By HMAN at 10:04 pm, Nov 16, 2007
By HMAN at 10:04 pm, Nov 16, 2007
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ANSWERS TO QUESTIONS
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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 that one dollar in the future. Thus, capital budgeting systems such as payback, which equate the bird in the hand with one in the bush (rather than more than one) do not accurately reflect either the investment opportunities of society, or a shareholder preference for current, rather than future, consumption. As such, they are nonoptimal.
2. If the payback period is used as the criterion for assigning priorities to investment projects, the highest priority will be assigned to projects with the shortest payback period. Funds available for investment may be unavailable for long-term projects if short-term projects are acquired first.
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 not a problem for ranking projects unless the firm may be faced with a capital rationing constraint. For example, when faced with a single-period constraint, profitability index rankings will prove more useful in project selection.
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 174 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 difference between the present value of the benefits discounted at the required return (or cost of capital) and the investment. One essential difference between the two approaches is the implied rate of return on the reinvestment of the cash flows. The IRR assumes that the cash flows are reinvested at the IRR while the NPV assumes reinvestment at the required rate of return. Under conditions of capital rationing, or mutually exclusive projects, and of sharply rising cost of capital, this difference is very important since only one assumption is correct. In addition, problems in rankings can occur because of differences in the scale of investment and project life.
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 not be adequate to satisfy a cost of capital of, say, 10 percent. It is a popular profitability measure because of its simplicity and practicality.
In a limited sense, the payback is a measure of risk. It emphasizes short-term cash flows that are important for small growing concerns. It emphasizes those cash flows that can be predicted with greatest accuracy. When used in conjunction with the NPV method, the payback can improve the decision-making process.
6. A project is mutually exclusive with another if acceptance of one rules out acceptance of the other. A dependent or contingent project depends on the acceptance of another project before it can be accepted.
7. If the use of capital budgeting techniques is widespread, capital will be allocated to the most efficient uses in society. Savings in the economy will be channeled to the most promising investment opportunities. As a result, economic growth and want satisfaction will be maximized. All of this depends on the accurate measurement of the benefits to be realized from an investment.
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-by-project basis. In other words, capital rationing may not apply to all projects, but only to smaller ones. Beyond the desire to facilitate the administration of capital budgeting, many companies ration capital because they do not want to go to the external market for financing. While this is suboptimal if projects are available that provide returns in excess of those required, we should recognize that this reason for capital rationing frequently prevails.
9. Problems may result if the reinvestment rate available to the
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 176 it is lower then the IRR), and the life of the project is fairly long. For example, we should not be overly concerned with a three- year project where the IRR is 16 percent but the reinvestment rate is only 13 percent. However, we should be concerned if the IRR of a 20-year project is 32 percent but the reinvestment rate is only 13 percent.
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 fact, be equal to the present value of all cash flows occurring after the projects discounted payback period.
If we reject this independent project, we would not be maximizing the value of the firm. Thus, if a firm not subject to capital rationing sets a single maximum discounted payback period as a cutoff for all independent projects, it runs the real risk of rejecting long-lived, but still positive-NPV projects.
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 cash flows at the cost of capital. However, it fails to consider cash flows occurring after the expiration of the discounted payback period;
consequently, we cannot regard it as a measure of profitability.
In addition, the maximum acceptable discounted payback period, which serves as the cutoff standard, is a purely subjective choice.
The NPV method holds several advantages over the discounted payback period method. For example, the NPV method considers all cash flows for a project, reveals the absolute dollar value added to the firm by project acceptance, and handles correctly even unconventional cash-flow patterns.
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SOLUTIONS TO PROBLEMS
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1. Payback period (PBP):
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PROJECT A
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YEAR Cash Flows Cumulative Inflows ————————————————————————————————————————————
0 ($9,000)(-b) -- 1 5,000 $ 5,000 2(a) 4,000 9,000(c) 3 3,000(d) 12,000
————————————————————————————————————————————
PBP = a + (b - c)/d
= 2 + ($9,000 - $9,000)/$3,000 = 2 years
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PROJECT B
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YEAR Cash Flows Cumulative Inflows ————————————————————————————————————————————
0 ($12,000)(-b) -- 1 5,000 $ 5,000 2(a) 5,000 10,000(c) 3 8,000(d) 18,000
————————————————————————————————————————————
PBP = a + (b - c)/d
= 2 + ($12,000 - $10,000)/$8,000 = 2.25 years
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 178
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PROJECT A
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Present Value
Discount Factor Present YEAR Cash Flow (15%) Value
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0 $( 9,000) 1.000 $( 9,000) 1 5,000 .870 4,350 2 4,000 .756 3,024 3 3,000 .658 1,974 ————————
Net present value = $ 348*
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*(Note: using a computer, rather than a present value table, we get $346.)
