Question

The dividend for Should I, Inc., is currently $2.05 per share. It is expected to grow at 24 percent next year and then decline linearly to a perpetual rate of 6 percent beginning in four years. If you required a return of 13 percent on the stock, what is the most you would pay per share? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Price of a stock is the present value of all future cash flows receivable from the stock discounted at required rate of return

Future cash flows are expected dividend and expected share price at the end of the period after which constant growth will follow

Linear growth rate decline

= 24% in year 1

Year 2 = 24 - 24 / 4 = 18%

Year 3 = 18 – 24 / 4 = 12%

Year 4 and onwards = 12 – 24 / 4 = 6%

Expected dividend next year ( D1 )

= Current dividend x ( 1 + Growth )

= $2.05 x 1.24

= $2.542

Similarly, D2 = $2.542 x 1.18

= $2.99956

D3 = $2.99956 x 1.12

= $3.3595072

D4 = $3.3595072 x 1.06

= $3.561077632

Price of the stock expected at the end of year 4

= D5 / (Re – G)

= $3.561077632 x 1.06 / (0.13 – 0.06)

= $53.924889856

Present value factor

= 1 / (1 + r) ^ n

Where,

r = Discount rate = 13% or 0.13

n = Years = 1 to 4

So, PV Factor for year 2 will be

= 1 / (1.13^2)

= 1 / 1.2769

= 0.783146683373796

The following table shows the calculations

Calculations		A	B	C = A x B
Year	Particulars	Cash Flow	PV Factor	Present Value
1	Dividend	2.542	0.884956	2.249557522
2	Dividend	2.99956	0.783147	2.349095466
3	Dividend	3.359507	0.69305	2.32830701
4	Dividend	3.561078	0.613319	2.184075602
4	Expected price	53.92489	0.613319	33.07314484
			Price	42.18

So, as per above calculations, the expected stock price is $42.18