Question

Stephens, Inc. is considering investing in one of two mutually exclusive 4-year projects. Project A requires equipment with a cost of $140,000 and increases net income by $5,000, $10,000, $20,000 and $30,000 in years 1-4, respectively. Project B requires equipment with a cost of $200,000 and increases cash flow by $70,000 per year in years 1-4. Both projects have a 4-year life and the equipment will be depreciated using straight-line depreciation.

What is the NPV of project A at a discount rate of 10% (round to the nearest dollar)?

What is the NPV of project B at a discount rate of 15%?

What is the internal rate of return of project A?

What is the payback period of project A?

At what discount rate do the projects have equal NPV?

Answer 1

For project A, it is given increase in the net inome. To find the cashflows, we need to add the depreciation each year to the net income

Depreciation=$140,000/4=$35,000

Add this $35,000 to each year net income to arrive at the cashflows for 4 years.

For project B, it has already been given cashflows. No need to add depreciation.

1.2.3&4. We can find NPV and IRR by using EXCEL

NPV of Project A=NPV(rate,Year1 to Year4 cashflows)-cost

NPV of Project A=(10%, Year1 to Year4 cashflows)-140,000=$19,271.91

NPV of Project B=(15%, Year1 to Year4 cashflows)-200,000=-$151.51

IRR of Project A=IRR(values)=IRR(Year 0 to Year4 cashflows)=15.69%

Payback period: In how many years, firm can retain the investment.

Payback period for A: It is 3 years: Firm can able to get $140,000 with in 3 years($40,000+$45,000+$55,000)

5. The projects which have equal NPV with a discount rate is called cross over rate.

The cross over rate can be found as per the below steps

Subtract project A cash flows from Project B

Cost=$200,000-$140,000=$60,000

Year1 cashflow=$70,000-$40,000=$30,000

Year2 cashflow=$70,000-$45,000=$25,000

Year3 cashflow=$70,000-$55,000=$15,000

Year4 cashflow=$70,000-$65,000=$5,000

The cross over rate can be found by IRR function in EXCEL

=IRR(values)

=IRR(Year 0 to Year 4 cashflows)

Cross over rate=12.58%