Part I : Checking the Data E QU ITY VAL U ATION IN R Cli Ang - PowerPoint PPT Presentation

Part I : Checking the Data E QU ITY VAL U ATION IN R Cli � Ang Senior Vice President , Compass Le x econ

Importance of Checking Projections Garbage - In → Garbage - O u t Yo u ha v e to get comfortable w ith all elements of the projections Most elements are modeled as a percentage of re v en u es or percentage of change in re v en u es EQUITY VALUATION IN R

Vis u all y Inspecting the Data # Create two vectors: one for historical (hist) revenues # and another for projected (proj) revenues hist <- c(28.4, 32.2, 36.8, 39.8, 44.3, 51.1, 60.4, 58.4, 62.5, 69.9, rep(0, 5)) proj <- c(rep(0,10), 73.7, 77.8, 86.8, 93.6, 85.3) rev_all <- rbind(hist, proj) colnames(rev_all) <- seq(2008, 2022, 1) # Create bar plot of revenues data barplot(rev_all, col = c("red", "blue"), main = "Historical vs. Projected Revenues") legend("topleft", legend = c("Historical", "Projected"), fill = c("red", "blue")) EQUITY VALUATION IN R

Bar Plot EQUITY VALUATION IN R

Using Trend Anal y sis # Create one vector of historical and projected revenues rev <- data.frame(c(28.4, 32.2, 36.8, 39.8, 44.3, 51.1, 60.4, 58.4, 62.5, 69.9, 73.7, 77.8, 86.8, 93.6, 85.3)) rownames(rev) <- seq(2008, 2022, 1) names(rev) <- "rev" # Add trend and shift variables rev$trend <- seq(1, 15, 1) rev$shift <- c(rep(0, 10), rep(1, 5)) EQUITY VALUATION IN R

reg <- lm(rev ~ trend + shift, data = rev) summary(reg) # Call: # lm(formula = rev ~ trend + shift, data = rev) # # Residuals: # Min 1Q Median 3Q Max # -7.2232 -1.5508 -0.2843 0.7700 5.6184 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) 23.4011 2.2066 10.61 1.89e-07 *** # trend 4.5416 0.3511 12.94 2.09e-08 *** # shift 0.9978 3.2179 0.31 0.762 # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # # Residual standard error: 3.377 on 12 degrees of freedom # Multiple R-squared: 0.9777, Adjusted R-squared: 0.974 # F-statistic: 263.3 on 2 and 12 DF, p-value: 1.222e-10 EQUITY VALUATION IN R

Let ' s practice ! E QU ITY VAL U ATION IN R

Part I : Checking the Perpet u it y Gro w th Rate E QU ITY VAL U ATION IN R Cli � Ang Senior Vice President , Compass Le x econ

Checking the Perpet u it y Gro w th Rate Perpet u it y Gro w th Rate ( PGR ) is a s u stainable gro w th rate It cannot be greater than the o v erall gro w th rate of the econom y It is a gro w th rate that is � nanced b y the operations of the � rm EQUITY VALUATION IN R

Determinants of the Perpet u it y Gro w th Rate The PGR is bo u nded b y the follo w ing relationship : PGR = Rein v estment Rate * Ret u rn on Eq u it y, w here Rein v estment Rate = ( CapE x + Incr . in WC - D & A ) / A � er - Ta x Income Ret u rn on Eq u it y eq u als the Cost of Eq u it y in stead y- state EQUITY VALUATION IN R

E x ample S u ppose y o u ha v e a � rm w ith a rein v estment rate of 20% and an ROE of 10%. Can the � rm s u stain an ass u med PGR of 4%? reinvestment <- 0.20 roe <- 0.10 reinvestment * roe 0.02 pgr <- 0.04 pgr / roe 0.4 EQUITY VALUATION IN R

Let ' s practice ! E QU ITY VAL U ATION IN R

Part II : Di v idend Disco u nt Model E QU ITY VAL U ATION IN R Cli � Ang Senior Vice President , Compass Le x econ

Single - Stage Di v idend Disco u nt Model There are t w o t y pes of stocks � rms iss u e : preferred stocks and common stocks Man y preferred and common stocks pa y di v idends Di v idends are t y picall y the " cash � o w s " that in v estors recei v e from holding stocks We can then disco u nt this stream of di v idends to v al u e the stock EQUITY VALUATION IN R

Disco u nting Di v idends Constant Di v idend Stream Di v idend w ith Constant Gro w th V = div / k V = div /( k − g ) t +1 t +1 = $50 and k = 6.25%. = $50 , k = 6.25%, and g = S u ppose div S u ppose div t +1 t +1 2%. div <- 50 k <- 0.0625 div <- 50 div / k k <- 0.0625 g <- 0.02 div / (k - g) 800 1176.471 EQUITY VALUATION IN R

T w o - Stage DDM - No Di v idends D u ring First Stage Yo u can still u se a DDM e v en for � rms that do not c u rrentl y pa y di v idends Firms w ith high gro w th ma y not pa y di v idends no w, b u t one can reasonabl y e x pect the � rm ' s gro w th to slo w do w n and begin pa y ing di v idends at some point in the f u t u re EQUITY VALUATION IN R

What to do then ? Use a 2- stage Model 1 st stage : No di v idends for T y ears 2 nd stage : E x pect � rm to pa y di v idends beginning Year T + 1 Mathematicall y: V = 0 + ( div /( k − g )) ∗ (1/(1 + k ) ) T T +1 EQUITY VALUATION IN R

E x ample Year 1 2 3 4 5 6 7 ... Di v idends 0 0 0 0 0 $50 $51 ... div6 <- 50 g <- 0.02 k <- 0.0625 0 + (div6 / (k - g)) * (1 / (1 + k)^6) 817.7253 EQUITY VALUATION IN R

Let ' s practice ! E QU ITY VAL U ATION IN R