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P12-7 Personal Finance: Impact of inflation on investments (LG 2; Easy)
a. c.
Year
Investmen
t Cash
Flows
Current
NPV (a)
Higher
Inflation
NPV (b)
Lower
Inflation
NPV (c)
0
1
(40,000)
12,000
(40,000)
11,267.61
(40,000)
11,111.11
(40,000)
11,428.57
d. If the primary effect of inflation is to raise the discount rate, then NPV will fall. Of course, for
which case the relationship between changes in the inflation rate and NPV is less clear.
P12-8 Simulation (LG 2; Intermediate)
a. Ogden Corporation could use a computer simulation to generate the probability distribution for
NPV by randomly generating cash outflows and cash inflows based on the assumed
distribution (normal) and statistical parameters (mean, standard deviation) for these two inputs.
b. The advantages to computer simulations include the decision maker’s ability to view a
continuum of risk-return tradeoffs instead of a single-point estimate. The computer simulation,
however, is not feasible for risk analysis.
P12-9 Risk-adjusted discount rates: Basic (LG 4; Intermediate)
a.
Project E, with the highest NPV, is preferred.
b. RADRE 0.10 (1.80 (0.15 0.10)) 0.19 RADRG 0.10 (0.60
changes. Project G has the highest NPV in the risk-adjusted analysis and should, therefore, be
chosen.
P12-10 Risk-adjusted discount rates—Tabular (LG 4; Intermediate)
a. Project A
Upfront project cost = $20,000 Project B
Upfront project cost = $30,000
Number of years 5
Number of years 5
P12-11 Personal Finance: Mutually exclusive investment and risk (LG 4; Intermediate)
a. Number of years 6, cost of capital 8.5%, annual cash inflows $3,000;
b. Number of years 6, cost of capital 10.5%, annual cash inflows $3,800;
upfront project cost = $12,000
c. Using NPV as her guide, Lara should select the second investment with the higher NPV.
d. The second investment is riskier. The higher required return implies a higher risk factor.
P12-12 Risk-adjusted rates of return using CAPM (LG 4; Challenge)
a. rX 7% 1.2(12% 7%) 7% 6% 13%
rY 7% 1.4(12% 7%) 7% 7% 14%
NPV calculation for X:
NPV = Present value of cash inflows – Upfront project cost
NPV calculation for Y:
Number of years = 4, cost of capital = 14%
b. If a straight 12% discount rate is used for both projects, project Y has the higher NPV. But
when, RADRs are used to discount the cash flows, project X has the higher NPV. Because the
two projects have different levels of risk, the RADR approach is preferred.
P12-13 Risk classes and RADR (LG 4; Basic)
a. Project X
Number of years = 5, cost of capital (RADR) 22%
Solve for NPV $14.930.45
Project Y
Number of years = 5, cost of capital (RADR) 13%
Project Z
Number of years = 5, cost of capital (RADR) 15%, upfront project cost $310,000
b. Projects X and Y are acceptable with positive NPVs, while Project Z with a negative NPV is
not. Project X, with the higher NPV, should be undertaken.
P12-14 Unequal lives: ANPV approach (LG 5; Intermediate)
a. Machine A
Project cost (CF0) −$92,000, cash inflows (CF1-6) $12,000; number of years = 6;
and cost of capital 12%.
Solve for NPV $7,643.29
Rank Machine
3 A
Note: Machine A is not acceptable and can be rejected without any additional analysis.
b. Machine A
Number of years 6, cost of capital 12%, PV $42,663.11
Machine B
Number of years 4, cost of capital 12%, PV $6,646.58
c. Machine B should be acquired because it offers the highest ANPV. The ranking without
consideration of the difference in project lives puts Machine C on top.
P12-15 Unequal lives: ANPV approach (LG 5; Intermediate)
a. Project X
Cash flows: CF0 −$78,000, CF1 $17,000, CF2 $25,000, CF3 $33,000, CF4 $41,000
Cost of capital 14%
Cost of capital 14%
Solve for NPV $3,582.96 Rank Project
b. Project X
Number of periods 4, cost of capital 14%, PV $
c. Project Y should be acquired because it offers the highest ANPV. The ranking without
consideration of the difference in project lives puts project Z on top.
P12-16 Unequal lives: ANPV approach (LG 5; Intermediate)
a. Sell
Cash flows: project cost (CF0) −$200,000, CF1 $200,000, CF2 $250,000; and
cost of capital 12%. Solve for NPV $177,869.90
License
Rank Alternative
b. Sell
Number of years 2, cost of capital 12%, PV $
Solve for ANPV (annual payment equivalent project NPV) $105,245.28
License
c. Comparing NPVs of projects with unequal lives favors projects with cash flows over longer periods.
P12-17 NPV and ANPV decisions (LG 5; Challenge)
a. – b. Unequal-Life Decisions
Annualized Net Present Value (ANPV)
Samsung Sony
Cost
Annual Benefits
$(2,350)
$900
$(2,700)
$1,000
a. Cash flows: Upfront cost (CF0) −$2,350, CF1 $900, CF2 $900, CF3 $900 + $400
$1,300; and discount rate 9%. Solve for NPVSamsung $237.04.
b. Number of years 3, discount rate 9%, and PV $237.04.
d. Number of years 4, discount rate 9%, and PV $787.67. Solve for ANPVSony $243.13.
e. Richard and Linda should select the Sony set because its ANPV of $243.13 is greater than the
$93.64 ANPV of Samsung.
P12-18 Real options and the strategic NPV (LG 6; Intermediate)
a. Value of real options value of abandonment value of expansion value of delay
b. Because of the added value from the options, Rene should recommend acceptance of the
capital expenditures for the equipment.
c. In general this problem illustrates recognizing the value of real options can transform a project
P12-19 Capital rationing—IRR and NPV approaches (LG 6; Intermediate)
a. Rank by IRR
Project IRR Initial Investment Total Investment
A 17
D 16
Projects F, E, and G require a total investment of $4,500,000 and provide a total present value
b. Rank by NPV (NPV PV – Initial investment)
Project NPV Initial Investment
F $500,000 $2,500,00
0
A 400,000 5,000,000
C 300,000 2,000,000
Project A can be eliminated because, while it has an acceptable NPV, its initial investment
exceeds the capital budget. Projects F and C require a total initial investment of $4,500,000
c. The internal rate of return approach uses the entire $4,500,000 capital budget but provides
d. The firm should implement Projects B, F, and G, as explained in part c.
P12-20 Capital Rationing: NPV Approach (LG 6; Intermediate)
Project Initial investment NPV at 13% PV
A $300,000 $ 84,000 $384,000
B 200,000 10,000 210,000
C 100,000 25,000 125,000
b. The optimal group of projects is Projects C, F, and G, resulting in a total net present value of
found using the net present value approach.
P12-21 Ethics problem (LG 4; Challenge)
Student answers will vary. Some students might argue that companies should be held accountable
for any and all pollution that they cause. Other students may take the larger view that the appropriate
