# Elan Practice Q: Equity- Free Cash Flow Valuation

Hey guys- stuck on problem #15 from Elan’s Equity- FCF Valuation practice questions. Any help would be appreciated:

Shamrock Ltd’s most recent FCFE per share amounted to \$0.6. An analyst has the following expectations regarding the company’s growth in FCFE:

• FCFE will grow at a rate of 40% for the next three years, during which the investors’ required rate of return will be 20%.

• During the following two years, FCFE growth will decline by 15% per year towards its stable long-term growth rate. During this time, investors’ required rate of return will be 16%

• From year 6 onwards, FCFE will grow at a stable long-term growth rate of 10%, during which investors’ required rate of return will be 12%.

The intrinsic value of the company’s stock today is closest to:

A. \$59

B. \$58

C \$56

Elan shows the answer to this as B- \$58. I’m stuck here. I know I’m supposed to start by calculating FCFE up through to the stable growth period, then get the terminal value. But where do I go from there? Elan’s explanation is only a table with discount factors and present values that come to a sum of \$58.02. Any helpful would be greatly appreciated.

First, forecast the future free cashflows

FCFE @ t=1, 0.6*1.4--------------------------------------------0.84

FCFE @ t=2, 0.6*(1.4^2)--------------------------------------1.176

FCFE @ t=3, 0.6*(1.4^3)--------------------------------------1.6464

FCFE @ t=4, 0.6*(1.4^3)*(1.25)-----------------------------2.058

FCFE @ t=5, 0.6*(1.4^3)*(1.25)*(1.1)---------------------2.2638

FCFE @ t=6, 0.6*(1.4^3)*(1.25)*(1.1^2)------------------2.49018

Secondly, find the terminal value

V @ t=5, 2.49018/(12%-10%)--------------------------------124.509

Thirdly, discount the forecasted freecashflows and terminal value (this is the tricky part because discount rates are different for different stages)

K= 20% (for the first 3 years)

K=16% (for the next 2 years)

Ke= 12% (beyond 5 years)

FCFE @ t=1, --------------0.84--------------------------------------------------------------0.84/1.2=0.7

FCFE @ t=2, --------------1.176------------------------------------------------------------1.176/1.2^2=0.82

FCFE @ t=3, --------------1.6464-----------------------------------------------------------1.6464/1.2^3=0.95

FCFE @ t=4, --------------2.058------------------------------------------------------------2.058/[(1.16)*(1.2^3)]=1.03

FCFE @ t=5, -------------2.2638+124.509(Terminal value)= 126.7728-----------126.7728/[(1.16^2)*(1.2^3)] = 54.52

The key to solve this question is to recognize the fact that discount rates are different for different periods.

Usually, we are given the problems in which discount rate is a single rate regardless of the time period. But here they are not same. e.g the FCFE at time=4 will first be discounted at 16% for one year. By discounting it for one year, this cashflow has moved in time and is now 3 years away from being realized. Now, you will discount it for 3 years using your required rate for the first 3 years.

I hope this question does not pop up in paper. Same for me! That’s a doozy- thanks for the help