Garvin Enterprises is considering a project that has the following cash flow and WACC data. What is the project's discounted payback? Enter your answer rounded to two decimal places. For example, if your answer is 12.345 then enter as 12.35 in the answer box.
WACC:
9%
Year:
0
1
2
3
Cash flows:
-$1,100
$550
$550
$550
To find the discounted payback period, we need to calculate the present value of the cash flows and determine the point at which the cumulative present value equals or exceeds the initial investment.
The present value of the cash flows can be calculated using the formula:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate (WACC), and n is the year.
Using the WACC of 9%, the present value of the cash flows in each year is as follows:
Year 0: PV = -$1,100 / (1 + 0.09)^0 = -$1,100
Year 1: PV = $550 / (1 + 0.09)^1 = $550 / 1.09 = $504.59
Year 2: PV = $550 / (1 + 0.09)^2 = $550 / 1.1881 = $462.41
Year 3: PV = $550 / (1 + 0.09)^3 = $550 / 1.2950 = $424.47
Now, we can calculate the cumulative present value:
Cumulative present value year 0: -$1,100
Cumulative present value year 1: -$1,100 + $504.59 = -$595.41
Cumulative present value year 2: -$595.41 + $462.41 = -$133.00
Cumulative present value year 3: -$133.00 + $424.47 = $291.47
The discounted payback period is the year at which the cumulative present value becomes positive. In this case, the cumulative present value becomes positive in year 3. Therefore, the discounted payback is 3 years.
Answer: 3.00
To calculate the discounted payback period, we need to determine the present value of the cash flows and then accumulate them until the cumulative sum is greater than or equal to zero.
The formula to calculate the present value of cash flows is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate (WACC), and n is the year.
Using the given WACC of 9% and the cash flows provided:
Year 0: PV = -$1,100 / (1 + 0.09)^0 = -$1,100
Year 1: PV = $550 / (1 + 0.09)^1 = $504.59
Year 2: PV = $550 / (1 + 0.09)^2 = $462.43
Year 3: PV = $550 / (1 + 0.09)^3 = $424.51
Now, let's calculate the cumulative discounted cash flows:
Year 0: -$1,100
Year 1: -$1,100 + $504.59 = -$595.41
Year 2: -$595.41 + $462.43 = -$132.98
Year 3: -$132.98 + $424.51 = $291.53
Since the cumulative discounted cash flow becomes positive in the third year, the discounted payback period is between year 2 and year 3.
To find the exact discounted payback, let's calculate the remaining amount needed to reach zero:
Remaining amount = -$291.53 / $424.51 = 0.6877
Now, we can calculate the discounted payback period:
Discounted payback period = Year 2 + Remaining amount = 2 + 0.6877 = 2.6877
Rounding to two decimal places, the discounted payback period for this project is approximately 2.69 years.
To calculate the project's discounted payback, we need to find the cumulative present value of the cash flows until it becomes positive.
First, we need to calculate the present value of each cash flow using the discounted cash flow formula:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate (WACC), and n is the year.
Using the WACC of 9% and the cash flows provided, the present values of the cash flows are as follows:
Year 0: PV = -1100 / (1 + 0.09)^0 = -1100
Year 1: PV = 550 / (1 + 0.09)^1 = 504.59
Year 2: PV = 550 / (1 + 0.09)^2 = 462.15
Year 3: PV = 550 / (1 + 0.09)^3 = 423.74
Now, let's calculate the cumulative present value of the cash flows:
Cumulative PV at Year 0: -1100
Cumulative PV at Year 1: -1100 + 504.59 = -595.41
Cumulative PV at Year 2: -595.41 + 462.15 = -133.26
Cumulative PV at Year 3: -133.26 + 423.74 = 290.48
The discounted payback is the point in time where the cumulative present value becomes positive. In this case, it happens after Year 2. Therefore, the discounted payback is 2 years and the answer, rounded to two decimal places, is 2.00.