CHAPTER 16 Capital Expenditure Decisions ANSWERS TO REVIEW QUESTIONS 16-5 (1) The decision rule used to accept or reject an investment proposal under the netpresent-value method is stated as follows: Accept the proposal if the net present value is zero or positive. (2) The decision rule used to accept or reject an investment proposal under the internalrate-of-return method is as follows: Accept the investment proposal if its internal rate of return is equal to or greater than the hurdle rate. 16-8 Four assumptions underlying discounted-cash-flow analysis are as follows: (1) In the present-value calculations, all cash flows are treated as though they occur at year end. (2) Discounted-cash-flow analyses treat the cash flows associated with an investment project as though they were known with certainty. (3) Both the NPV and IRR methods assume that each cash inflow is immediately reinvested in another project that earns a return for the organization. In the NPV method, each cash inflow is assumed to be reinvested at the same rate used to compute the project’s NPV. In the IRR method, each cash inflow is assumed to be reinvested at the same rate as the project’s internal rate of return. (4) A discounted-cash-flow analysis assumes a perfect capital market. In a perfect capital market, money can be borrowed or lent at an interest rate equal to the cost of capital (or hurdle rate) used in the analysis. 16-18 The profitability index (PI) is defined as the present value of cash flows, exclusive of the initial investment, divided by the initial investment. Investment proposals sometimes are ranked by their profitability indexes, with a higher PI being ranked higher. Unfortunately, this method of ranking investment proposals suffers from some of the same drawbacks as other ranking methods. 16-21 There are two ways to define an investment project’s accounting rate of return: • Accounting rate of return = (average incremental revenue – average incremental expenses, including depreciation and income taxes) ÷ initial investment. • Accounting rate of return = (average incremental revenue – average incremental expenses, including depreciation and income taxes) ÷ average investment. The accounting rate of return and the internal rate of return on a capital project generally differ because the accounting rate of return calculation does not take into account the time value of money.
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SOLUTIONS TO EXERCISES EXERCISE 16-37 (25 MINUTES) 1.
The project’s payback period is 2.25 years, calculated as follows: After-Tax Cash Flows Year 1 ............................................................................................ $ 50,000 2 ............................................................................................ 45,000 st 10,000 (.25 × $40,000) 3 (1 quarter) ....................................................................... Total ..................................................................................... $105,000 Initial cost ............................................................................ $105,000
2.
The accounting rate of return is 18.1%, calculated as follows: Accounting rate of return
3.
=
average net income initial investment
=
$19,000 = 18.1% (rounded) $105,000
Net present value calculations: Year 0 1 2 3 4 5 Net present value
After-Tax Cash Flow $(105,000) 50,000 45,000 40,000 35,000 30,000
Discount Factor* 1.000 .862 .743 .641 .552 .476
Present Value $(105,000) 43,100 33,435 25,640 19,320 14,280 $ 30,775
*From Table III in Appendix A (r = .16).
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SOLUTIONS TO PROBLEMS PROBLEM 16-40 (30 MINUTES) 1.
Yes. This is a long-term decision, with cash flows that occur over a five-year period. Given that the cash flows have a “value” dependent on when they take place (e.g., cash inflows that occur in earlier years have a higher time value than cash inflows that take place in later years), discounting should be used to determine whether Community Challenges should outsource.
2.
Community Challenges is better off to manufacture the igniters. Outsource: Annual purchase (400,000 units x $62)……………….. $(24,800,000) Annuity discount factor (Table IV*: r = .14, n = 5)…… x 3.433 Net present value ………………………………………… $(85,138,400) Manufacture in-house: Annual variable manufacturing costs (400,000 units x $60)……………………………………………………. Annual salary and fringe benefits……………………… Total annual cash flow………………………………. Annuity discount factor (Table IV: r = .14, n = 5)…… Present value of annual cash flows…………………… New equipment (time 0)………………………………….. Repairs and maintenance: $4,500 x (3.433 – 1.647) (Table IV: r = .14, n = 3-5) …………………………… Equipment sale: $12,000 x .519 (Table III: r = .14, n = 5)……………………………………………………. Net present value………………………………………….
$(24,000,000) (95,000) $(24,095,000) x 3.433 $(82,718,135) (60,000) (8,037) 6,228 $(82,779,944)
Note: Depreciation is ignored because it is not a cash flow. *Discount factors from the tables in Appendix A. 3.
