

= 3.09/30 + 0.03

= 0.103 + 0.03

= 0.133 or 13.3%

b) Dividend in year 1 (D1) = 0.70 (1+ 0.20)

= 0.70 (1.20)

= 0.84

Dividend in year 2 (D2) = D1 (1+growth rate)

= 0.84 (1+0.20)

= 0.84 (1.20)

= 1.008

D3 = D2 (1+ constant growth rate)

= 1.008 (1+0.035)

= 1.008 (1.035)

= 1.04328

Price= D1/(1+required rate)^1 + D2/(1+required rate)^2 +( D3/required return - growth rate)/(1+required rate)^2

= 0.84/(1+0.15)^1 + 1.008/(1+0.15)^2 + (1.04328/0.15 -0.035) / (1+0.15)^2

= 0.84/1.15 + 1.008/(1.15)^2 + (1.04328/0.115)/(1.15)^2

= 0.73 + 1.008/1.3225 + 9.072 / 1.3225

= 0.73 + 0.76 + 6.86

= $8.35

C) Fom investors perspective

Debt :- Debt is a less risky asset and provides low returns. The investors get a fixed payment on debt in the form of interest.

Equity:- It is a high risk asset which providws high returns. The investors get dividend , but it depends on the company's policy.

From Issuers perspective.

Debt:- It is more risky from issuers perspective because it require a payment of fixed interest rate and also requires collateral when needed to be issued.

Equity:- It is less risky as compared to debt and doesn't involve any fixed payment. The return earned on it is higher than the debt because of discretion in payment of dividends by the company. The issuance of it does not require any collateral.

D) Geometric mean series:-

S = A + AR + AR^2 + AR^3 + .... + AR ^n+1. ...(equation 1)

Now, If R is smaller than 1 and N approaches to infinity , then R^n approaches to 0 i.e.,

S(infinity) = A + AR + AR^2 + .... + AR^n+1 + .... + AR^infinity,

Then , S(infinity) = A/ 1 - R .....(equation 2)

Dividend Discount Model can be defined as:

P0= D1/(1+k)^1 + D2/(1+k)^2 + D3/(1+k)^3 + ... equation(3)

Where P0 = present value of stock price per share
Dt = dividend per share in period t (t =1, 2,...,n)

K= required rate of return

G= growth rate
If dividends grow at a constant rate, say g, then,
D2 = D1(1 + g), D3= D2(1 + g) = D1(1 + g)^2, and so on.
Then, Equation (3) can be rewritten as:
P0= D1/(1+k) + D1(1+g)/(1+k)^2 + D1(1+g)^2 / (1+k)^3 + .... or

P0= D1/(1+k) + D1/(1+k) × (1+g)/(1+k) + D1/(1+k) × (1+g)^2 / (1+k)^2 + .... equation (4)

Comparing Equation (4) with Equation (1) i.e.,
P0= S, D1/1+k = A , and 1+g/1+k = R as in the equation (1)

Therefore, if 1+g/1+k < 1 or if k > g we can use equation (2) , to find out P0

i.e.,
P0= D1/(1+k)/1-[(1+g) (1+k)]

= D1/(1+k) ÷  [1+k - (1+g)]/1+k)

= D1/(1+k) ÷ (K - g)/ (1+k)

= D1/(k- g)

= D0(1+g)/(k-g)

This is how DDM model is derived.

Dividend discount model is used to derive the Price of of the stock. It is based on certain assumptions. The most important assumption are as follows :-

1) The company should be paying dividend forever

2) The growth rate should be constant.

3) Rate of return should be more than growth rate

Advantage of this model

1) It is easy to use and simple to understand.

Disadvantage:-

1) The biggest disadvantage is its assumptions that the dividend grows at a constant rate dies not work in reality.

2) If the growth rate is more than cost of capital then the price would be negative .