11. Countdown Telegraph Products, Inc. has the following dividends planned: The

Question

11. Countdown Telegraph Products, Inc. has the following dividends planned: The next dividend of $6 is scheduled for 4 months from today. Each subsequent dividend will be paid every 6 months. The dividends paid 10 months, 16 months, 22 months, and 28 months from today will be 5% higher than the previous dividend payment. Every dividend paid 34 months from today and after will be 1% lower than the previous dividend payment. If dividends will be paid forever, what is the present value of these planned payments if the effective annual interest rate is 7%?

Explanation / Answer

Soln : Need to calculate the PV of the dividend.

First Lets find out the perpetuity at 34 months as dividend is paid with 1% reduction every year and infinitely.

Perpetuity = dividend payment at 34th month/(rate-growth) = 6*1.05*1.05*1.05*1.05*0.99/0.07-(-0.01) = 7.22/0.08 = $ 90.25

Now, please refer the table for calculations of PV :

t is in years as for 4 months it will be 4/12

NPV = $104.73 ..................(summation of all PV given above in the table)

Please note we have converted months into years for discounting by dividing from 12

Months 0 4 10 16 22 28 34 Dividend value 6 6.3 6.615 6.95 7.29 90.25 discount rate 1.07 1.07 1.07 1.07 1.07 1.07 PV = (dividend value/1.07^t) 5.87 5.95 6.04 6.14 6.23 74.51

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