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PROJECT B
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Present Value
Discount Factor Present YEAR Cash Flow (15%) Value
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0 $(12,000) 1.000 $(12,000) 1 5,000 .870 4,350 2 5,000 .756 3,780 3 8,000 .658 5,264 ————————
Net present value = $ 1,394*
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*(Note: using a computer, rather than a present value table, we get $1,389.)
Profitability index:
Project A = ($4,350 + $3,024 + $1,974)/$9,000 = 1.039 Project B = ($4,350 + $3,780 + $5,264)/$12,000 = 1.116
2. The payback method (1) ignores cash flows occurring after the expiration of the payback period, (2) ignores the time value of money, and (3) makes use of a crude acceptance criterion, namely, a subjectively determined cutoff point.
3. a) 7.18 percent b) 23.38 percent c) 33.18 percent
d) IRR = $130/$1,000 = 13 percent (a perpetuity)
4. a) The IRR for project A is 34.90 percent.
The IRR for project B is 31.61 percent.
b) Required return NPVA NPVB ——————————————— ———— ————
0% $2,000 $4,000
5 1,546 2,936
10 1,170 2,098
20 589 894
30 166 101
35 -3 -194
c) NPV
$4,000
3,000
2,000
1,000
0 5 10 15 20 25 30 35 40 Percent
A B
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 180 d) The superior project will be the one having the highest NPV
at the required rate of return. Below about 28 percent, B dominates; at about 28 percent and above, A dominates. We are assuming that the required rate of return is the same for each project and that there is no capital rationing.
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 PBT 2,400 (960) 2,624 4,774 4,775 6,387 8,000
Taxes (34%) 816 (326) 892 1,623 1,624 2,172 2,720 Cash flow
(Savings
- Taxes) 7,184 8,326 7,108 6,377 6,376 5,828 5,280
Project B
Savings $5,000 $5,000 $6,000 $6,000 $7,000 $7,000 $7,000 Depr. (4,000) (6,400) (3,840) (2,304) (2,304) (1,152) 0 PBT 1,000 (1,400) 2,160 3,696 4,696 5,848 7,000
Taxes (34%) 340 (476) 734 1,257 1,597 1,988 2,380 Cash flow
(Savings
- Taxes) 4,660 5,476 5,266 4,743 5,403 5,012 4,620
a) ————————————————————————————————————————————
PROJECT A
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YEAR Cash Flows Cumulative Inflows ————————————————————————————————————————————
0 ($28,000)(-b) -- 1 7,184 $ 7,184 2 8,326 15,510 3(a) 7,108 22,618(c) 4 6,377(d) 22,995
————————————————————————————————————————————
PBP = a + (b - c)/d
= 3 + ($28,000 - $22,618)/$6,377 = 3.84 years
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PROJECT B
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YEAR Cash Flows Cumulative Inflows ————————————————————————————————————————————
0 ($20,000)(-b) -- 1 4,660 $ 4,660 2 5,476 10,136 3(a) 5,266 15,402(c) 4 4,743(d) 20,145
————————————————————————————————————————————
PBP = a + (b - c)/d
= 3 + ($20,000 - $15,402)/$4,743 = 3.97 years
b)
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PROJECT A
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Present Value
Discount Factor Present YEAR Cash Flow (14%) Value
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0 $(28,000) 1.000 $(28,000) 1 7,184 .877 6,300 2 8,326 .769 6,403 3 7,108 .675 4,798 4 6,377 .592 3,775 5 6,376 .519 3,309 6 5,828 .456 2,658 7 5,280 .400 2,112 ————————
Net present value = $ 1,355*
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*(Note: using a computer, rather than a present value table, we get $1,358.51.)
