mr bob is to receive an annual dividend of #8,500 for 8years.the first dividends comes in at thr end of 5years.determine the present value of his dividend income if the relevant rate is 7.5%p.a
(2):in the above question above, suppose the first dividend comes in a year from now,what will be the present value of the dividends? will the result be different if the first dividend is received now?
Remember that the formula for an annuity, which we have to use,
works only if payments are made at the end of an interest period.
Make a time graph to make sure you get the times correct
At the beginning of year 5,
PV = 8500( 1 - 1.075^-8)/.075
Now, we have bring that value to the left 4 interest periods, so
PV of the dividends
= (1.075^-4)[8500( 1 - 1.075^-8)/.075]
= ....
2nd part of your question:
PV of the 8 dividends, the first one a year from now
= 8500( 1 - 1.075^-8)/.075
= ...
If the first payment is received now, then only 7 remaining dividends
fit the formula, so
PV = 8500 + 8500( 1 - 1.075^-7)/.075
= ....
I will let you do all that button-pushing on your calculator