The company would be financially indifferent if the net present value (NPV) of the manufacture alternative equals the NPV of the outsource alternative. Thus: Let X = purchase price 3.433 x 400,000X = $82,779,944 1,373,200X = $82,779,944 X = $60.28 (rounded)
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PROBLEM 16-43 (50 MINUTES) 1.
See the following table.
2.
See the following table.
3.
See the following table.
4.
The administrator should recommend that the clinic be built, because its net present value is positive.
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PROBLEM 16-43 (CONTINUED) Type of Cash Flow 20x0 20x1 20x2 20x3 20x4 20x5 20x6 20x7 20x8 20x9 (1) Construction of clinic $(390,000) $(390,000) (2) Equipment purchase (150,000) (3) Staffing $(800,000) $(800,000) $(800,000) $(800,000) $(800,000) $(800,000) $(800,000) $(800,000) (4) Other operating costs (200,000) (200,000) (200,000) (200,000) (200,000) (200,000) (200,000) (200,000) (5) Increased charitable contributions 250,000 250,000 250,000 250,000 250,000 250,000 250,000 250,000 (6) Cost savings at hospital 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 (7) Cost of refurbishment (180,000) (9) Salvage value 290,000 Incremental cash flow $ 250,000 $ 250,000 $ 250,000 $ 70,000 $ 250,000 $ 250,000 $ 250,000 $ 540,000 $(390,000) $(540,000) Discount factor* × 1.000 × .893 × .797 × .712 × .636 × .567 × .507 × .452 × .404 × .361 Present value $ 199,250 $ 178,000 $ 39,690 $ 126,750 $ 113,000 $(390,000) $(482,220) $ 159,000 $ 101,000 $ 194,940 1444444444444444444442444444444444444444443 Sum=$239,410 Net present value
*Table III in Appendix A: r = .12.
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PROBLEM 16-51 (45 MINUTES)
1.
Net-present value analysis of the machine replacement: 20x1 Acquisition cost ........................................................ $(1,000,000) After-tax operating cost savings [$300,000 × (1 – .40)] ...............................................
20x2
20x3
20x4
20x5
$180,000
$180,000
$180,000
$180,000
Depreciation tax shield: Acquisition MACRS Tax Year Cost Percentage Rate 20x2: 20x3 20x4 20x5
$1,000,000 $1,000,000 $1,000,000 $1,000,000
× 33.33% × 44.45% × 14.81% × 7.41%
× .40 × .40 × .40 × .40
................ ................ ................ ................
133,320 177,800 59,240
Salvage value of old machine: Cash proceeds from sale ..................................... Gain on sale .......................................... $60,000 Tax rate .................................................. × .40 Tax on gain ........................................... $24,000 Total after-tax cash flow ...........................................
$
Discount factor (Table III in Appendix A) ...............
×
Present value ............................................................
$
Net present value ......................................................
60,000 (24,000) (964,00 0) 1. 000 (964,00 0)
$313,320 × . 893 * $279,795
$357,800 × . 797 * $285,167 Sum = $(95,368)
*Rounded. McGraw-Hill/Irwin 16-6
29,640
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$239,240 × . 712 * $170,339
$209,640 ×
. 636 $133,331 *
PROBLEM 16-51 (CONTINUED) 2.
The machine replacement’s internal rate of return is between 6% and 8%. The project’s net present value is positive if a 6% discount rate is used, but it is negative if an 8% discount rate is used.
Year 20x1 ................. 20x2 ................. 20x3 ................. 20x4 ................. 20x5 ................. Net present value 3.
Total After-Tax Cash Flow (from requirement 1) $(964,000) 313,320 357,800 239,240 209,640
6% Present Discount Value Factor (using 6%) 1.000 $(964,000) .943 295,461 .890 318,442 .840 200,962 .792 166,035 $ 16,900
8% Discount Factor 1.000 .926 .857 .794 .735
Present Value (using 8%) $(964,000) 290,134 306,635 189,957 154,085 $ (23,189)
The payback period on the machine replacement is between three and four years.
Year 20x2 .......................................... 20x3 .......................................... 20x4 .......................................... Subtotal .................................... 20x5 .......................................... Total ..........................................
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Total After-Tax Cash Inflow (from requirement 1) $ 313,320 357,800 239,240 $ 910,360< $964,000 = initial net cash outflow 209,640 $1,120,000> $964,000 = initial net cash outflow
© 2005 The McGraw-Hill Companies, Inc. 16-7
PROBLEM 16-51 (CONTINUED) 4.