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 182
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PROJECT B
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Present Value
Discount Factor Present YEAR Cash Flow (14%) Value
———————————————————————————————————————————————————————————————————
0 $(20,000) 1.000 $(20,000) 1 4,660 .877 4,087 2 5,476 .769 4,211 3 5,266 .675 3,555 4 4,743 .592 2,808 5 5,403 .519 2,804 6 5,012 .456 2,285 7 4,620 .400 1,848 ————————
Net present value = $ 1,598*
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*(Note: using a computer, rather than a present value table, we get $1,599.83.)
c) PI project A = $29,355/$28,000 = 1.05 PI project B = $21,598/$20,000 = 1.08
d) IRR project A = 15.68 percent IRR project B = 16.58 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 c. Depreciation,
new 19,998 26,670 8,886 4,446 0 ———————— ———————— ———————— ———————— ————————
d. Profit change before tax
(b) - (c) 2 (6,670) 11,114 15,554 20,000 e. Taxes
(d) x (38%) 1 (2,535) 4,223 5,911 7,600 ———————— ———————— ———————— ———————— ————————
f. Profit change after tax
(d) - (e) 1 (4,135) 6,891 9,643 12,400 g. Net cash flow
(f) + (c)
or (b) - (e) $19,999 $22,535 $15,777 $14,089 $12,400
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PRESENT VALUE
DISCOUNT FACTOR PRESENT YEAR CASH FLOW (15%) VALUE
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0 $(60,000) 1.000 $(60,000)
1 19,999 .870 17,399 2 22,535 .756 17,036 3 15,777 .658 10,381
4 14,089 .572 8,059 5 12,400 .497 6,163 ————————
Net present value = $ (962)
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Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 184 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 c. Depreciation,
new 19,998 26,670 8,886 4,446 0 ———————— ———————— ———————— ———————— ————————
d. Profit change before tax
(b) - (c) 2 (5,470) 13,586 19,374 25,250 e. Taxes
(d) x (38%) 1 (2,079) 5,163 7,362 9,595 ———————— ———————— ———————— ———————— ————————
f. Profit change after tax
(d) - (e) 1 (3,391) 8,423 12,012 15,655 g. Net cash flow
(f) + (c)
or (b) - (e) $19,999 $23,279 $17,309 $16,458 $15,655
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PRESENT VALUE
DISCOUNT FACTOR PRESENT YEAR CASH FLOW (15%) VALUE
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0 $(60,000) 1.000 $(60,000)
1 19,999 .870 17,399 2 23,279 .756 17,599 3 17,309 .658 11,389
4 16,458 .572 9,414 5 15,655 .497 7,781 ————————
Net present value = $ 3,582
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Net present value of project at 15 percent = $3,582
The project is now acceptable where before it was not. This assumes the discount rate is the same as before, 15 percent, and does not vary with inflation.
b) Cash outflow at time 0 = $60,000 + $10,000 = $ -70,000 Present value of cash inflows from Part (7a) = 63,582 Present value of $10,000 received at the
end of year 5 (working capital recovered)
$10,000(PVIF15%,5) = $10,000(.497) = 4,970 Net present value $ - 1,448
8. a) Selecting those projects with the highest profitability index values would indicate
Project Amount PI Net Present Value 1 $500,000 1.22 $110,000 3 350,000 1.20 70,000 ———————— ————————
$850,000 $180,000
However, utilizing "close to" full budgeting will be better.
Project Amount PI Net Present Value 1 $ 500,000 1.22 $110,000 4 450,000 1.18 81,000 ————————— ————————
$ 950,000 $191,000
b) No. The resort should accept all projects with a positive NPV. If capital is not available to finance them at the discount rate used, a higher discount rate should be used that more adequately reflects the costs of financing.
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 186 9. a)
Incremental Time 8% Amount of cash outflow: savings of
of cash discount ————————————————————————— Rockbuilt over outflow factor Rockbuilt Bulldog Bulldog truck
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0 1.000 $(74,000) $ (59,000) $(15,000) 1 .926 (2,000) (3,000) 1,000 2 .857 (2,000) (4,500) 2,500 3 .794 (2,000) (6,000) 4,000 4 .735 (2,000) (22,500) 20,500 5 .681 (13,000) (9,000) (4,000) 6 .630 (4,000) (10,500) 6,500 7 .583 (4,000) (12,000) 8,000 8 .540 5,000* (8,500)** 13,500 ————————— ——————————— —————————
Present value of
cash flows at 8% $(91,626) $(111,266) $ 19,637 ————————————————
* $4,000 maintenance cost plus salvage value of $9,000.
