Week 4 Chapter 8 - Q&A - Calculator&Formula

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1. Share Values [igLO 8.1] The Benalla Ferry Company just paid a dividend of $215 per share. The dividends are expected to grow at a constant rate of 4 per cent per year indefinitely. If investors require a return of 10.5 per cent on the company’s shares, what is the current price? What will the price be in three years? In 15 years? 1. The constant dividend growth model is: Pi=D;x(1+g/(R-g) So the price of the share today is: Po= Do(l +2)Y(R-g) Po=S2.15(1.04)/(0.105 - 0.04) Po=S34.40 The dividend at Year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so: P3;=Dx(1 +g)(R-g) P3=Do(1 +g)*/(R-g) P3=$2.15(1.04)*/(0.105 — 0.04) P3 = 53870 We can do the same thing to find the dividend in Year 16, which gives us the price in Year 15, so: Pis=Dis(1 +g)(R—-g) Pis=Do(1 + g)"°/(R - g) Pys = $2.15(1.04)16/(0.105 — 0.04) Pis=$61.95 There is another feature of the constant dividend growth model: The share price grows at the dividend growth rate. So, if we know the share price today, we can find the future value for any time in the future for which we want to calculate the share price. In this problem, we want to know the share price in three years, and we have already calculated the share price today. The share price in three years will be: Pi=Py1 +g)* P;=$34.40(1 + 0.04) P =$38.70 And the share price in 15 years will be: Pis= Pyl + g)"* Pis = $34.40(1 + 0.04)'S Pis=$61.95 2. Share Values [I‘:' LO 81] The next dividend payment by Leongatha Togas Limited will be $2.34 per share. The dividends are anticipated to maintain a growth rate of 4.5 per cent forever. If the shares currently sell for $37 per share, what is the required return? 2. We need to find the required return per share. Using the constant growth model, we can solve the equation for R. Doing so, we find: R=(DvPo) + g R =(S2.34/S37) + 0.045 R=0.1082, or 10.82%

3. Share Values [[Z'LO &1] For the company in the previous problem, what is the dividend yield? What is the expected capital gains yield? 3. The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = Di/Po Dividend yield = $2.34/$37 Dividend yield = 0.0632, or 6.32% The capital gains yield, or percentage increase in the share price, is the same as the dividend growth rate, so: Capital gains yield = 4.5% 8. Valuing preference shares [Z'LO 8.1] Mathoura Fine Fashions Limited has an issue of preference shares outstanding that pays a $3.40 dividend every year in perpetuity. If this issue currently sells for $91 per share, what is the required retum? 8. The price of a preference share is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero per cent. Remember, most preference shares pay a fixed dividend, so the growth rate is zero. Using this equation, we find the price per preference share is: R=D/Py R=83.40/591 R=0.0374, or 3.74% 9. Share Valuation and Required Return [ LO 8] Red Limited, Yellow Corporation and Blue Company each will pay a dividend of $3.65 next year. The growth rate in dividends. for all three companies is 4 per cent. The required retur for each company’s shares is 8 per cent, 1 per cent and 14 per cent, respectively. What is the share price for each company? What do you conclude about the relationship between the required return and the share price? 9. We can use the constant dividend growth model, which is: Pi=Dx(1+g/R-g) So the price of each company’s share today is: Red share price = $3.65/(0.08 — 0.04) = $91.25 Yellow share price = $3.65/(0.11 — 0.04) = $52.14 Blue share price = $3.65/(0.14 — 0.04) = $36.50 As the required return increases, the share price decreases. This is a function of the time value of money: A higher discount rate decreases the present value of cash flows. It is also important to note that relatively small changes in the required return can have a dramatic impact on the share price.

15, Non-constant Growth [[Z'LO 8.1] Clackiine Bearings Limited is a young start-up company. No dividends will be paid on the shares over the next nine years because the firm needs to plough back its eamings to fuel growth. The company will pay a dividend of $17 per share 10 years from today and willincrease the dividend by 3.9 per cent per year thereafter. If the required return on the shares is 12.5 per cent, what is the current share price? 15. Here we have a share that pays no dividends for 10 years. Once the share begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember that the general constant dividend growth formula is: Pi=[Dix(1+gJ(R-g) This means that since we will use the dividend in Year 10, we will be finding the share price in Year 9. The dividend growth model is similar to the PVA and the PV of a perpetuity: The equation gives you the PV one period before the first payment. So, the price of the share in Year 9 will be: Py=Dio/R-g) Py=S17/(0.125 - 0.039) Py =8197.67 The price of the share today is the PV of the share price in the future. We discount the future share price at the required return. The price of the share today will be: Py=$197.67/1.125° Po=$68.48 17 Non-constant Dividends [(Z'LO 8] Mollymook Fashions is expected to pay the following dividends over the next four years: $13, $9, $6 and $2.75. Afterward, the company pledges to maintain a constant 5 per cent growth rate in dividends forever. If the required return on the shares is 1075 per cent, what is the current share price? 17. With non-constant dividends, we find the price of the share when the dividends level off at a constant growth rate, and then find the PV of the future share price, plus the PV of all dividends during the nonconstant dividend period. The share begins constant dividend growth in Year 4, so we can find the price of the share in Year 4, at the beginning of the constant dividend growth, as: Ps=Dy(1 +g)(R-g) P3=82.75(1.05)/(0.1075 - 0.05) Py=850.22 The price of the share today is the PV of the first four dividends, plus the PV of the Year 4 share price. So, the price of the share today will be: Py =$13/1.1075 + $9/1.1075% + $6/1.1075° + $2.75/1.1075% + $50.22/1.1075* Po=858.70

