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Capital Budgeting Techniques
“These hieroglyphics have evidently a meaning. If it is a
purely arbitrary one, it may be impossible for us to solve
it. If, on the other hand, it is systematic, I have no doubt
that we shall yet get to the bottom of it.”
SHERLOCK HOLMES
IN THE ADVENTURE OF THE DANCING MEN
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ANSWERS TO QUESTIONS
1. The time value of money refers to the fact that money has an opportunity cost, i.e., its
reinvestment rate. Given a positive interest rate, a dollar invested today will yield more than
2. If the payback period is used as the criterion for assigning priorities to investment projects,
3. It is often the case that larger projects will provide greater absolute dollar increases in the
value of the firm than smaller projects, simply because of the scale of the projects. This is
4. The internal rate of return (IRR) is the discount rate that makes the present value of the
benefits generated by a project equal to the investment. The net present value (NPV) is the
5. The payback period is unsound because the time value of money is ignored. Also, the cash
flows after payback are ignored. Finally, the payback period of, say, three years may or may
6. A project is mutually exclusive with another if acceptance of one, rules out acceptance of the
7. If the use of capital budgeting, techniques is widespread, capital will be allocated to the
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8. Capital rationing is done to facilitate the approval process. A division may be given an
annual budget for smaller projects, with larger projects having to be approved on a project-
9. Problems may result if the reinvestment rate available to the company differs sharply from
the internal rate of return (usually it is lower then the IRR), and the life of the project is
10. Yes, it should bother you. For a conventional project (i.e., a project whose cash-flow stream
changes signs only once), if the discounted payback period is less than the projects useful
life, the project will have a positive net present value (NPV). The projects NPV would, in
The discounted payback period method, overcomes one shortcoming of the traditional
payback period method. It accounts for the time value of money (and risk) by discounting
The NPV method holds several advantages over the discounted payback period method. For
SOLUTIONS TO PROBLEMS
1. Payback period (PBP):
PROJECT A
YEAR Cash Flows Cumulative Inflows
0 ($9,000) (–b)
–
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition, Instructor’s Manual
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PROJECT B
YEAR Cash Flows Cumulative Inflows
0 ($12,000)(–b)
– –
PROJECT A
YEAR
Cash Flows
Present Value
Discount Factor
(15%)
Present
Value
0 $(9,000) 1.000 $ (9,000)
*(Note: using a computer, rather than a present value table, we get $346.)
PROJECT B
YEAR
Cash Flows
Present Value
Discount Factor
(15%)
Present
Value
0 $(12,000) 1.000 $(12,000)
Profitability index:
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2. The payback method (i) ignores cash flows occurring after the expiration of the payback
3. a. 7.18 percent
b. Required return NPVA NPVB
0% $2,000 $4,000
5 1,546 2,936
10 1,170 2,098
c.
d. The superior project will be the one having the highest NPV at the required rate of
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition, Instructor’s Manual
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5. Cash Flows:
Project A
Savings $8,000 $8,000 $8,000 $8,000 $8,000 $8,000 $8,000
Depr. (5,600) (8,960) (5,376) (3,226) (3,225) (1,613) 0
a.
PROJECT A
YEAR Cash Flows Cumulative Inflows
0 ($28,000) (–b)
- -
PBP = a + (b – c) / d
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PROJECT B
Year Cash Flows Cumulative Inflows
0 ($20,000)(–b)
- -
PBP = a + (b – c) / d
b.
PROJECT A
YEAR
Cash Flows
Present Value
Discount Factor
(14%)
Present
Value
0 $(28,000) 1.000 $(28,000)
1 7,184 .877 6,300
*(Note: using a computer, rather than a present value table, we get $1,358.51.)
Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition, Instructor’s Manual
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© Pearson Education Limited 2008
PROJECT B
YEAR
Cash Flows
Present Value
Discount Factor
(14%)
Present
Value
0 $(20,000) 1.000 $(20,000)
1 4,660 .877 4,087
c. PI project A = $29,355/$28,000 = 1.05
d. IRR project A = 15.68 percent
6. Relevant cash flows:
0
a. Initial cash
outflow ($60,000)
1 2 3 4 5
b. Savings $20,000 $20,000 $20,000 $20,000 $20,000
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Year
Cash flow
Present value discount
factor (15%)
Present
value
0 $(60,000) 1.000 $(60,000)
The net present value of the project at 15 percent = – $962. The project is not acceptable.
7. a. Relevant cash flows:
0
(a) Initial cash
outflow ($60,000)
1 2 3 4 5
(b) Savings $20,000 $21,200 $22,472 $23,820 $25,250
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YEAR
CASH FLOW
PRESENT VALUE
DISCOUNT FACTOR
(15%)
PRESENT
VALUE
0 $(60,000) 1.000 $(60,000)
Net present value of project at 15 percent = $3,582
The project is now acceptable wherein before it was not. This assumes that the discount rate
is as same as before, 15 percent, and does not vary with inflation.
b. Cash outflow at time 0 = $60,000 + $10,000 = $ –70,000
8. a. Selecting those projects with the highest profitability index values would indicate the
following:
Project Amount PI Net Present Value
1 $500,000 1.22 $110,000
b. No. The resort should accept all projects with a positive NPV. If capital is not available
