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XYZ just paid a dividend of $ 2.65 on its shares. The dividend growth rate is...

XYZ just paid a dividend of $ 2.65 on its shares. The dividend growth rate is expected to be constant 4% per annum forever. Investors demand a return of 16% for the first three years, a return of 14% for the next three years and a return of 11% thereafter. What is the current price of this financial instrument?

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Expert Solution

Current price is $ 32.74

As per dividend discount model, current price of financial instrument is the present value of future dividend.
Step-1:Present value of dividend of first 6 years
Present value of dividend of year:
1 = 2.65 * 1.04^1 * 1.16^-1 = $       2.38
2 = 2.65 * 1.04^2 * 1.16^-2 = $       2.13
3 = 2.65 * 1.04^3 * 1.16^-3 = $       1.91
4 = 2.65 * 1.04^4 * 1.16^-3 * 1.14^-1 = $       1.74
5 = 2.65 * 1.04^5 * 1.16^-3 * 1.14^-2 = $       1.59
6 = 2.65 * 1.04^6 * 1.16^-3 * 1.14^-3 = $       1.45
Total $    11.20
Step-2:Present value of dividend after year 6
Present value = D6*(1+g)/(k-g)*DF6 Where,
= $    21.54 D6 2.65 * 1.04^6 = $       3.35
g = 4%
k 11%
DF6 1.16^-3 * 1.14^-3 = 0.432426
Step-3:Sum of present value of future dividends
Sum of present value of future dividends = $    11.20 + $    21.54
= $    32.74

jeff jeffy answered 1 year ago
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