Question

In: Finance

Please show your work A company just paid a dividend of $6 and expects the dividend...

Please show your work

A company just paid a dividend of $6 and expects the dividend to decrease 10% this year, decrease 20% next year and then grow at a constant rate of 5% thereafter. If your required rate of return for the company is 10%, what is the per share value today?

A. $74.50 B. $76.25 C. $78.22 D. $80.14 E. $83.45

Expert Solution

Step-1, Dividend for the next 2 years

Dividend in Year 0 (D0) = $6.00 per share

Dividend in Year 1 (D1) = $5.40 per share [$6.00 per share x 90%]

Dividend in Year 2 (D2) = $4.32 per share [$5.40 per share x 80%]

Step-2, The Price of the stock in year 2 (P2)

Dividend Growth Rate after 2 years (g) = 5% per year

Required Rate of Return (Ke) = 10%

Therefore, the Share Price in year 2 (P2) = D2(1 + g) / (Ke – g)

= $4.32(1 + 0.05) / (0.10 – 0.05)

= $4.5360 / 0.05

= $90.72 per share

Step-3, Value of the share today

As per Dividend Discount Model, the selling price of the stock is the aggregate of the Present Value of the future dividend payments and the present value the share price in year 2

Year	Cash flow ($)	Present Value factor at 10%	Present Value of cash flows ($)

1	5.40	0.90909	4.91
2	4.32	0.82645	3.57
2	90.72	0.82645	74.97

TOTAL			83.45

“Therefore, the Value of the share today will be $83.45”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.

jeff jeffy answered 10 months ago

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