With a salvage value of zero on the new machine, the machine replacement’s net present value is $(95,368). Thus, the after-tax discounted cash flow from the salvage of the new machine on December 31, 20x5 would have to exceed $95,368. Dividing by the year 4, 12% discount factor, the after-tax cash flow would have to exceed $149,950 ($95,368 ÷ .636, rounded). Let X denote the new machine’s salvage value on December 31, 20x5. Then the gain on sale will also be X, since the new machine will be fully depreciated. The tax on this gain will be .40X. Therefore, the following equation must hold: X – .40X
=
$149,950
.60X
=
$149,950
X
=
$249,917 (rounded)
Thus, the salvage value of the new machine must exceed $249,917 in order to turn the machine replacement into a positive net-present-value project. Check: Cash proceeds from sale of new machine .............................................. Gain on sale ....................................................................... $249,917 × .40 Tax rate ............................................................................... Tax on gain ......................................................................... $ 99,967 After-tax cash flow from sale ........................................... Discount factor (4 years, 12%) ......................................... Present value of cash flow from sale ..............................
$249,917 (99,967) $149,950 × .636 $ 95,368
Adding the $95,368 to the negative net present value calculated in requirement (1) of $(95,368), the new net present value is zero.
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PROBLEM 16-52 (35 MINUTES) 1.
(a) Mall restaurant: Net after-tax cash inflows ........................................................................... $ 50,000 × Annuity discount factor (r = .10, n = 20) ................................................ × 8.514 Present value of annual cash flows ........................................................... $425,700 Cash outflow at time 0 ................................................................................ 400,000 Net present value ......................................................................................... $ 25,700 (b) Downtown restaurant: Net after-tax cash inflows ........................................................................... $ 35,800 × Annuity discount factor (r = .10, n = 10) ................................................ × 6.145 Present value of annual cash flows ........................................................... $219,991 Cash outflow at time 0 ................................................................................ 200,000 Net present value ......................................................................................... $ 19,991
2.
Profitability index =
present value of cash flows, exclusive of initial investment initial investment
(a) Mall restaurant: Profitability index =
$425,700 = 1.06 (rounded) $400,000
(b) Downtown restaurant: Profitability index =
$219,991 = 1.10 (rounded) $200,000
3.
The mall site ranks first on NPV, but the downtown site ranks first on the profitability index.
4.
The two proposed restaurant projects have different lives, which makes it particularly difficult to rank them. It is not clear what will happen in years 11 through 20 if the downtown site is chosen.
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PROBLEM 16-53 (30 MINUTES) 1.
Payback period =
initial investment annual after - tax cash inflow
(a) Mall restaurant: Payback period =
$400,000 = 8 years $50,000
(b) Downtown restaurant: Payback period =
2.
Accounting rate of return =
$200,000 = 5.6 years (rounded) $35,800
⎛ average ⎞ ⎛ average incremental expenses ⎞ ⎟ ⎜ ⎟ ⎜ ⎜ incremental ⎟ − ⎜ (including depreciation and ⎟ ⎟ ⎜ revenue ⎟ ⎜ income taxes) ⎝ ⎠ ⎝ ⎠ initial investment
(a) Mall restaurant: Accounting rate of return =
$50,000 = 12.5% $400,000
(b) Downtown restaurant: Accounting rate of return =
$35,800 = 17.9% $200,000
3.
The owner’s criteria will lead to selection of the downtown site.
4.
Neither the payback period nor the accounting-rate-of-return method considers the time value of money. Moreover, the payback method ignores cash flows beyond the payback period. On the positive side, both methods can provide a simple means of screening a large number of investment proposals.
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PROBLEM 16-54 (35 MINUTES) 1. Payback period = 3 years* *Initial investment = $120,000 = (3)($40,000) = sum of net incremental cash flows during first 3 years.
2. Accounting rate of return (ARR) using initial investment: ARR = ($74,000* - $59,000†) / $120,000 = .125 *$74,000 =($70,000 + $72,000 + $74,000 + $76,000 + $78,000) / 5 †$59,000
= [$30,000 + $32,000 + $34,000 + $38,000 + $41,000 + (5)($24,000)] / 5
3. Accounting rate of return (ARR) using average investment: ARR = ($74,000* - $59,000*) / $60,000† = .25 *See requirement (2). †Average investment using straight-line depreciation = ($120,000
+ 0) / 2 = $60,000
4. Discounted-cash-flow methods take into account the time value of money, whereas the payback and accounting-rate-of-return methods do not. 5. No, this would not be ethical. The theater’s board is entitled to fair and objective information about the project. (Refer to the ethical standards for managerial accountants listed in Chapter 1 of the text, particularly the section entitled “Objectivity.”)
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