Masulis Inc is considering a project that has the following cash flow and WACC Data .what is the project discounted payback
WACC 10%
years 0 1 2 3 4
CASH FLOW -700 525 485 445 405
To calculate the discounted payback period, it is necessary to reduce the cash flow to the present value (year 0) by applying the given WACC (weighted average cost of capital). For year 1, we simply divide by 1.1. For year 2, we divide by 1.1², and so on.
Here is a tabulated version of the calculations. It is difficult to align the column heading, so they are given here:
1. Year
2. Cash Flow
3. Present value of Cash Flow, based on WACC of 10%
4. Cumulative present value of cash flow obtained by adding current year value to previous cumulative value.
0 -700.00 -700.00 -700.00
1 +525.00 +477.27 -222.73
2 +485.00 +400.83 +178.10
3 +445.00 +334.33 +512.43
4 +405.00 +276.62 +789.05
Note that the (+) signs have been added to align the columns properly, and have no other significance.
Conclusion, since the cumulative discounted cash flow goes from negative (-222.73) to positive (+178.10) during year 1, we conclude that the discounted payback is approximately 19 months.
To calculate the discounted payback period of the project, we need to find the present value of each cash flow and then sum them up until the total reaches zero or positive.
1. Calculate the present value (PV) of each cash flow using the formula:
PV = CF / (1 + r)^n
Where:
CF = Cash Flow
r = Discount rate (WACC)
n = Year
Applying the formula, we get:
Year 0:
PV = -700 / (1 + 0.1)^0
PV = -700
Year 1:
PV = 525 / (1 + 0.1)^1
PV = 477.27
Year 2:
PV = 485 / (1 + 0.1)^2
PV = 392.56
Year 3:
PV = 445 / (1 + 0.1)^3
PV = 340.92
Year 4:
PV = 405 / (1 + 0.1)^4
PV = 294.51
2. Calculate the cumulative discounted cash flows by summing up the present values:
Cumulative Discounted CF:
Year 0: -700
Year 1: -700 + 477.27 = -222.73
Year 2: -222.73 + 392.56 = 169.83
Year 3: 169.83 + 340.92 = 510.75
Year 4: 510.75 + 294.51 = 805.26
3. Determine the year when the cumulative discounted cash flow becomes positive (or zero). In this case, it becomes positive in Year 3.
Therefore, the project discounted payback period is 3 years.
To calculate the project discounted payback, you need to determine the present value of each cash flow and then analyze how long it takes to recover the initial investment in present value terms. Here's how you can calculate it step by step:
1. Calculate the present value (PV) of each cash flow using the formula:
PV = Cash Flow / (1 + WACC)^n
Where:
- Cash Flow: The amount of cash flow for each year
- WACC: Weighted Average Cost of Capital (in this case, 10%)
- n: The number of years for each cash flow
In this case, the cash flows and years are as follows:
Year 0: Cash Flow = -700
Year 1: Cash Flow = 525
Year 2: Cash Flow = 485
Year 3: Cash Flow = 445
Year 4: Cash Flow = 405
Using the formula, the present value of each cash flow is:
PV0 = -700 / (1 + 0.10)^0 = -700
PV1 = 525 / (1 + 0.10)^1 = 477.27
PV2 = 485 / (1 + 0.10)^2 = 400.83
PV3 = 445 / (1 + 0.10)^3 = 339.18
PV4 = 405 / (1 + 0.10)^4 = 289.98
2. Calculate the cumulative present value of the cash flows.
To calculate the discounted payback period, you add up the present values of the cash flows until the cumulative present value is equal to or greater than the initial investment.
Cumulative present value for each year:
Year 0: Cumulative PV = PV0 = -700
Year 1: Cumulative PV = PV0 + PV1 = -700 + 477.27 = -222.73
Year 2: Cumulative PV = PV0 + PV1 + PV2 = -700 + 477.27 + 400.83 = 177.10
Year 3: Cumulative PV = PV0 + PV1 + PV2 + PV3 = -700 + 477.27 + 400.83 + 339.18 = 216.28
Year 4: Cumulative PV = PV0 + PV1 + PV2 + PV3 + PV4 = -700 + 477.27 + 400.83 + 339.18 + 289.98 = 506.46
3. Determine the discounted payback period.
The discounted payback period is the number of years it takes for the cumulative present value to equal or exceed the initial investment. In this case, the initial investment is -700.
Comparing the cumulative present value to the initial investment, we can see that it takes around 2 years to recover the initial investment:
Year 0: Cumulative PV = -700 < 700 (not recovered)
Year 1: Cumulative PV = -222.73 < 700 (not recovered)
Year 2: Cumulative PV = 177.10 < 700 (not recovered)
Year 3: Cumulative PV = 216.28 < 700 (not recovered)
Year 4: Cumulative PV = 506.46 >= 700 (recovered)
Therefore, the discounted payback period for this project is approximately 2 years.