The Seattle Corporation has been presented with an investment opportunity which will yield cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost the firm $150,000 today, and the firm's cost of capital is 10 percent. Assume cash flows occur evenly during the year, 1/365th each day. What is the payback period for this investment?
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A. B. C. D. E.D
Using the even cash flow distribution assumption, the project will completely recover initial investment after 30/35 = 0.86 of Year 5:
Payback = 4 + 30/35 = 4.86 years.
To calculate the payback period for an investment, we need to determine the time it takes for the cash inflows to recover the initial investment.
In this case, the investment opportunity costs $150,000 today and generates cash flows over a period of 10 years. The cash flows are $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10.
To calculate the payback period, we'll start by adding up the cash flows until we recover the initial investment. Let's go step by step:
Step 1: Calculate the present value of each cash flow using the firm's cost of capital. We'll use a discounted cash flow (DCF) approach, where the present value (PV) of each cash flow is calculated as follows:
PV = Cash Flow / (1 + r)^n
Where:
The discount rate is given as 10%, so r = 0.10.
For each year, we'll calculate the present value of the cash flow:
Year 1: PV1 = $30,000 / (1 + 0.10)^1 = $30,000 / 1.10 = $27,272.73 Year 2: PV2 = $30,000 / (1 + 0.10)^2 = $30,000 / 1.21 = $24,793.39 Year 3: PV3 = $30,000 / (1 + 0.10)^3 = $30,000 / 1.33 = $22,556.39 Year 4: PV4 = $30,000 / (1 + 0.10)^4 = $30,000 / 1.46 = $20,548.09 Year 5: PV5 = $35,000 / (1 + 0.10)^5 = $35,000 / 1.61 = $21,739.13 Year 6: PV6 = $35,000 / (1 + 0.10)^6 = $35,000 / 1.77 = $19,774.01 Year 7: PV7 = $35,000 / (1 + 0.10)^7 = $35,000 / 1.95 = $17,948.72 Year 8: PV8 = $35,000 / (1 + 0.10)^8 = $35,000 / 2.15 = $16,279.07 Year 9: PV9 = $35,000 / (1 + 0.10)^9 = $35,000 / 2.37 = $14,684.81 Year 10: PV10 = $40,000 / (1 + 0.10)^10 = $40,000 / 2.61 = $15,326.35
Step 2: Calculate the cumulative present value of the cash flows until we recover the initial investment. We'll sum up the present values until the cumulative sum exceeds or equals the initial investment of $150,000.
Cumulative Present Value (CPV) = PV1 + PV2 + PV3 + PV4 + PV5 + PV6 + PV7 + PV8 + PV9 + PV10
CPV = $27,272.73 + $24,793.39 + $22,556.39 + $20,548.09 + $