** $13,500 maintenance cost plus salvage value of $5,000.
The Rockbuilt bid should be accepted as the lower maintenance and rebuilding expenses more than offset its higher cost.
b)
Incremental Time 15% Amount of cash outflow: savings of
of cash discount ————————————————————————— Rockbuilt over outflow factor Rockbuilt Bulldog Bulldog truck
——————————————————————————————————————————————————————————————————
0 1.000 $(74,000) $ (59,000) $(15,000) 1 .870 (2,000) (3,000) 1,000 2 .756 (2,000) (4,500) 2,500 3 .658 (2,000) (6,000) 4,000 4 .572 (2,000) (22,500) 20,500 5 .497 (13,000) (9,000) (4,000) 6 .432 (4,000) (10,500) 6,500 7 .376 (4,000) (12,000) 8,000 8 .327 5,000* (8,500)** 13,500 ————————— ——————————— —————————
Present value of
cash flows at 15% $(87,770) $(98,130.5) $ 10,360.5 ————————————————
* $4,000 maintenance cost plus salvage value of $9,000.
** $13,500 maintenance cost plus salvage value of $5,000.
No. With a higher discount rate, more distant cash outflows become less important relative to the initial outlay. But, the lower maintenance and rebuilding expenses related to the Rockbuilt bid continue to more than offset its higher cost.
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 188 ________________________________________________________________________
SOLUTIONS TO SELF-CORRECTION PROBLEMS
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1. a. ——————————————————————————————————————————————————————————————
PRESENT VALUE
DISCOUNT FACTOR PRESENT YEAR CASH FLOW (15%) VALUE ——————————————————————————————————————————————————————————————
0 $ (700,000) 1.000 $(700,000)
1 (1,000,000) .870 (870,000) 2 250,000 .756 189,000 3 300,000 .658 197,400
4 350,000 .572 200,200 5-10 400,000 2.164* 865,600**
——————————
Net present value = $(117,800) ——————————————————————————————————————————————————————————————
* PVIFA of 5.019 for 10 years minus PVIFA of 2.855 for 4 years.
** Total for years 5-10.
As the net present value is negative, the project is unacceptable.
b. The internal rate of return is 13.21 percent. If the trial- and-error method were used, we would have the following:
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14% 14% 13% 13%
DISCOUNT PRESENT DISCOUNT PRESENT YEAR CASH FLOW FACTOR VALUE FACTOR VALUE
————————————————————————————————————————————————————————————————————————
0 $ (700,000) 1.000 $(700,000) 1.000 $(700,000) 1 (1,000,000) .877 (877,000) .885 (885,000) 2 250,000 .769 192,250 .783 195,750
3 300,000 .675 202,500 .693 207,900 4 350,000 .592 207,200 .613 214,550 5-10 400,000 2.302* 920,800** 2.452* 980,800**
—————————— —————————
Net present value $ (54,250) $ 14,000
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* PVIFA for 10 years minus PVIFA for 4 years.
** Total for years 5-10.
To approximate the actual rate, we interpolate between 13 and 14 percent as follows:
┌— ┌— .13 $ 14,000 —┐ —┐
│ X │ │ $14,000 │
.01 │ └— IRR 0 —┘ │ $68,250 │ │
└— .14 $(54,240) —┘
X $14,000 (.01) x ($14,000)
——— = ——————— Therefore, X = ——————————————————— = .0021 .01 $68,250 $68,250
and IRR = .13 + X = .13 + .0021 = .1321, or 13.21 percent. As the internal rate of return is less than the required rate of return, the project would not be acceptable.
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 190 c. The project would be acceptable.
d. Payback period = 6 years. (-$700,000 - $1,000,000 + $250,000 + $300,000 + $350,000 + $400,000 + $400,000 = 0)
2.
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PRESENT VALUE
DISCOUNT FACTOR PRESENT YEAR CASH FLOW (14%) VALUE
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0 $(404,424) 1.000 $(404,424)
1 86,890 .877 76,203 2 106,474 .769 81,879 3 91,612 .675 61,838
4 84,801 .592 50,202 5 84,801 .519 44,012 6 75,400 .456 34,382
7 66,000 .400 26,400 8 92,400 .351 32,432 —————————
Net present value = $ 2,924
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As the net present value is positive, the project is acceptable.
3.
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INVESTMENT PRESENT VALUE OF NET PROJECT REQUIRED FUTURE CASH FLOWS PRESENT VALUE
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1 $200,000 $290,000 $ 90,000
2 115,000 185,000 70,000 3 270,000 400,000 130,000 1,2 315,000 475,000 160,000 1,3 440,000 690,000 250,000 2,3 385,000 620,000 235,000 1,2,3 680,000 910,000 230,000
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Projects 1 and 3 should be chosen as they provide the highest net present value.
Van Horne and Wachowicz: Fundamentals of Financial Management, 12e 192
14
Risk and Managerial (Real) Options in Capital Budgeting
“Risk? Risk is our business. That’s what this starship is all about. That’s why we’re aboard her!”