Estimate the implied growth of high multiple equities

Implied Growth Rate.R

function (lgr, pe.market, pe.stock, years = 10, 
                                    irr = lgr) {
    # Args:
    #   lgr: the "low growth rate", or the expected earnings growth of the
    #     market at large
    #   pe.low: the market price / earnings ratio for equities
    #   pe.high: the p/e ratio of the high multiple equity
    #   irr: the investor's targeted IRR - most likely this should == lgr
    #   years: the number of years you want to look out
    # Returns: the implied earnings growth of the high multiple equity
    
    years <- 1:years
    market.earnings <- 1 / pe.market
    stock.earnings <- 1 / pe.stock    


    # given a growth rate for the "high growth" equity, and a sequence
    # of years, this function calcuates the discounted difference in
    # revenue between the high-growth equity and the low-growth equity
    forgone.earnings <- function (gr) {
        
        sum(( (stock.earnings * (1 + gr)^years) - (market.earnings * (1 + lgr)^years) ) / (1 + irr)^years)
        
    }
    
    # this finds the value of the growth rate at which the 
    # "forgone.earnings" of the high-growth stock is 0
    uniroot(forgone.earnings, c(-1, 10))$root
    
}


# FB
Implied.Growth.Rate(0.05, 15, 171) #=> ~ 0.50

# Amazon
Implied.Growth.Rate(0.05, 15, 312) #=> 0.61

# LinkedIn
Implied.Growth.Rate(0.05, 15, 1040) #=> 0.86