(1):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?
To determine the present value of Mr. Bob's dividend income, we need to calculate the present value of each individual dividend and then sum them up.
For question (1), where the first dividend comes in at the end of 5 years, we need to use the formula for the present value of an ordinary annuity:
Present Value = Dividend Amount * (1 - (1 + r)^(-n)) / r
Where:
- Dividend Amount is the annual dividend of #8,500
- r is the relevant rate, 7.5% or 0.075 in decimal form
- n is the number of years, which is 8 years
Now let's substitute the values into the formula:
Present Value = 8,500 * (1 - (1 + 0.075)^(-8)) / 0.075
Calculating this expression will give us the present value of the dividend income for question (1).
For question (2), when the first dividend comes in a year from now, we need to adjust the formula slightly. We will have one less period, so n will be 7. The new expression would be:
Present Value = 8,500 * (1 - (1 + 0.075)^(-7)) / 0.075
If the first dividend is received now, we would use the original formula with n being 8, as there is no delay in receiving the first dividend. Therefore, the present value calculation would be the same as in question (1).
So, to summarize:
- For question (1), where the first dividend comes in at the end of 5 years, calculate the present value using the first formula.
- For question (2), where the first dividend comes in a year from now, calculate the present value using the second formula.
- If the first dividend is received now, the present value is the same as in question (1).