Question

I have another question on finance : stock evaluation for answer verification as follows:

Compute the current value of a share of common stock of a company whose most recent dividen was $2.50 and is expected to grow at 3% for the next 5 years; after which the dividend growth rate will increase to 6% per year indefinetely. Assume 10% required rate of return.

My answer:

Does this question imply us to use the variable stock valuation formula. If yes, is my answer below correct?

P0 = SUM [D₀ x (1+g₁)^t/(1+r)^t] + [ (1/(1+r)ⁿ x (D_n+1)/(r-g₂))]

Where

D0 = $2.50

g1 = 3% = 0.03

g2 = 6% = 0.06

R = 10% = 0.10

Year	D0	(1+g1)t	(1+r)t	D0(1+g1)t = Dt	D0(1+g1)t /1+r)t
1	2.5	1.03	1.1	2.58	2.35
2	2.5	1.06	1.21	2.65	2.19
3	2.5	1.09	1.33	2.73	2.05
4	2.5	1.13	1.46	2.83	1.94
5	2.5	1.16	1.61	2.90	1.80
SUM					10.33

First, find the present value of dividends during initial growth period

SUM [D₀ x (1+g₁)^t/(1+r)^t]

= $10.33

Next, find the present value of price of stock at the end of initial growth period

[ (1/(1+r)ⁿ x (D_n+1)/(r-g₂))]

where;

n = 5

D_n+1 = D₆ = D₅(1+g₂)^t=1 = 2.9 (1 + 0.06) = 3.07

(r-g₂) = 0.10 - 0.06 = 0.04

(1+r)ⁿ = (1+0.10) ⁵= (1.1)⁵ = 1.61

So ;

[ (1/(1+r)ⁿ x (D_n+1)/(r-g₂))] = [1/1.61] x [3.07/0.04]

= 0.62 x 76.75 = 47.58

So the current value of a share of common stock is as follows:

$10.33 + 47.58 = 57.92 (ANWER)

is this correct?

Also;

As a rational investor, what would you do if the expected rate of return of a stock is above its required rate of return? Explain

Should we sell the stock then knowing that the expected rate of return is already higher and with that money we can actually use it to invest in other stocks?

Answer 1

The method used is correct , however since your rounded off your initial calculations , the final answer differs slightly.

if expected return > required return for the stock, we will buy/hold the stock since the stock is an undervalued stock, which means its price is lower than 57.99 its intrinsic/fair value

Explanation for the 2nd question:

required return is the minimum return that the stock should provide for it to be a fairly-valued stock

if the expected return for the stock that we anticipate is greater than the required return , we consider that stock to be undervalued since it is providing value which is > than its fair value. For such a stock , the price will be lower than its fair price (price as per the risk and return of the stock) . We will hold the stock since we now know that it is undervalued and in the future we expect its price to rise to its actual/fair value/intrinsic value. We will sell the stock once that price increase has happened.