Chapter Outline
4. When cash flows are unequal, trial and error must be used;
select any reasonable discount rate and compute the NPV.
a. If amount is positive, recompute NPV using higher
discount rate; if amount is negative, recompute NPV using
lower discount rate.
b. Continue steps until two consecutive computations result
in NPVs that have different signs (positive and negative);
IRR lies between these two discount rates; value can be
estimated.
c. Spreadsheet software and calculators can also be used to
compute the IRR. (See Appendix 24A)
5. Compare IRR with hurdle rate (or minimum acceptable rate of
return); if IRR exceeds hurdle rate, invest.
6. If evaluating multiple projects, rank by extent to which IRR
exceeds hurdle rate.
7. IRR is not subject to limitations of NPV when comparing
1. Payback period and accounting rate of return do not consider
time value of money; NPV and IRR do.
2. Payback period method is simple; sometimes used when
limited cash to invest and a number of projects to choose
from. Gives manager an estimate of how soon the initial
investment can be recovered.
3. Accounting rate of return is a percent computed using accrual
income instead of cash flows, and is an average rate for the
entire investment period; annual returns are not reflected.
4. Net Present Value (NPV):
a. Considers all estimated cash flows of project; can be
5. Internal Rate of Return (IRR):
a. Considers all estimated cash flows of project.
b. Readily computed when cash flows are equal, but requires
trial and error estimation when cash flows are unequal.
c. Allows comparisons of projects with different investment
amounts.
d. Does not reflect changes in risk over life of project.
Notes
24-7
Chapter Outline
IV. Decision AnalysisBreak-Even Time (BET) A variation of the
payback period method – overcomes the limitation of not using the
time value of money
A. The future cash flows are restated in terms of their present values;
B. The payback period is computed using these present values
C. Break-even time (BET) is useful measure; managers know when
to expect cash flows to yield net positive returns.
D. If BET is less than estimated life of investment, positive net
present value can be expected from investment.
To compare and rank alternative investment projects, choose
the project with the lowest break-even time.
V. Using Excel to Compute Net Present Value and Internal Rate of
Return (Appendix A)
A. These calculations can be performed simply and accurately by
Notes
24-8
Chapter 24 Alternate Demonstration Problem
A company is planning to buy a new machine at a cost of $200,000. The
machine is expected to last for 10 years and have no salvage value at the
end of its useful life. Straight-line depreciation will be used. The company
expects to save 10,000 hours of direct labor each year because of the new
machine, as well as $4,000 each year in other operating costs.
Management’s best estimate is that on average the hourly rate for the labor
saved will be $5.50. With the exception of the initial purchase, assume all
cash flows take place at the end of the year, and a tax rate of 40%.
Required:
1. Calculate the payback period on the investment in new machinery.
2. Calculate the rate of return on the average investment.
3. Calculate the net present value of the investment and profitability index:
(a) Ignoring income taxes, using a discount rate of 10%.
(b) Including the effect of taxes, using a 10% discount rate.
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Solution: Chapter 24 Alternate Demonstration Problem
24-10
1. First, calculate annual net cash flow:
Determine increase in after-tax net income:
Labor savings: 10,000 hours @ $5.50 per hour $55,000
Other operating savings 4,000
Annual cash savings before tax 59,000
Then, add back depreciation expense (noncash):
Increase in net income after tax $23,400
2. The rate of return on average investment equals the increase in net income after
tax divided by the amount of the average investment.
3(a) There is a cash savings of $59,000 each year for 10 years if income taxes are
ignored. The present value factor for a 10-year annuity at 10% is 6.1446.
Present value of cash savings ($59,000 x 6.1446) $362,531
Present value of investment 200,000
3(b) There is a cash savings of only $43,400 each year for 10 years if income taxes are
considered.
Present value of cash savings ($43,400 x 6.1446) $266,676
Present value of investment 200,000
24-11