Question

You are considering starting a new business. You estimate that the business will generate a net revenue of $20,000 each year for five years and you will be able to sell the equipment at the end of five years for $10,000. Using an interest rate of 5% and discrete compounding, how much could you invest at year zero and break even over the five years? Draw a cash flow diagram. Please show me the work not in excel.

Answer 1

Solution :-

At break even point, Present value of cash inflows = Present value of cash outflow (Initial investment).

Present value of cash flows = Annual net revenue * [ 1 - (1 + r)-T] / r + Equipment salvage value / (1 + r)T

= 20000 * [ 1 - (1 + 0.05)-5 ] / 0.05 + 10000 / (1 + 0.05)5 (Where r = interest rate and T = time period in years)

= 20000 * [ 1 - (1.05)-5 ] / 0.05 + 10000 / (1.05)5

= 20000 * (1 - 0.7835) / 0.05 + 10000 / 1.2763

= 20000 * 0.2165 / 0.05 + 7835.15 (approx)

= 20000 * 4.33 + 7835.15

= 86600 + 7835.15

= $ 94435.15 (Rounded off to $ 94,435).

At the break even point, Initial investment = Present value of annual cash inflows = $ 94,435.

Conclusion :- Investment to be made in 0 years (now) to break even during five years = $ 94,435 (approx).