Final answer:
The discounted payback period is the length of time it takes for the present value of the expected cash inflows from a project to equal or exceed the initial cost of the project. To calculate the discounted payback period, we need to calculate the present value of each cash inflow using the required rate of return, and then determine how many years it takes for the sum of the present values to equal or exceed the initial cost. In this case, the answer is closest to option b. 2.45 years.
Step-by-step explanation:
The discounted payback period is the length of time it takes for the present value of the expected cash inflows from a project to equal or exceed the initial cost of the project. To calculate the discounted payback period, we need to calculate the present value of each cash inflow using the required rate of return, and then determine how many years it takes for the sum of the present values to equal or exceed the initial cost.
In this case, the initial cost is $18,400, and the expected cash inflows are $7,200, $8,900, and $7,500 over years 1 to 3, respectively. The required rate of return is 11.2 percent.
Using the formula for present value, the present value of the cash inflows in year 1 is $7,200 / (1 + 0.112)^1 = $6,486.61. The present value of the cash inflows in year 2 is $8,900 / (1 + 0.112)^2 = $7,470.43. The present value of the cash inflows in year 3 is $7,500 / (1 + 0.112)^3 = $5,885.05.
Now, we can calculate the discounted payback period. Subtracting each present value from the initial cost:
$18,400 - $6,486.61 = $11,913.39
$11,913.39 - $7,470.43 = $4,442.96
$4,442.96 - $5,885.05 = -$1,442.09
The discounted payback period is between 2 and 3 years. Since the present value becomes negative in year 3, the payback period is less than 3 years. To find the exact payback period, we can calculate the fractional portion of the year needed to recover the remaining amount:
(-$1,442.09) / $5,885.05 = -0.244837
The discounted payback period is approximately 2.244837 years. Therefore, the answer is closest to option b. 2.45 years.