Chapter 14 Capital Budgeting Decisions Solutions to Questions 14-1 Capital budgeting screening decisions concern whether a proposed investment project passes a preset hurdle, such as a 15% rate of return Capital budgeting preference decisions are concerned with choosing from among two or more alternative investment projects, each of which has passed the hurdle 14-2 The “time value of money” refers to the fact that a dollar received today is more valuable than a dollar received in the future simply because a dollar received today can be invested to yield more than a dollar in the future 14-3 Discounting is the process of computing the present value of a future cash flow Discounting gives recognition to the time value of money and makes it possible to meaningfully add together cash flows that occur at different times 14-4 Accounting net income is based on accruals rather than on cash flows Both the net present value and internal rate of return methods focus on cash flows 14-5 Discounted cash flow methods are superior to other methods of making capital budgeting decisions because they recognize the time value of money and take into account all future cash flows 14-6 Net present value is the present value of cash inflows less the present value of the cash outflows The net present value can be negative if the present value of the outflows is greater than the present value of the inflows 14-7 One simplifying assumption is that all cash flows occur at the end of a period Another is that all cash flows generated by an investment project are immediately reinvested at a rate of return equal to the discount rate 14-8 No The cost of capital is not simply the interest paid on long-term debt The cost of capital is a weighted average of the individual costs of all sources of financing, both debt and equity 14-9 The internal rate of return is the rate of return on an investment project over its life It is computed by finding the discount rate that results in a zero net present value for the project 14-10 The cost of capital is a hurdle that must be cleared before an investment project will be accepted In the case of the net present value method, the cost of capital is used as the discount rate If the net present value of the project is positive, then the project is acceptable because its rate of return is greater than the cost of capital In the case of the internal rate of return method, the cost of capital is compared to a project’s internal rate of return If the project’s internal rate of return is greater than the cost of capital, then the project is acceptable 14-11 No As the discount rate increases, the present value of a given future cash flow decreases For example, the present value factor for a discount rate of 12% for cash to be received ten years from now is 0.322, whereas the present value factor for a discount rate of 14% over the same period is 0.270 If the cash to be received © The McGraw-Hill Companies, Inc., 2010 20 Managerial Accounting, 13th Edition in ten years is $10,000, the present value in the first case is $3,220, but only $2,700 in the second case Thus, as the discount rate increases, the present value of a given future cash flow decreases 14-12 The internal rate of return is more than 14% since the net present value is positive The internal rate of return would be 14% only if the net present value (evaluated using a 14% discount rate) is zero The internal rate of return would be less than 14% if the net present value (evaluated using a 14% discount rate) is negative 14-13 The project profitability index is computed by dividing the net present value of the cash flows from an investment project by the investment required The index measures the profit (in terms of net present value) provided by each dollar of investment in a project The higher the project profitability index, the more desirable is the investment project 14-14 The payback period is the length of time for an investment to fully recover its initial cost out of the cash receipts that it generates The payback method is used as a screening tool for investment proposals The payback method is useful when a company has cash flow problems The payback method is also used in industries where obsolescence is very rapid 14-15 Neither the payback method nor the simple rate of return method considers the time value of money Under both methods, a dollar received in the future is weighed the same as a dollar received today Furthermore, the payback method ignores all cash flows that occur after the initial investment has been recovered © The McGraw-Hill Companies, Inc., 2010 21 Managerial Accounting, 13th Edition Exercise 14-1 (10 minutes) Item Year(s) Annual cost savings 1-8 Initial investment Net present value Now Cash Flow $7,000 4.968 $ 34,776 $(40,00 0) 1.000 (40,000) $ (5,224) Item Annual cost savings Initial investment Net cash flow Cash Flow $7,000 $(40,00 0) Present 12% Value of Facto Cash r Flows Years Total Cash Flows $ 56,000 (40,000) $ 16,000 © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Chapter 14 22 Exercise 14-2 (30 minutes) Annual savings in part-time help Added contribution margin from expanded sales (1,000 dozen × $1.20 per dozen) Annual cash inflows $3,800 1,200 $5,000 Factor of the internal Investment required = rate of return Annual cash inflow = $18,600 = 3.720 $5,000 Looking in Exhibit 14B-2, and scanning along the six-period