Question

3. 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 2.70% 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 (Do) and the discounted value of the dividends expected to be paid 10 and 20 years from now (D10 and D20). Assume that the stock's required return (r) is 8.40%. Note: Carry and round the calculations to four decimal places. Time Period Dividend's Expected Expected Dividend's Future Value Present Value Now End of Year 10 End of Year 20 End of Year 50 $1.0000 $1.3053$0.3395 1.7038$0.582 using the red curve (cross symbols), plot the present value of each of the expected future dividends for years 10, 20, and 50. The resulting curve will llustrate how the PV of a particular dividend payment will decrease depending on how far from today the dividend is expected to be received. Note: Round each of the discounted values of the of dividends to the nearest tenth decimal place before plotting it on the graph. You can mouse over the points in the graph to see their coordinates. DIVIDENDS Is 5.00 Discounted Dividends 4.00 FV of Dividends 3.00 2.00 10, 1.3 1.00 PV of Dividends 0.00 0 10 20 30 40 50 60 YEARS DIVIDENDS Is) 5.00 Discounted Dividends 4.00 FV of Dividends 3.00 2.00 20, 1.7 1.00 PV of Dividends 0.00 0 10 20 30 40 50 60 YEARS DIVIDENDS I$) 5.00 Discounted Dividends 4.00 51, 3.8 FV of Dividends 3.00 2.00 1.00 PV of Dividends 0.00 0 10 20 30 40 50 60 YEARS

Answer 1

Here ,

Dividend of current year (D₀) = $1.00

Dividend Growth rate (g) = 2.70%

Dividend of nth year (D_n) = D₀ ( 1+g) ⁿ

Discount rate (r) = 8.40%

Present value of dividend = $\frac{D_n}{(1+r)^n}$

Time Period		Dividend Expected Future Value		Expected Dividend's Present value
Now				$1.00
End of Year 10	1*(1.027^10)=	$1.3053	1.3053/(1.084^10)=	$0.5827
End of Year 20	1*(1.027^20)=	$1.7038	1.7038/(1.084^20)=	$0.3395
End of Year 50	1*(1.027^50)=	$3.7890	3.7890/(1.084^50)=	$0.0672