Non-constant Non-constant growth model growth model You are - PDF document

Non-constant Non-constant growth model growth model You are calculating the intrinsic value of a You are calculating the intrinsic value of a certain stock using the non-constant certain stock using the non-constant growth model. The company recently paid growth model. The company recently paid a dividend of $1.00 and you expect their $1.00 and you expect their a dividend of dividends to grow at 12% annually for the dividends to grow at 12% annually for the next 2 years. After that, you expect the next 2 years. After that, you expect the dividends to grow at 5% for the dividends to grow at 5% for the foreseeable future. If you require a 10% foreseeable future. If you require a 10% return on this stock, what is the intrinsic return on this stock, what is the intrinsic value? value? Stewllenium Radio 24-1 Stewllenium Radio 24- 1

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 D 0 = 1.00 Stewllenium Radio 24-2 Stewllenium Radio 24- 2

Non-Constant Growth Non-Constant Growth Dividend Valuation Steps Dividend Valuation Steps 1. Calculate all dividends in first growth period and 1. Calculate all dividends in first growth period and first dividend in constant growth period. first dividend in constant growth period. 2. Calculate Present Value of all dividends in first 2. Calculate Present Value of all dividends in first growth period. growth period. (PV 0 in this example) (PV 1-2 in this example) 1-2 0 3. Use Constant Growth Model to find PV of all 3. Use Constant Growth Model to find PV of all dividends in constant growth period. dividends in constant growth period. 4. 4. Discount PV of constant growth period dividends Discount PV of constant growth period dividends back to time zero. back to time zero. (PV 0 in this example) (PV 03- 3- ∞ ∞ in this example) 5. Add up present values from #2 and #4. 5. Add up present values from #2 and #4. (PV 0 (PV 1-2 + PV + PV 0 ∞ = PV = PV 0 ∞ = Price) = Price) 01-2 03- 3- ∞ 01- 1- ∞ Stewllenium Radio 24-3 Stewllenium Radio 24- 3

Non-Constant Growth Non-Constant Growth Dividend Valuation Steps Dividend Valuation Steps 1. Calculate all dividends in first growth period and 1. Calculate all dividends in first growth period and first dividend in constant growth period. first dividend in constant growth period. 2. Calculate Present Value of all dividends in first 2. Calculate Present Value of all dividends in first growth period. growth period. (PV 0 in this example) (PV 1-2 in this example) 1-2 0 3. Use Constant Growth Model to find PV of all 3. Use Constant Growth Model to find PV of all dividends in constant growth period. dividends in constant growth period. 4. 4. Discount PV of constant growth period dividends Discount PV of constant growth period dividends back to time zero. back to time zero. (PV 0 in this example) (PV 03- 3- ∞ ∞ in this example) 5. Add up present values from #2 and #4. 5. Add up present values from #2 and #4. (PV 0 (PV 1-2 + PV + PV 0 ∞ = PV = PV 0 ∞ = Price) = Price) 01-2 03- 3- ∞ 01- 1- ∞ Stewllenium Radio 24-4 Stewllenium Radio 24- 4

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 D 0 = 1.00 Stewllenium Radio 24-5 Stewllenium Radio 24- 5

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 D 0 = 1.00 1.12 Stewllenium Radio 24-6 Stewllenium Radio 24- 6

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 D 0 = 1.00 1.12 Stewllenium Radio 24-7 Stewllenium Radio 24- 7

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 1.3117 D 0 = 1.00 1.12 1.3117 Stewllenium Radio 24-8 Stewllenium Radio 24- 8

Non-Constant Growth Non-Constant Growth Dividend Valuation Steps Dividend Valuation Steps 1. Calculate all dividends in first growth period and 1. Calculate all dividends in first growth period and first dividend in constant growth period. first dividend in constant growth period. 2. Calculate Present Value of all dividends in first 2. Calculate Present Value of all dividends in first growth period. growth period. (PV 0 in this example) (PV 1-2 in this example) 1-2 0 3. Use Constant Growth Model to find PV of all 3. Use Constant Growth Model to find PV of all dividends in constant growth period. dividends in constant growth period. 4. 4. Discount PV of constant growth period dividends Discount PV of constant growth period dividends back to time zero. back to time zero. (PV 0 in this example) (PV 03- 3- ∞ ∞ in this example) 5. Add up present values from #2 and #4. 5. Add up present values from #2 and #4. (PV 0 (PV 1-2 + PV + PV 0 ∞ = PV = PV 0 ∞ = Price) = Price) 01-2 03- 3- ∞ 01- 1- ∞ Stewllenium Radio 24-9 Stewllenium Radio 24- 9

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 1.3117 D 0 = 1.00 1.12 1.3117 Stewllenium Radio 24-10 Stewllenium Radio 24- 10

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 1.3117 D 0 = 1.00 1.12 1.3117 1.0182 1.0182 Stewllenium Radio 24-11 Stewllenium Radio 24- 11

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 1.3117 D 0 = 1.00 1.12 1.3117 1.0182 1.0182 1.0367 1.0367 Stewllenium Radio 24-12 Stewllenium Radio 24- 12

Non-Constant Growth Non-Constant Growth Dividend Valuation Steps Dividend Valuation Steps 1. Calculate all dividends in first growth period and 1. Calculate all dividends in first growth period and first dividend in constant growth period. first dividend in constant growth period. 2. Calculate Present Value of all dividends in first 2. Calculate Present Value of all dividends in first growth period. growth period. (PV 0 in this example) (PV 1-2 in this example) 1-2 0 3. Use Constant Growth Model to find PV of all 3. Use Constant Growth Model to find PV of all dividends in constant growth period. dividends in constant growth period. 4. 4. Discount PV of constant growth period dividends Discount PV of constant growth period dividends back to time zero. back to time zero. (PV 0 in this example) (PV 03- 3- ∞ ∞ in this example) 5. Add up present values from #2 and #4. 5. Add up present values from #2 and #4. (PV 0 (PV 1-2 + PV + PV 0 ∞ = PV = PV 0 ∞ = Price) = Price) 01-2 03- 3- ∞ 01- 1- ∞ Stewllenium Radio 24-13 Stewllenium Radio 24- 13

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 1.3117 D 0 = 1.00 1.12 1.3117 1.0182 D 3 1.0182 D 3 $ $ P 2 = P 2 = 1.0367 r - g 2 1.0367 r - g 2 Stewllenium Radio 24-14 Stewllenium Radio 24- 14

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 1.3117 D 0 = 1.00 1.12 1.3117 1.0182 D 3 1.0182 D 3 $ $ P 2 = P 2 = 1.0367 r - g 2 1.0367 r - g 2 1.3117 1.3117 0.10 - 0.05 0.10 - 0.05 Stewllenium Radio 24-15 Stewllenium Radio 24- 15

Valuing common stock Valuing common stock with nonconstant growth with nonconstant growth 0 1 2 3 0 1 2 3 r s = 10% r s = 10% ... ... g 1 = 12% g 1 = 12% g g 2 = 5% g 1 = 12% g 1 = 12% 2 = 5% D 0 = 1.00 1.12 1.2544 1.2544 1.3117 D 0 = 1.00 1.12 1.3117 1.0182 D 3 1.0182 D 3 $ $ P 2 = P 2 = 1.0367 r - g 2 1.0367 r - g 2 1.3117 1.3117 $ $ P 2 = 26.342 = 26.342 = P 2 = 0.10 - 0.05 0.10 - 0.05 Stewllenium Radio 24- Stewllenium Radio 24-16 16