506
PROBLEMS
P15–1
1. a. Average annual rate of return for both projects:
( )
2÷ 0$+000,800$
5÷ 000,330$
=
000,400$
000,66$
= 16.5%
b. Net present value analysis:
Present Value of
Net Cash Flows Net Cash Flows
Present Value of Distrib. Center Tracking Distrib. Center Tracking
Year $1 at 15% Expansion Technology Expansion Technology
2. The report to the capital investment committee can take many forms. The
report should, as a minimum, present the following points:
a. Both projects offer the same average annual rate of return.
507
P15–2
1. a. Cash payback period for both products: 2 years (the year in which accu-
mulated net cash flows equal $400,000), shown as follows:
Canadian Cycling European Hiking
Net Cash Cumulative Net Cash Cumulative
Year Flows Net Cash Flows Year Flows Net Cash Flows
b. Net present value analysis:
Present Value of Present Value of
Net Cash Flows Net Cash Flows
Canadian European Canadian European
Year $1 at 10% Cycling Hiking Cycling Hiking
1 0.909 $220,000 $188,000 $199,980 $170,892
2. The report can take many forms and should include, as a minimum, the fol-
lowing points:
a. Both products offer the same total net cash flows.
b. Both products offer the same cash payback period.
508
P15–3
1.
Product Line Expansion
Present Value Net Cash Present Value of
Year of $1 at 15% Flows Net Cash Flows
1 0.870 $ 490,000 $ 426,300
Computer System Upgrade
Present Value Net Cash Present Value of
Year of $1 at 15% Flows Net Cash Flows
1 0.870 $350,000 $ 304,500
Internet Bill-Pay
Present Value Net Cash Present Value of
Year of $1 at 15% Flows Net Cash Flows
1 0.870 $224,000 $ 194,880
P15–3, Concluded
2. Present Value Index =
Invested Be to Amount
Flows Cash Net of ValuePresent Total
3. The computer system upgrade has the largest present value index. Although
the product line expansion has the largest net present value, it returns less
510
P15–4
1. a. Radio Station
Annual net cash flows (at the end of each of 4 years) …………… $ 560,000
Present value of an annuity of $1 at 10% for 4 years (Exhibit 2) × 3.170
Present value of annual net cash flows ………………………………… $ 1,775,200
Less amount to be invested ………………………………………………… 1,598,800
Net present value ………………………………………………………………… $ 176,400
TV Station
b. Present Value Index =
Invested Be to Amount
Flows Cash Net of ValuePresent Total
2. a. Present Value Factor for an Annuity of $1 =
Flows Cash Net Annual
Invested Be to Amount
Radio Station:
= 2.855
TV Station:
000,120,1$
440,401,3$
= 3.037
P15–4, Concluded
3. By using the internal rate of return method, all proposals are placed on a
common basis. Also, by using the internal rate of return method, it can be
P15–5
1. Net present value analysis:
Site A
Annual net cash flows (at the end of each of 6 years) ………………… $ 400,000
Present value of an annuity of $1 at 20% for 6 years (Exhibit 2) …. × 3.326
Site B
Annual net cash flows (at the end of each of 4 years) ………………… $ 500,000
2. Net present value analysis:
Present Value of
Present Value of Net Cash Flows Net Cash Flows
Year $1 at 20% Site A Site B Site A Site B
1 0.833 $ 400,000 $ 500,000 $ 333,200 $ 416,500
2 0.694 400,000 500,000 277,600 347,000
3 0.579 400,000 500,000 231,600 289,500
4 0.482 400,000 500,000 192,800 241,000
4 (residual value) 0.482 300,000 0 144,600 0
3. To: Investment Committee
Both Sites A and B have a positive net present value. This means that both
projects meet our minimum expected return of 20% and would be acceptable
513
P15–6
1. Proposal Sierra: 3 years and 6 months cash payback period, as follows:
Net Cash Cumulative
Year Flows Net Cash Flows
1 $250,000 $250,000
2 250,000 500,000
3 250,000 750,000
6 months* 100,000 850,000
*The net cash flows required is $100,000 out of $400,000 in Year 3 or 1/4. Thus,
1/4 of 12 months is 3 months.
Proposal Uniform: 2 years and 9 months cash payback period, as follows:
Net Cash Cumulative
Year Flows Net Cash Flows
1 $200,000 $200,000
2 200,000 400,000
9 months* 150,000 550,000
514
P15–6, Continued
2. Proposal Sierra: 9.4% average rate of return, determined as follows:
( )
2÷0$+000,850$
5÷000,200$
=
000,425$
000,40$
= 9.4% (Rounded)
Proposal Tango: 27.3% average rate of return, determined as follows:
( )
2÷0$+000,380$
5÷000,140$
515
P15–6, Continued
3. Of the four proposed investments, only Proposals Tango and Uniform meet
the company’s requirements, as the following table indicates:
Cash Payback Average Rate Accept for
4.
