Ln(X) = T * ln [(1 + stock growth rate)/(1+ market growth rate)]
When you fine ‘X’, you multiply that times the given market multiple, and that will give you your P/E ratio for that time.
You are using a log (ln) because you are trying to find the inverse of an exponential growth rate.
Recall that for the first question, T is 10 and the growth rate of Lauren is .18 and the growth rate of the S&P is .08, and there are no dividends. So our equation will be:
ln (x) = 10 ln (1.18/1.08)
ln (x) = 10 ln (1.09259)
ln (x) = 10 (0.08855)
ln (x) = 0.8855
To get the ln(X), you can use the exponential
Function in excel. This is ‘exp’
x = 2.424
To find the P/E ratio, multiply 2.424 times the market multiple of 18. This 43.6
Repeat this process for the T of 5 years to get the answer to 6b.
ln (x) = .8855
To get the inverse of the ln(x), use the 'exp' function in excel
0.88552.424196
P/E43.63553