Answer:
Explanation:
To solve this problem, we need to calculate the present value of the cash flows in both cases - the case where the payments are made at the beginning of each year and the case where the payments are made at the end of each year - and compare the two values.
First, let's calculate the present value of the cash flows when payments are made at the end of each year. We can use the formula for the present value of an ordinary annuity:
PV = PMT x [(1 - (1 / (1 + r)n)) / r]
where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.
In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:
PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] = R141,798.06
Now let's calculate the present value of the cash flows when payments are made at the beginning of each year. To do this, we can use the formula for the present value of an annuity due:
PV = PMT x [(1 - (1 / (1 + r)n)) / r] x (1 + r)
where PV is the present value, PMT is the payment amount, r is the discount rate, n is the number of periods, and (1 + r) adjusts the formula for the fact that payments are being made at the beginning of each year.
In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:
PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] x (1 + 0.09) = R153,094.97
So the present value of the cash flows when payments are made at the beginning of each year is R153,094.97, and the present value of the cash flows when payments are made at the end of each year is R141,798.06. Therefore, the difference in present value is:
R153,094.97 - R141,798.06 = R11,296.91
So, receiving the payments at the beginning rather than at the end of each year would result in a present value that is R11,296.91 higher.