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home / study / questions and answers / business / finance / (payback period, net present value, profitability, ... Question -------------------------------------------------------------------------------- (payback period, net present value, profitability, and internal rate of return calculations) You are considering a project with an initial cash outlay of $88,000 and expected cash flows of $27,280 at the end of each year for six years. The discount rate for this project is 9.7 percent. What are the project's payback and discounted paycheck periods? What is the project's NPV? What is the PI? What is the IRR?

Explanation / Answer

initial cash outlay = 88000

expected cash flows = 27280

discount rate = 9.7 percent

Project Payback period = Initial Cash Outlay/Expected Cash Flow

Project Payback period = 88000/27280

Project Payback period = 3.23 Years

Discounted paycheck periods = 4 + 961.50/17171.62

Discounted paycheck periods = 4.06 years

PV of Cash Inflow = Annual Cash Inflow*(1-(1+r)^-n)/r

PV of Cash Inflow = 27280*(1-(1+9.7%)^-6)/9.7%

PV of Cash Inflow = $ 119,863.37

Project's NPV = PV of Cash Inflow - PV of Cash Outflow

Project's NPV = 119863.37-88000

Project's NPV = $ 31,863.37

PI = PV of Cash Inflow / PV of Cash Outflow

PI = 119863.37/88000

PI = 1.36 Years

IRR is the rate at which NPV is equal to zero i.e

PV of Cash Inflow = PV of Cash Outflow

27280 *PVIFA(r,6) = 88000

PVIFA(r,6) = 88000/27280

PVIFA(r,6) = 3.225806

Using PV table we get

r = 21.24%

IRR = 21.24%

Year Cash Flow PV of Cash Inflow @ 9.7% Cummulative Cash Flow 0 -88000 -88000.00 -88000.00 1 27280 24867.82 -63132.18 2 27280 22668.93 -40463.24 3 27280 20664.48 -19798.76 4 27280 18837.27 -961.50 5 27280 17171.62 16210.12 6 27280 15653.25 31863.37

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