Stock valuation

Question

last year the company paid a dividend of $ 3.40. it expects zero growth in the next year. in year 2, 5% growth is expected, in year 3 and 4 company is not paying any dividend. in year 5 company is paying new dividend which is $5, in year 6 growth is 10%. and thereafter growth will be constant 8%. what is the maximum price per share that an investor who requires a return of 14%.

Answer 1

The maximum price per share the investor should pay is approximately $55.94.

Here is the teacher-style explanation.

The investor requires a 14% return, so we discount all future dividends at 14%.

Last year’s dividend was $3.40.

Step 1: Find the expected dividends

Year 1: Zero growth

D1=3.40D_1 = 3.40D1​=3.40Year 2: 5% growth

D2=3.40×1.05=3.57D_2 = 3.40 \times 1.05 = 3.57D2​=3.40×1.05=3.57Year 3 and Year 4: No dividend

D3=0,D4=0D_3 = 0,\quad D_4 = 0D3​=0,D4​=0Year 5: Dividend is given

D5=5.00D_5 = 5.00D5​=5.00Year 6: 10% growth from Year 5

D6=5.00×1.10=5.50D_6 = 5.00 \times 1.10 = 5.50D6​=5.00×1.10=5.50After Year 6, dividends grow constantly at 8%.

Step 2: Find the stock value at Year 5

At the end of Year 5, we use the constant growth model:

P5=D6r−gP_5 = \frac{D_6}{r-g}P5​=r−gD6​​ P5=5.500.14−0.08P_5 = \frac{5.50}{0.14 - 0.08}P5​=0.14−0.085.50​ P5=5.500.06=91.67P_5 = \frac{5.50}{0.06} = 91.67P5​=0.065.50​=91.67So, at the end of Year 5, the stock is worth $91.67.

Step 3: Discount the cash flows back to today

P0=D1(1.14)1+D2(1.14)2+D5+P5(1.14)5P_0 = \frac{D_1}{(1.14)^1} + \frac{D_2}{(1.14)^2} + \frac{D_5 + P_5}{(1.14)^5}P0​=(1.14)1D1​​+(1.14)2D2​​+(1.14)5D5​+P5​​ P0=3.401.14+3.57(1.14)2+5.00+91.67(1.14)5P_0 = \frac{3.40}{1.14} + \frac{3.57}{(1.14)^2} + \frac{5.00 + 91.67}{(1.14)^5}P0​=1.143.40​+(1.14)23.57​+(1.14)55.00+91.67​ P0=2.98+2.75+50.21P_0 = 2.98 + 2.75 + 50.21P0​=2.98+2.75+50.21 P0=55.94P_0 = 55.94P0​=55.94Final Answer

The maximum price the investor should pay for the stock is:

$55.94\boxed{\$55.94}$55.94​So, if the stock is selling for less than $55.94, it may be attractive. If it is selling for more than $55.94, the investor would not earn the required 14% return.