Use the information for the question(s)below.
Iota Industries is an all-equity firm with 50 million shares outstanding.Iota has $200 million in cash and expects future free cash flows of $75 million per year.Management plans to use the cash to expand the firm's operations,which in turn will increase future free cash flows by 12%.Iota's cost of capital is 10% and assume that capital markets are perfect.
-The value of Iota if they use the $200 million to expand is closest to:
A)$825 million.
B)$688 million.
C)$840 million.
D)$950 million.

Question

Quizplus · Accepted Answer

To calculate the value of Iota after expansion, we need to use the discounted cash flow (DCF) method. 
First, we need to calculate the present value of free cash flows from year 1 to infinite. 
PV of FCFs = (FCF1 / (1+r)^1) + (FCF2 / (1+r)^2) + ...
where FCF1 = $75 million, r = 10%, and growth rate = 12%
FCF2 = $75 million * 1.12 = $84 million
FCF3 = $84 million * 1.12 = $94.08 million

and so on, we can use perpetuity formula to calculate growth rate of infinite time period.

PV of FCFs = ($75 million / (1+10%)^1) + ($84 million / (1+10%)^2) + ($94.08 million / (1+10%)^3)+...+ ($94.08 million(1 + 5%)) / (10% - 5%)(1+10%)^3

PV of FCFs = $818.18 million

Then, we need to add the cash balance to the PV of FCFs.
Value of Iota = PV of FCFs + cash balance
Value of Iota = $818.18 million + $200 million = $1,018.18 million
The closest option is C) $840 million.

Use the Information for the Question(s)below