In: Finance
Calculate the present value of a stock if this stock is expected to pay $1.75 dividend in the next six years and then in year 7 and thereafter it pays $2 constant dividend forever. The interest rate is 8%. Please provide excel formula and step-by-step explanations on your calculation to get your final answer.
Step 1: The present value of the first six years of dividends
PV = PV(rate, nper, pmt, [fv], [type])
rate = 8%
nper = 6
pmt = 1.75
PV = PV(8%,6,1.75)
Ignore [fv] and [type] they are optional
PV = $8.090039412
Step 2: The present value of the constant dividend from year 7 and beyond
PV = Div7/r
This formula gives the present value as of year 6. So...
PV6 = Div7/r
PV6 = 2/0.08
PV6 = $25
Now, we need to discount this to get the present value as of today
PV = PV6/(1 + r)^6
PV = 25/(1 + 0.08)^6
PV = $15.7542406721
Step 3: Add the results from step 1 and step 2 to get the final answer
The present value of the stock = 8.090039412 + 15.7542406721
The present value of the stock = $23.8442800841