Question

A stock is expected to pay a dividend of $10 in one year. Its future annual dividends are expected to grow by 20% pa. The next dividend of $10 will be in one year, and the year after that the dividend will be $12 (=10*(1+0.2)^1), and a year later $14.4 (=10*(1+0.2)^2) and so on forever. Its required total return is 50% pa. The total required return and growth rate of dividends are given as effective annual rates. Calculate the payback period of buying the stock and holding onto it forever, assuming that the dividends are received as at each time, not smoothly over each year. Note that you will have to find the price of the stock first.

Answer 1

Price of Stock is nothing but PV of CFs from it.

Particulars	Amount
D1	$           10.00
Growth rate	20%
Ke	50%

Price = D1 / [ Ke - g ]
= $ 10 / [ 50 % - 20 % ]
= $ 10 / [ 30 % ]
= $ 33.33

Where
D1 = Expected Div after 1 Year
P0 = Price Today
Ke = Required Ret
g = Growth Rate

Payback period:

Payback period is the period in which initial investment is recovered.

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
If Actual PBP > Expected PBP - Project will be rejected
Actual PBP </= Expected PBP - Project will be accepted

It ignores cash flows after Pay back period & Time Value of money

Only Few CFs ( Div are considered as Payback period considers only CFs upto Pay back period.)

Year	Opening Balance	Cash Flow	Closing Balance
1	$                  33.33	$            10.00	$               23.33
2	$                  23.33	$            12.00	$               11.33
3	$                  11.33	$            14.40	$                -3.07
4	$                  -3.07	$            17.28	$              -20.35
5	$                -20.35	$            20.74	$              -41.09
6	$                -41.09	$            24.88	$              -65.97

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 2 Years + [ $ 11.33 / $ 14.4 ]
= 2 Years + 0.79 Years
= 2.79 Years

Payback Period is 2.79 Years

PBP Refer Payback Period