Question

1. A rapidly growing firm is currently paying a dividend of $90. The dividend growth rate is expected to be 12% for the next 6 years. The dividend growth rate after the first 6 years is expected to be 3% annually. The expected return on the market is 8%, the risk free rate is 3% and the firm’s Beta is 25.
   1. Calculate the estimated price (intrinsic value) for a share of this firm’s stock.
   2. What does this firm’s Beta measure?
   3. Use Goal Seek to determine what the current dividend would need to be to yield an estimated price (intrinsic value) of $95.

Answer 1

The intrinsic value of shares can be calculated by two stage model of dividend discounting and Gordon model of constant dividend growth model.

d_i = dividend at different year,

r= required rate of return ,

g = constant dividend growth rate

here , value of 'r' will be calculated by use of CAPM model.

r = 0.03 + 25 ( 0.08-0.03) =1.28 = 128%

calculation of V1, dividend growth rate 12% for first six years

Year	dividend	Pv(dividend @ r%)
0	$90.00	$0.000
1	$100.80	$44.211
2	$112.90	$21.717
3	$126.44	$10.668
4	$141.62	$5.241
5	$158.61	$2.574
6	$177.64	$1.265
	V1	$85.676

dividend growth rate g = 3% =0.03

V_{2 = $ 1.012}

_{V = $ 86.687}

_{Answer C) for intrinsic value (V) = $ 95 .}

_{Dividend Yield on current year = $ 98.63}

_{Using Goal seek , shown in below}

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3 dividend 0 $90.00 1 $100.80 2 $112.90 3 $126.44 4 $141.62 5 $158.61 6 $177.64 Pv(dividend @1%) Year 4 Goal Seelk $0.000 $A4.211 $21.717 $10.668 $5.241 $2.574 $1.265 Set cell: To value: By changing cell: $C$16 95 10 12 13 14 15 16 17 $85.676 $1.012 $86.687 V2

3 Goal Seek Status dividend 0$98.63 1 $110.47 2 $123.72 3 $138.57 4$155.20 5 $173.82 6 $194.68 Py(dividend @1%) Year 4 $0.000 $48.450 $23.800 $11.691 $5.743 $2.821 $1.386 Goal Seeking with Cell C16 found a solution. Step Pause Target value: 95 Current value: $95.000 10 12 13 14 15 16 17 $93.891 $1.109 $95.000 V1 V2