Question

09problem 3/4/2019 20:30 9/14/2015 Chapter 9. Solution for End-of-Chapter Comprehensive/Spreadsheet problem Problem 9-22 Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. This same growth rate is expected to last for another 2 years, then to decline to gn = 6%. a. If D0 = $1.60 and rs = 10%, what is TTC's stock worth today? What are its expected dividend and capital gains yields at this time, that is, during Year 1? 1. Find the price today. D0 $1.60 rs 10.0% gs 20% Short-run g; for Years 1-2 only. gn 6% Long-run g; for Year 3 and all following years. 20% 6% Year 0 1 2 3 Dividend $1.6000 $1.9200 $2.3040 $2.4422 PV of dividends $1.7455 $1.9041 $2.4422 $50.4595 $61.0560 = Horizon value = P2 = 4.0% = rs - gn $54.1091 = P0 2. Find the expected dividend yield. Recall that the expected dividend yield is equal to the next expected annual dividend divided by the price at the beginning of the period. Dividend yield = D1 / P0 Dividend yield = $1.9200 / $54.1091 Dividend yield = 3.55% 3. Find the expected capital gains yield. The capital gains yield can be calculated by simply subtracting the dividend yield from the expected total return. Cap. gain yield = Expected total return − Dividend yield Cap. gain yield = 10.0% − 3.55% Cap. gain yield = 6.45% Alternatively, we can recognize that the capital gains yield measures capital appreciation, hence solve for the price in one year, then divide the change in price from today to one year from now by the current price. To find the price one year from now, we will have to find the present values of the horizon value and second year dividend at time period one. P 1 = P 2 + D 2 (1 + rs) P 1 = $61.0560 + $2.3040 1.10 P 1 = $57.60 Cap. gain yield = (P1 – P0) / P0 Cap. gain yield = $3.49 / $54.1091 Cap. gain yield = 6.45% b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years. How would this affect the price, dividend yield, and capital gains yield? 1. Find the price today.

Answer 1

a)
	Year	Dividend	Growth Rate	Dividend after Growth
	0	$1.6
	1	$1.60 x 1.20	20.00%	$1.92
	2	$1.89 x 1.20	20.00%	$2.3
	3	$2.23 x 1.06	6.00%	$2.44
Terminal value p2 = Dividend in year 3 /(rs - g) ; $2.44/(10% -6%)	$61.06
	Year	Cash flow	PV @ 10%	Present Value
	1	$1.92	0.9091	$1.75
	2	$2.3	0.8264	$1.9
	Terminal value	$61.0560	0.8264	$50.46
			TTC's Stock Worth	$54.10909
b)
Dividend Yield = D1/P0 = $1.92/$54.11	3.55%
C)
Capital Yield = Expected Return - dividend yield = 10% - 3.55%	6.45%
d)
Year	Dividend	Growth Rate	Dividend after Growth
0	$1.6
1	$1.60 x 1.20	20.00%	$1.92
2	$1.92 x 1.20	20.00%	$2.3
3	$2.3 x 1.20	20.00%	$2.76
4	$2.76 x 1.20	20.00%	$3.32
5	$3.32 x 1.20	20.00%	$3.98
6	$3.98 x 1.06	6.00%	$4.22
Terminal value p5 = Dividend in year 6 /(rs - g) ; $4.22/(10% -6%)	$105.50477
Year	Cash flow	PV @ 10%	Present Value
1	$1.92	0.9091	$1.75
2	$2.3	0.8264	$1.9
3	$2.76	0.7513	$2.08
4	$3.32	0.6830	$2.27
5	$3.98	0.6209	$2.47
TV	$105.5	0.6209	$65.51
		TTC's Stock Worth	$75.97514
Dividend Yield = D6/P0 = $4.22/$75.97514	5.55%
Capital Yield = Expected Return - dividend yield = 10% - 5.55%	4.45%