# Confused about discounting final CF on Elan Equity Question

FCF Valuation PQ 15:

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

FCFE will grow at a rate of 40% for the next 3 years, during which 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%.

What is the intrinsic value of the company’s stock today?

I get that you take each year’s FCFE, multiply it by 1+g and then divide this by 1+r^T for each CF, what I don’t get is how elan have discounted the final CF. They show the calcutions in a table rather than an equation, and they also use discount factors rather than the equation I just described. I got the terminal value and the final CF value correct (combined they make a CF of 126.77), I just don’t know how they have discounted that to a PV of 54.52.

Oh and FYI - the answer is apparently \$58.02

1.2 * 1.2 * 1.2 * 1.16 * 1.16 = 2.32 = investors’ total required return on equity in Y1 * Y2 * … * Y5.

126.77 at Y5 / 2.32 = 54.52 at Y0 (now.)