Question

4. Expected dividends as a basis for stock values

The following graph shows the value of a stock’s dividends over time. The stock’s current dividend is $1.00 per share, and dividends are expected to grow at a constant rate of 4.50% per year. The intrinsic value of a stock should equal the sum of the present value (PV) of all of the dividends that a stock is supposed to pay in the future, but many people find it difficult to imagine adding up an infinite number of dividends.

Calculate the present value (PV) of the dividend paid today (D₀) and the discounted value of the dividends expected to be paid 10, 20, and 50 years from now (D10, D20, D50D10, D20, D50). Assume that the stock’s required return (rss) is 5.40%.

Note: Carry and round the calculations to four decimal places.

Time Period	Dividend’s Expected Future Value	Dividend’s Expected Present Value
Now
End of Year 10
End of Year 20
End of Year 50

Using the blue curve (circle symbols), plot the future value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will illustrate how the FV of a particular dividend payment will increase depending on how far from today the dividend is expected to be received.

Note: Round each of the discounted values of the dividends to the nearest tenth decimal place before plotting it on the graph. You can mouse over the points in the graph to see their coordinates.

Expected Dividends010203040506010.008.006.004.002.000DIVIDENDS ($)YEARSPV of DividendsFV of Dividends

Answer 1

SEE THE IMAGE. ANY DOUBTS, FEEL FREE TO ASK. THUMBS UP PLEASE

C w ? ENG 07:05 01-08-2020 70 35 Х AW34 . AU AV AW AX AY AZ BA BB BC BD BE BE BG BH 34 35 36 37 38 39 40 41 42 current dividend 1 43 44 45 46 4.50% 5.40% Time period GROWTH RATE Dividend's expected Future value 47 48 DISCOUNT RATE = expected dividend's present value 1 1.4106/(1+0.054)^10 = 1.9898/(1+0.054)^20 5.5849/(1+0.054)^50 = 0.9178 now End of year 10 End of year 20 End of year 50 49 50 51 52 1*(1 + 0.045)^10 = 1*(1 + 0.045)^20 = 1*(1 + 0.045)^50 = 1.5530 2.4117 0.8424 0.6513 9.0326 53 54 55 56 57 ra Sheet1 Sheet4 PV FV DIVIDEND EMV Sheet2 MEAN STDV assignment DEAR prob sd cov TIME SERIES corr REGRESSION range CAMERA IN ... +

C w ? ENG 07:05 01-08-2020 70 35 Х BI79 < . AV AW AX AY AZ BA BB BC BD BE BE BG BH BI 56 57 58 59 60 10.0000 9.0000 9.0326 61 62 year 10 8.0000 63 future dividend present value of dividend 1.5530 0.9178 2.4117 0.8424 9.0326 0.6513 7.0000 64 20 50 6.0000 65 66 67 future dividend DIVIDEND 5.0000 68 4.0000 69 3.0000 present value of dividend 2.4117 2.0000 70 71 72 1.5530 1.0000 0.9178 0.6513 0.8424 1 0.0000 73 74 0 10 20 30 40 50 60 YEARS 75 76 77 78 79 Sheet1 Sheet4 PV FV DIVIDEND EMV Sheet2 MEAN STDV assignment DEAR prob sd COV TIME SERIES corr REGRESSION range CAMERA IN... +