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8. Supernormal Growth [ LO 811 Synovec Company is growing quickly. Dividends are expected to grow at a rate of 30 per cent for the next three years, with the growth rate falling off to a constant 4 per cent thereater.If the required retun is 11 per cent and the company just paid a dividend of $2.45, what is the current share price? 18. With supernormal dividends, we find the price of the share when the dividends level off at a constant growth rate, and then find the PV of the future share price, plus the PV of all dividends during the supernormal growth period. The share begins constant growth in Year 4, so we can find the price of the share in Year 3, one year before the constant dividend growth begins, as: Py=Ds(1+g)(R-g) Py =Dy(1 +gi)(1 + g)(R—-g) P3=$2.45(1.30)°(1.04)/(0.11 - 0.04) P3=$79.97 The price of the share today is the PV of the first three dividends, plus the PV of the Year 3 share price. The price of the share today will be: Po=$2.45(1.30)/1.11 + $2.45(1.30)%/1.11% + $2.45(1.30)*/1.11° + §79.97/1.11% Po=$68.64 We could also use the two-stage dividend growth model for this problem, which is: Po=[Do(1 +gi)/(R-g){1 - [(1 +g)/(1 +R)J'}+ [(1 +g1)/(1 + R)I[Do(1 + g2)/(R - g2)] Po=[$2.45(1.30)/(0.11 — 0.30)][1 — (1.30/1.11)°] + [(1 + 0.30)/(1 + 0.11)P[$2.45(1.04)/(0.11 - 0.04)] Py=$68.64 20, Negative Growth [Z'LO 8.1] Antiques R Us is a mature manufacturing firm. The company just paid a dividend of $9.80, but management expects to reduce the payout by 4 per cent per year indefinitely. If you require a return of 9.5 per cent on the shares, what will you pay for a share today? 20. The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognise the negative growth. So, the price of the share today will be: Po=Do(1 +g)(R-g) Po=$9.80(1 — 0.04)/[(0.095 — (~0.04)] Po=569.69

33. Share valuation [11_':' LO 81] Most companies pay half-yearly dividends on their ordinary shares rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers or maintains the current dividend once a year and then pays this dividend out in equal half-yearly instalments to its shareholders. a. Suppose a company currently pays an annual dividend of $3.40 on its ordinary shares in a single annual instalment and management plans on raising this dividend by 3.8 per cent per year indefinitely. If the required return on the shares is 10.5 per cent, what is the current share price? b. Now suppose the company in (a) actually pays its annual dividend in equal half-yearly instalments; thus, the company has just paid a dividend of $1.70 per share, as it did for the previous half-year. What is your value for the current share price now? (Hint. Find the equivalent annual end-of-year dividend for each year) Comment on whether you think this model of share valuation is appropriate. 33. a. Using the constant dividend growth model, the price of the share paying annual dividends will be: Po=Do(l +g)(R-g) Po = $3.40(1.038)/(0.105 — 0.038) Po=$52.67 b. If the company pays half-yearly dividends instead of annual dividends, the half- yearly dividend will be half of the annual dividend, or: Half-yearly dividend = $3.40(1.038)/2 Half-yearly dividend = $1.7646 To find the equivalent annual dividend, we must assume that the half-yearly dividends are reinvested at the required return. We can then use this interest rate to find the equivalent annual dividend. In other words, when we receive the half-yearly dividend, we reinvest it at the required return on the share. So, the effective half- yearly rate is: Effective half-yearly rate = 1.105%° — 1 Effective half-yearly rate = 0.0512, or 5.12% The effective annual dividend will be the FVA of the half-yearly dividend payments at the effective half-yearly required return. In this case, the effective annual dividend will be: Effective D) = $1.7646(FVIFAs 120.2) Effective D) = $3.62 Now, we can use the constant dividend growth model to find the current share price as: Po=$3.62/(0.105 — 0.038) Po=$54.02 Note that we cannot find the half-yearly effective required return and growth rate to find the value of the share. This would assume the dividends increased each quarter, not each year. Chapter review and self-test problems 81 Dividend growth and share valuation The Perth Shipping Company has just paid a cash dividend of $2 per share. Investors require a 16 per cent return from investments such as this. If the dividend is expected to grow at a steady 8 per cent per year, what is the current value of the shares? What will the shares be worth in five years? 8.2 More dividend growth and share valuation In Self-Test Problem 8.1, what would the shares sell for today if the dividend was expected to grow at 20 per cent per year for the next three years and then settle down to 8 per cent per year indefinitely? Self-Test - No Answers