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.)
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
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