Southern California Publishing Company is trying to decide whether to revise its popular textbook, Financial Psychoanalysis Made Simple. The company has estimated that the revision will cost $65,000. Cash flows from increased sales will be $20,000 the first year. These cash flows will increase by 3 percent per year. The book will go out of print four years from now. Assume that the initial cost is paid now and revenues are received at the end of each year. If the company requires a return of 8 percent for such an investment, calculate the present value of the cash inflows of the project.

Present value of the cash inflow= $69,086.97

Explanation:

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.

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

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hope this !