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# Payback, NPV, IRR

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Corporate Finance Question: P10-21 Payback, NPV, and IRR

Rieger International is attempting to evaluate the feasibility of investing \$95,000 in a piece of equipment that has a 5 year life. The firm has estimated the cash inflows associated with the proposal as shown in the following table. The firm has a 12% cost of capital.

Year (t) Cash inflows (CFt) should be a little t
1 \$20,000
2 \$25,000
3 \$30,000
4 \$35,000
5 \$40,000

a.) Calculate the payback period for the proposed investment.
b.) Calculate the net present value (NPV) for the proposed investment.
c.) Calculate the internal rate of return (IRR), rounded to the nearest whole percent, for the proposed investment.
d.) Evaluate the acceptability of the proposed investment using NPV and IRR. What recommendation would you make relative to implementation of the project? Why?

#### Solution Preview

See the attached file.

a.) Payback period
The formula to calculate payback period of a project depends on whether the cash flow per period from the project is even or uneven. When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:

Payback period = A + (B/C)

Where,
A is the last period with a negative cumulative cash flow;
B is the absolute value of cumulative cash flow at the end of the period A;
C is the total cash flow during the period after A

Therefore, the payback period for this investment would be calculated as follows:

Year Cash Flow Net Cash Flow (NCF)
Initial Outlay -95,000 -95,000
Year 1 20,000 -75,000
Year 2 25,000 -50,000
Year 3 30,000 -20,000
Year 4 35,000 15,000
Year 5 40,000 55,000

We can see that after ...

#### Solution Summary

The solution determines the payback, NPV and IRR

\$2.49