Calculating Equity Value

Equity Valuation in R

Cliff Ang

Senior Vice President, Compass Lexecon

Present Value

The firm's equity value is equal to:

$$ V = \sum_{t=1}^T \frac{FCFE_t}{(1 + k_e)^t} + \frac{TV_T}{(1 + k_e)^T} $$

The two terms on the RHS of the equation are as follows:

Present Value of the FCFE during the projection period
Present Value of the Terminal Value

PV of FCFE in R

Suppose the FCFE for each of the first five years is $100 million. Assuming a cost of equity of 15%, the present value of each cash flow is:

k_e <- 0.15
cf <- rep(100, 5)
cf <- data.frame(cf)

cf$period <- seq(1, 5, 1)

cf$pv_factor <- 1 / (1 + k_e)^cf$period
cf$pv <- cf$cf * cf$pv_factor
cf

   cf period pv_factor       pv
1 100      1 0.8695652 86.95652
2 100      2 0.7561437 75.61437
3 100      3 0.6575162 65.75162
4 100      4 0.5717532 57.17532
5 100      5 0.4971767 49.71767

pv_fcfe <- sum(cf$pv)
pv_fcfe

335.2155

PV of Terminal Value in R

tv_yr5 <- 858.333

k_e <- 0.15

pv_tv <- tv_yr5 / (1 + k_e)^5
pv_tv

426.7432

Equity Value and Equity Value Per Share

# Combine PV of FCFE and PV of Terminal Value
equity_value <- pv_fcfe + pv_tv
equity_value

761.9587

# To Convert to a Per Share Number
# Assume 15 million shares outstanding
shout <- 15
equity_per_share <- equity_value / shout
equity_per_share

50.79725

Let's practice!

Equity Valuation in R