4/16/2010

Chapter 7. Ch 7-20 Build a Model

Rework Problem 7-19. 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 (g1 = g2 = 20%).

a. If D0 = $1.60, rs = 10%, and gn = 6%, what is TTC's stock worth today? What are its expected dividend yield and capital gains yield at this time?

1. Find the price today.

D0 $1.60

rs 10.0%

gs 20% Short-run g; for Years 1-2 only.

gL 6% Long-run g; for Year 3 and all following years.

20% 6%

Year 0 1 2 3

Dividend

PV of dividends

= D3

= Terminal value = P2 =

= rs – gL

= 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 = /

Dividend yield =

3. Find the expected capital gains yield.

The capital gains yield can be calculated by simply subtracting the dividend yield from the total expected return.

Cap. Gain yield= Expected return – Dividend yield

Cap. Gain yield= –

Cap. Gain yield=

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 terminal value and second year dividend to time period one.

P1 = P2 + D2

(1 + rs)

P1 = +

P1 =

Cap. Gain yield= (P1 – P0) / P0

Cap. Gain yield= /

Cap. Gain yield=

b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years. How would this affect its price, dividend yield, and capital gains yield?

1. Find the price today.

D0 $1.60

rs 10.0%

gS 20% Short-run g; for Years 1-5 only.

gL 6% Long-run g; for Year 6 and all following years.

20% 6%

Year 0 1 2 3 4 5 6

Dividend

PV of dividends

= D6

Horizon value = P5 = =

= P0 = rs – gL

Part 2. Finding the expected dividend yield.

Dividend yield = D1 / P0

Dividend yield = /

Dividend yield =

Part 3. Finding the expected capital gains yield.

Cap. Gain yield= Expected return – Dividend yield

Cap. Gain yield= –

Cap. Gain yield=

c. What will TTC's dividend yield and capital gains yield be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth, and the calculations are very easy.)

We used the 5-year supernormal growth scenario for this calculation, but ultimately it does not matter which example you use, as they both yield the same result.

Dividend yield = Dn+1 / Pn

Dividend yield = /

Dividend yield =

Cap. Gain yield= Expected return – Dividend yield

Cap. Gain yield= –

Cap. Gain yield=

Upon reflection, we see that these calculations were unnecessary because the constant growth assumption holds that the long-term growth rate is the dividend growth rate and the capital gains yield, hence we could have simply subtracted the long-run growth rate from the required return to find the dividend yield.

Chapter 7. Ch 7-20 Build a Model

Rework Problem 7-19. 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 (g1 = g2 = 20%).

a. If D0 = $1.60, rs = 10%, and gn = 6%, what is TTC's stock worth today? What are its expected dividend yield and capital gains yield at this time?

1. Find the price today.

D0 $1.60

rs 10.0%

gs 20% Short-run g; for Years 1-2 only.

gL 6% Long-run g; for Year 3 and all following years.

20% 6%

Year 0 1 2 3

Dividend

PV of dividends

= D3

= Terminal value = P2 =

= rs – gL

= 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 = /

Dividend yield =

3. Find the expected capital gains yield.

The capital gains yield can be calculated by simply subtracting the dividend yield from the total expected return.

Cap. Gain yield= Expected return – Dividend yield

Cap. Gain yield= –

Cap. Gain yield=

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 terminal value and second year dividend to time period one.

P1 = P2 + D2

(1 + rs)

P1 = +

P1 =

Cap. Gain yield= (P1 – P0) / P0

Cap. Gain yield= /

Cap. Gain yield=

b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years. How would this affect its price, dividend yield, and capital gains yield?

1. Find the price today.

D0 $1.60

rs 10.0%

gS 20% Short-run g; for Years 1-5 only.

gL 6% Long-run g; for Year 6 and all following years.

20% 6%

Year 0 1 2 3 4 5 6

Dividend

PV of dividends

= D6

Horizon value = P5 = =

= P0 = rs – gL

Part 2. Finding the expected dividend yield.

Dividend yield = D1 / P0

Dividend yield = /

Dividend yield =

Part 3. Finding the expected capital gains yield.

Cap. Gain yield= Expected return – Dividend yield

Cap. Gain yield= –

Cap. Gain yield=

c. What will TTC's dividend yield and capital gains yield be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth, and the calculations are very easy.)

We used the 5-year supernormal growth scenario for this calculation, but ultimately it does not matter which example you use, as they both yield the same result.

Dividend yield = Dn+1 / Pn

Dividend yield = /

Dividend yield =

Cap. Gain yield= Expected return – Dividend yield

Cap. Gain yield= –

Cap. Gain yield=

Upon reflection, we see that these calculations were unnecessary because the constant growth assumption holds that the long-term growth rate is the dividend growth rate and the capital gains yield, hence we could have simply subtracted the long-run growth rate from the required return to find the dividend yield.

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