Question

The callway cattle company is considering the construction of a feed-handling system. the new system will provide annual savings of $200,000 and the initial investment outlay is $500,000. callaway's management has used a simple payback period method for evaluating new investments in the past but plans to calculate the discounted payback period to analyze the investment. assuming the discount rate used is 10%, calculate the project's discounted payback period:

a. 2.03 years
b. 3.02 years
c. 3 years
d. 4 years

Answer 1

The discounted payback period is the time it takes for the present value of the cash flows from an investment to equal or exceed its initial investment. To calculate the discounted payback period, we need to find the present value of the annual savings and compare it to the initial investment. The discount rate is given as 10%.

Step-by-step explanation:

The discounted payback period is the time it takes for the present value of the cash flows from an investment to equal or exceed its initial investment. To calculate the discounted payback period, we need to find the present value of the annual savings and compare it to the initial investment. The discount rate is given as 10%.

Using the formula for present value, we can find the present value of the annual savings. PV = A / (1 + r)^n, where PV is the present value, A is the annual savings, r is the discount rate, and n is the number of years.

In this case, the annual savings is $200,000, the discount rate is 10%, and the initial investment is $500,000. Plugging these values into the formula, we get:

PV = $200,000 / (1 + 0.1)^1 = $181,818.18

The initial investment of $500,000 needs to be paid back with the discounted cash flows. Dividing the initial investment by the discounted cash flow, we can calculate the discounted payback period:

Discounted Payback Period = $500,000 / $181,818.18 = 2.75 years.

Based on the available options, the closest answer is C. 3 years.