Proposal Tango
Present Value Net Cash Present Value of
Year of $1 at 12% Flows Net Cash Flows
1 0.893 $ 560,000 $ 500,080
2 0.797 540,000 430,380
Proposal Uniform
Present Value Net Cash Present Value of
Year of $1 at 12% Flows Net Cash Flows
1 0.893 $200,000 $178,600
2 0.797 200,000 159,400
P15–6, Concluded
5. Present Value Index =
Invested Be toAmount
Flow CashNet of luePresent Va Total
6. Based on the net present value, the proposals should be ranked as follows:
Proposal Tango: $330,800
Proposal Uniform: $159,660
7. Based on the present value index (the amount of present value per dollar
8. The present value indexes indicate that although Proposal Tango has the
larger net present value, it is not as attractive as Proposal Uniform in terms of
the amount of present value per dollar invested. Proposal Tango requires the
CASES
Case 15–1
The plant manager wants a project to become accepted and places pressure
on the analyst to come up with the “right numbers.” Zuhair is right when he
states that the net present value analysis has many assumptions and room for
interpretation. Many use this room for interpretation to work the numbers until
they satisfy the minimum return (hurdle) rate. In fact, some analysts state that
they start with the hurdle rate and work back into the numbers. Clearly, this is not
what should be expected of Erin.
This very difficult issue revolves around the nature of ethical dilemmas. Erin has
brief tenure with the organization. Erin has very little organizational clout and
could easily find her career short-circuited by crossing Zuhair. It might be tempt-
ing for Erin to slide on this one—after all, who would know? If the project is even-
tually a failure, it’s unlikely that the decision would come back to haunt Erin.
Much time will have passed, and Erin will likely be in another job in the company.
The decision to confront Zuhair has immediate repercussions. This is the heart of
real world ethical dilemmas. The dilemma occurs when the ethical decision has
grave short-term consequences (Zuhair short-circuits the career) and few seem-
ingly long-term rewards (no one sees the ethical decision), while the unethical
decision looks appealing in the short term (Zuhair is my friend) and potentially
safe in the long term (who’s going to find out?). The ethical management ac-
518
Case 15–2
1. Annual salary …………………………………………………………………… $ 50,000
Present value of $1 annuity for 10 years at 10% ………………… × 6.145
2. Annual tuition at the beginning of the graduate year …………. $ (15,000)
Annual salary …………………………………………………………………… $ 65,000
Present value of $1 annuity for 9 years at 10% ………………….. × 5.759
Present value salary to end of graduate year …………………….. $ 374,335
Present value of $1 for 1 year at 10% ………………………………… × 0.909
0 1 2 3 4 5 6 7 8 9 10
($15,000) $65,000 $65,000 $65,000 $65,000 $65,000 $65,000 $65,000 $65,000 $65,000
$340,271 ($65,000 5.759) 0.909
$325,271
3. Present value of graduate option………………………………………. $325,271
Present value of undergraduate option ……………………………… 307,250
Net benefit of graduate option ………………………………………….. $ 18,021
519
Case 15–3
1. Since all the net cash flows are incurred in the local economy under this
assumption, it is likely that the internal rate of return of the new plant will
decline. This is because the cash profits earned on the plant will be less in
2. If the plant produced for export only, then the expenses would be incurred in
local currency, while the revenues would be earned in U.S. dollars. This could
work in favor of the project because the expenses in U.S. dollar terms would
decline. For example, if the local wages were 16 units of local currency per
Case 15–4
In all three companies, the executives indicate that financial investment analysis
plays a minor role in the selection of projects. The reason is that all three compa-
nies deal with products that have highly uncertain future cash flows. Thus, any
attempt at a financial investment analysis could be highly suspect. Instead, these
Case 15–5
1. (All amounts are in millions.)
20Y5 cash flows:
Gross ticket sales …………………………………………………. $ 240
Production cost ……………………………………………………. (200)
Net present value:
Present Value Net Cash Present Value of
Year of $1 at 20% Flows Net Cash Flows
20Y5 0.833 $(40) $ (33)
20Y6 0.694 50 35
20Y7 0.579 25 14
20Y8 0.482 10 5
Net present value ………………………………………………………. $ 21
2. Even though the film lost money at the box office, the project was financially
Case 15–6
This activity could be assigned individually or in groups. This activity has the stu–
dent(s) perform a capital investment analysis for a printer/copier/scanner/fax
machine, using information available to them on the Internet and from local busi-
nesses. The actual answer depends on the actual numbers determined by the stu–