Answer:
Present value of the cash inflow= $69,086.97
Explanation:
<em>An annuity is a series of annual cash outflows or inflows which payable or receivable for a certain number of periods. If the annual cash flow is expected to increase by a certain percentage yearly, it is called a growing annuity.
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To work out the the present value of a growing annuity, we use the formula:
PV = A/(r-g) × (1- (1+g/1+r)^n)
A- annual cash flow - 20,000
r- rate of return - 8%
g- growth rate - 3%
n- number of years- 4
I will break out the formula into two parts to make the workings very clear to follow. So applying this formula, we can work out the present value of the growing annuity (winnings) as follows.
A/(r-g) = 20,000/(0.08-0.03)
= $400,000
(1- (1+g/1+r)^n)
= 1 -(1.03/1.08)^4 =0.17271
PV = A/(r-g) × (1- (1+g/1+r)^n) =400,000
× 0.17271 =69,086.97
Present value of the cash inflow = $69,086.97
