Question

If a project costs $100,000 and is expected to return $25,000 annually, how long does it take to recover the initial investment? What would be the discounted payback period at i=15%? Assume that the cash flows occur continuously throughout the year.

Answer 1

The payback period for a project costing $100,000 with an annual return of $25,000 is 4 years. To calculate the discounted payback period at a 15% interest rate, the cash flows need to be discounted to present value using continuous compounding.

Step-by-step explanation:

If a project costs $100,000 and is expected to return $25,000 annually, to recover the initial investment without considering the time value of money, we simply divide the project cost by the annual return. This gives us a payback period of 4 years ($100,000 / $25,000 = 4).

To calculate the discounted payback period at an interest rate (i) of 15%, we need to discount the cash flows to their present value using the formula for continuous compounding: PV = P * e^(-rt), where PV is the present value, P is the payment per time period, r is the interest rate, and t is the time period. Since the cash flows occur continuously, we have to integrate this formula over time to find when the sum of discounted cash flows equals the initial investment.