### CFA Practice Question

Consider the following annual growth forecasts for a common stock:

Growth in years 1-2 = 50%
Growth in years 3-4 = 25%
Growth after year 4 = 10%

Assuming that the last dividend was \$0.45 per share, and the required rate of return is 20% per year, what is the value of this common stock?
A. \$13.81
B. \$11.15
C. \$8.36
Explanation: To determine the value of a common stock experiencing temporary supernormal growth, use the following equation:

{V = {[d0 * (1 + gs)^1] / k} + {[d1 * (1 + gs)^2} + ... {dn * (1 + gs)^n} + {[dn * (1 + gs)^n * (1 + gn] / (k - g)}/ (1 + k)^n}}

Where: V = the value of common stock at t0, d0 = the dividend at t0, d1 = the dividend at t1, dn = the dividend at tn, gs = the supernormal rate of growth, gn = the normal rate of growth, n = the time period "n", and k = the required rate of return.

In this example, there is a transitional growth period of two years, during which the growth rate is expected to grow at 25% annually. This period will follow the two-year supernormal growth period, and would be denoted as "g subset t" if we were to reproduce the equation illustrated above. The calculation of the value of this common stock is illustrated as follows:

{V = {[\$0.45 * (1.50)^1] / (1.20)} + {[\$0.45 * (1.50)^2] / (1.20)^2} + {[\$0.45 * (1.50)^2 * (1.25)^1] / (1.20)^3} + {[\$0.45 * (1.50)^2 * (1.25)^2] / (1.20)^4} + {{[\$0.45 * (1.50)^2 * (1.25)^2 * (1.10)^1]/ (0.20 - 0.10)}/ (1.20)^4}

which can be deduced to the following: {V = [\$0.5625 + \$0.703125 + \$0.732422 + \$0.762939 + \$8.392334] = \$11.15}

User Comment
smiley25 1.5 mins good luck.
ontrack i had that-good luck. i guessed correctly!!!
AkashKB The force is strong with ontrack
takor ...and may that strong force be with us all on the exam day!!!
Mlgraber Thank you
mpapwa22 I know exctly wht to do with this question but i took about 3 minutes. Its rough. what to do......go the ontrack way...
shiva5555 Its not that hard. Just do the main stock price. It comes out to like 8.50 from there its obvious that B is the right answer.
fenix55555 Someone know how to compute this with BAII?
MaresaJaden Calculate the cash flows and plug them into the calculator...
birdperson as MaresaJaden said, using the CF button is the best way to solve these in my opinion.
tzanchan That is why you need to budget your time effectively. There are some questions that can be answered in 30 seconds.
Nadjones How are the dividends growing...
CF1= (.45)*(1.5) or .675
CF2= (.675)*(1.5) or 1.0125
CF3= (1..125)*(1.2) or 1.2656
CF4= (1.2656)*(1.2) or 1.582
with a required rate of 20, your NPV = 2.76

From there the last divided grows @ 10% (or 1.582*1.1 = 1.74) and then you a constant constant growth formula. [{1.74/(.2-.1)} divided by (1.2^4)] = 8.39