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212 Zutter/Smart • Principles of Managerial Finance Brief, Eighth Edition
b. To find the number of years $10,000 would have to be received to make the project acceptable
by the IRR decision rule, use the NPER command in Excel. The proper syntax is:
c. To find the minimum cash inflows over 10 years that would make the project acceptable, use the
PMT command in Excel. The proper syntax is:
P10-19 NPV and IRR (LG 3, 4; Intermediate)
a. NPV = Present value of cash inflows – Initial investment ($18,250). In Excel, the present value of
cash inflows = PV(0.10,7,-4000) = $19,473.68. So, NPV = $19,473.68 – $18,250 = $1,223.68.
P10-20 NPV, with rankings (LG 3, 4; Intermediate)
15%
IRR = 9.70% IRR = 15.63% IRR = 19.44% IRR = 17.51%
Discount Rate =
Project A Project DProject B Project C
Note: IRR was obtained in Excel and the following syntax (cash flows arranged in the first four rows
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the IRR decision criterion indicates project A should be accepted.
Project B
NPV: In Excel, put 40000 in A1, 35000 in A2, 30000 in A3, 10000 in A4, and 5000 in A5.
Then, use the NPV command to obtain the present value of these inflows; proper syntax:
=NPV(discount rate,A1:A5) = NPV(0.12,A1:A5) = $94,161.79 . Now, to obtain project
17.75%. Given these points, the NPV profiles for project A and B may be drawn:
Note the two projects have NPVs
16.06%, both projects are profitable, but project B has a slightly higher NPV (and is, therefore,
more desirable). For discount rates below 14.777%, project A has the higher NPV (and is,
therefore, preferred).
Chapter 10 Capital Budgeting Techniques 217
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d. To obtain NPV profiles for projects A, B,
and C, begin by noting the NPV for all
three at a zero discount rate is the
undiscounted sum of project cash outflows
and inflows (NPVA = $40,000, NPVB =
$57,500, and NPVC = $52,500). Part b.
provides the NPVs for all three projects at a
13% discount rate. Part c. and the definition
of IRR indicate the discount rates at which
the NPV for all three projects is zero. The
NPV profiles are lines connecting these
three points for each project.
e. Project rankings:
Payback:
1 – Project A
NPV:
1 – Project B
IRR:
1 – Project A
P10-25 All techniques with NPV profile—mutually exclusive projects (LG 2, 3, 4, 5, 6; Challenge)
a. Payback period:
Project A
Initial investment = $80,000
Cash inflows in year 1 + year 2 + year 3 = $60,000
a row or column. If, for example, CF1 to CF5 appear in column A, rows 1 through 5, the present
value of cash inflows = NPV(A1:A5) = $83,659.68. In step two, subtract project cost from the
present value of cash inflows to find project NPV: NPVA = $83,659.68 – $80,000 = $3,659.68.
218 Zutter/Smart • Principles of Managerial Finance Brief, Eighth Edition
Project B
Project B: To use the IRR command in Excel, start by putting cash outflows and inflows in
adjacent cells starting with project cost expressed as a negative number. If, for
example, all cash flows are placed in the first six columns of row A:
Proper syntax is: =IRR(A1:F6) = 15.24%.
d. To find the NPV profiles for projects A and B, begin by generating a set of points representing
5.00% 26,126.73$ 14,942.15$
13.86765% 1,660.45$ 1,660.45$
14.61% -$ 750.15$
13.86765%, projects A and B have
the same NPV ($1,660.45)
13.86765% to 14.61%, both projects are profitable, but project B has the higher
NPV and is more attractive. Project A is more attractive at lower interest rates
because a greater percentage of its cash flows occur in later years.
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P10-26 Integrative—Multiple IRRs (LG 6; Basic)
a. Calculating the payback period for this project is difficult because of its unusual pattern of cash
flows. For example, there is no initial cash outflow; the cash flow in year 0 is an inflow. Outflows
occur in years 1 and 3. After 2 years, the project’s outflows are greater than its inflows, but that
reverses in year 3. Oscillating cash flows (positive-negative-positive-negative-positive)
NPV (13%) 1 2
IRR 2 1
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IRR= 15.95% IRR= 17.34%
NPV and IRR
The NPV decision criterion indicates both lathes are acceptable because NPVA and NPVB > 0. Lathe A
ranks ahead of B because of its larger NPV. IRR is the discount rate that makes project NPV = 0 for the
N
PV $58.13 $43.48
IRR 15.95% 17.34%
Rank 2 1
be excluded from the ranking of admissible
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434.00$ 237.00$
58.13$ 43.48$
-$ 13.08$
(25.07)$ -$
0.000%
15.950%
17.340%
13.000%
56.5% of cash inflows occur in years 4 and 5, compared with 49.1% for Lathe B. Changes in the
discount rate, other things equal, have a larger impact on the NPVs of projects with greater cash flows in
later years. For example, at a discount rate of 15.95%, NPVA = $0 and NPVB = $13.08. But as the rate
falls, NPVA rises faster than NPVB. As a result, NPVs are equal at 14.504%, and NPVA > NPVB at 13%.
Spreadsheet Exercise
Group Exercise
This assignment builds on the long-term investment projects in the previous chapter. Because students were
required to estimate relevant cash flows before reading this chapter, some numbers may have to be altered to
ensure each project has sensible payback periods. Allowing students to revisit previous estimates should make
their numbers more realistic and easier to work with.
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