Tutorial 6 for FIN2004, 2021/2022 Academic Year PDF

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Summary

Week 6 of Tutorials for Fin2704 in the National University of Singapore, 100% correct, thoroughly verified by the Teaching Assistant as well as the Professor and Course Coordinator...

Description

Tutorial 6 1-> Price of stock = Dividend Payment / (Required Return — Dividend Growth Rate)

Since the price of the stock is just the PV of all expected future dividends, the dividend growth rate is equal to the growth rate of the price of the stock

2-> It depends on the circumstances. Since the preferred stock might have a stated yield, the dividend payments are fixed; whereas for common stocks, it is possible for the dividend payments to grow. Also, if the preferred stock is callable or convertible into common shares, the price could also be higher as a result. However, the preferred stock is less risky as it has preference in terms of cash flows and liquidation.

3->

D0 = 1.80 D1 = 2.34 D2 = 3.042 D3 = 3.955 D4 = 4.192 TV3 = D4 / (r -g) = 4.192 / (0.13 - 0.06) = 59.8857 PV = FV / (1+r)^n P0 = [ 2.34 / 1.13 ] + [ 3.042 / 1.13^2 ] + [ 3.955 / 1.13^3 ] + [ 59.8857 / 1.13^3 ] = 2.0707 + 2.3823 + 2.7410 + 41.5038 = 48.70

4->

use growing perpetuity formula to find PV6 -> D7 / (r-g) PV6 = 4.9249 / (0.1 - 0.05) = 4.9249 / 0.05 = 98.4970

discount D4, D5, D6 and PV in P6 back to P3 P3 = [ 4.2543 / 1.12 ] + [ 4.4670 / 1.12^2 ] + [ 4.6903 / 1.12^3 ] + [ 98.4970 / 1.12^3 ] = 3.79848 + 3.56106 + 3.33846 + 70.10821 = 80.8062 discount D1, D2, D3 and PV in P3 back to P0 P0 = [ 3.6750 / 1.14 ] + [ 3.8588 / 1.14^2 ] + [ 4.0517 / 1.14^3 ] + [ 80.8062 / 1.14^3 ] = 3.22368 + 2.96922 + 2.73478 + 54.54188 = 63.47

5-> 0.13 = (D1/ 76) + g D1 = D0 * 1.25 D2 = D0 * (1.25^2) D3 = D0 * (1.25^3) D4 = D0 * (1.25^3) * 1.15 D5 = D0 * (1.25^3) * 1.15 * 1.08 = 2.4257 * D0 TV4 = D5 / (r-g) = D5 / (0.13 - 0.08) = D5 / 0.05 = 20 * D5 = 20 * 2.4257 * D0 = 48.514 * D0 P0 = PV of all expected future dividends + PV of TV4 P0 = ( D1 / 1.13 ) + ( D2 / 1.13^2 ) + ( D3 / 1.13^3 ) + ( D4 / 1.13^4 ) + ( 48.514*D0 / 1.13^4 ) = [ ( D0 * 1.25 ) / 1.13 ] + [ ( D0 * (1.25^2) ) / 1.13^2 ] + [ ( D0 * (1.25^3) ) / 1.13^3 ] + [ ( D0 * (1.25^3) * 1.15 ) / 1.13^4 ] + [ 29.754*D0 ] = ( 1.106 * D0 ) + ( 1.224 * D0 ) + ( 1.354 * D0 ) + ( 1.378 * D0 ) + ( 29.754 * D0 ) = 34.816 * D0 P0 = 76 = 34.816 * D0

D0 = 76 / 34.816 = 2.18 D1 = 2.18 * 1.25 = 2.73

6-> P0 = D1 / ( r — g ) = (10.46 * 0.96) / ( 0.115 — (—0.04) ) = 10.0416 / 0.155 = 64.78

7-> Dividend Yield = Dividend paid / Initial Share Price Stock W: D1 = 4.50 * 1.1 = 4.95 P0 = D1 / ( r-g ) = 4.95 / (0.19 - 0.10) = 55 Dividend Yield = D1 / P0 = 4.95 / 55 = 9% (Alternative Method) Dividend Yield = Expected return — Growth rate = 0.19 — 0.10 = 9% Capital Gains Yield = Expected Return — Dividend Yield = 0.19 — 0.09 = 10%

Stock X: D1 = 4.50 * 1.00 = 4.50 P0 = D1 / ( r-g ) = 4.50 / (0.19 - 0.00) = 23.684 Dividend Yield = D1 / P0 = 4.50 / 23.684 = 19% (Alternative Method) Dividend Yield = Expected return — Growth rate = 0.19 — 0.00 = 19% Capital Gains Yield = Expected Return — Dividend Yield = 0.19 — 0.19 = 0%

Stock Y: D1 = 4.50 * 0.95 = 4.275 P0 = D1 / ( r-g ) = 4.275 / (0.19 - (-0.05)) = 17.8125 Dividend Yield = D1 / P0 = 4.275 / 17.8125 = 24% (Alternative Method) Dividend Yield = Expected return — Growth rate = 0.19 — (-0.05) = 24% Capital Gains Yield = Expected Return — Dividend Yield = 0.19 — 0.24 = — 5%

Stock Z: D0 = 4.50 D1 = 4.50 * 1.2 = 5.40 D2 = 5.40 * 1.2 = 6.48 D3 = 6.48 * 1.12 = 7.2576 TV2 = D3 / (r-g) = 7.2576 / (0.19 — 0.12) = 103.68 P0 = [ 5.40 / 1.19 ] + [ 6.49 / 1.19^2 ] + [ 103.68 / 1.19^2 ] = 4.5378 + 4.5830 + 73.215 = 82.3358 Dividend Yield = D1 / P0 = 5.40 / 82.3358 = 6.56% Capital Gains Yield = Expected Return — Dividend Yield = 0.19 — 0.0656 = 12.44%

Although the Expected Return on all 4 stocks are the same at 19%, how the returns are distributed through Dividend Yield and Capital Gains Yield are different for each stock. Stocks with higher growth rates have a higher capital gain yield but lower dividend yield, whereas stocks with negative growth rates have negative capital gains yield but higher dividend yield.

8->

rf = 6% rm = 12% rm - rf = 6% Pmt = 5.20 Required rate of return r = rf + β*(rm - rf) = 0.06 + 0.06*β P = Pmt / r = 5.20 / (0.06 + 0.06*β) 0.88 P = 5.20 / ( 0.06 + 0.06*1.25*β) 0.88 P = 5.20 / (0.06 + 0.075β) 0.88 * [ 5.20 / (0.06 + 0.06*β) ] = 5.20 / (0.06 + 0.075β) 4.576 / (0.06 + 0.06*β) = 5.20 / (0.06 + 0.075β) 4.576 (0.06 + 0.075β) = 5.20 (0.06 + 0.06*β) 0.27456 + 0.3432β = 0.312 + 0.312β 0.0312β = 0.03744 β = 1.2 P = 5.20 / (0.06 + 0.06*1.2) = 39.393 New P = 0.88*P = 0.88*39.393 = 34.67...