line, we can see that a factor of 3.720 falls closest to the 16% rate of return The cash flows will not be even over the six-year life of the machine because of the extra $9,125 inflow in the sixth year Therefore, the above approach cannot be used to compute the internal rate of return in this situation Using trial-and-error or some other method, the internal rate of is 22%: Item Year(s) Initial investment Now Annual cash inflows 1-6 Salvage value Net present value Present Amount 22% Value of of Cash Facto Cash Flows r Flows $(18,600) 1.000 $(18,600) $5,000 3.167 $9,125 0.303 15,835 2,765 $ © The McGraw-Hill Companies, Inc., 2010 All rights reserved 23 Managerial Accounting, 13th Edition Exercise 14-3 (15 minutes) The equipment’s net present value without considering the intangible benefits would be: 20% Present Amount of Facto Value of Item Year(s) Cash Flows r Cash Flows Cost of the $(2,500,000 equipment Now ) 1.000 $(2,500,000) Annual cost savings 1-15 $400,000 4.675 1,870,000 Net present value $ (630,000) The annual value of the intangible benefits would have to be great enough to offset a $630,000 negative present value for the equipment This annual value can be computed as follows: Required increase in present value $630,000 = = $134,759 Factor for 15 years 4.675 © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Chapter 14 24 Exercise 14-4 (10 minutes) The project profitability index for each proposal is: Proposa l Number A B C D Net Present Value (a) $36,000 $38,000 $35,000 $40,000 Project Investmen Profitability Index t Required (a) ÷ (b) (b) $90,000 0.40 $100,000 0.38 $70,000 0.50 $120,000 0.33 The ranking is: Proposa l Number C A B D Project Profitability Index 0.50 0.40 0.38 0.33 Note that proposal D has the highest net present value, but it ranks lowest in terms of the project profitability index © The McGraw-Hill Companies, Inc., 2010 All rights reserved 25 Managerial Accounting, 13th Edition Exercise 14-5 (10 minutes) The payback period is determined as follows: Year 10 Investme nt $15,000 $8,000 Cash Inflow $1,000 $2,000 $2,500 $4,000 $5,000 $6,000 $5,000 $4,000 $3,000 $2,000 Unrecovered Investment $14,000 $20,000 $17,500 $13,500 $8,500 $2,500 $0 $0 $0 $0 The investment in the project is fully recovered in the 7th year To be more exact, the payback period is approximately 6.5 years Because the investment is recovered prior to the last year, the amount of the cash inflow in the last year has no effect on the payback period © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Chapter 14 26 Exercise 14-6 (10 minutes) This is a cost reduction project, so the simple rate of return would be computed as follows: Operating cost of old machine Less operating cost of new machine Less annual depreciation on the new machine ($120,000 ÷ 10 years) Annual incremental net operating income $ 30,000 12,000 Cost of the new machine Scrap value of old machine Initial investment $120,000 40,000 $ 80,000 12,000 $ 6,000 Simple rate = Annual incremental net operating income of return Initial investment = $6,000 = 7.5% $80,000 © The McGraw-Hill Companies, Inc., 2010 All rights reserved 27 Managerial Accounting, 13th Edition Exercise 14-7 (15 minutes) The payback period is: Payback period = Investment required Annual net cash inflow = ¥432,000 = 4.8 years ¥90,000 No, the equipment would not be purchased because the payback period (4.8 years) exceeds the company’s maximum payback time (4.0 years) The simple rate of return would be computed as follows: Annual cost savings ¥90,000 Less annual depreciation (Ơ432,000 ữ 12 36,000 years) Annual incremental net operating income ¥54,000 Simple rate of return = = Annual incremental net operating income Initial investment ¥54,000 = 12.5% ¥432,000 No, the equipment would not be purchased because its 12.5% rate of return is less than the company’s 14% required rate of return © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Chapter 14 28 Exercise 14-8 (10 minutes) Amount of Cash Flows Item Year(s) Project X: Initial investment Now $(35,000) Annual cash inflow 1-10 $9,000 Net present value Project Y: Initial investment Single cash inflow Net present value Now 10 18% Factor 1.000 4.494 Present Value of Cash Flows $(35,000) 40,446 $ 5,446 $(35,000) 1.000 $150,000 0.191 $(35,000) 28,650 $( 6,350) Project X should be selected Project Y does not provide the required 18% return, as shown by its negative net present value © The McGraw-Hill Companies, Inc., 2010 All rights reserved 29 Managerial Accounting, 13th Edition Exercise 14A-2 (10 minutes) Amount of Cash Flows 18% Investme Investment Year nt A B Factor $3,000 $12,000 0.847 $6,000 $9,000 0.718 $9,000 $6,000 0.609 $12,000 $3,000 0.516 Present Value of Cash Flows Investment Investme A nt B $ 2,541 $10,164 4,308 6,462 5,481 3,654 6,192 1,548 $18,522 $21,828 Investment project B is best © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14A 80 Exercise 14A-3 (10 minutes) The present value of the first option is $150,000, since the entire amount would be received immediately The present value of the second option is: Annual annuity: $14,000 × 7.469 (Exhibit 14B-2) $104,566 Lump-sum payment: $60,000 × 0.104 (Exhibit 14B-1) 6,240 Total present value $110,806 Thus, Julie should accept the first option, which has a much higher present value On the surface, the second option appears to be a better choice because it promises a total cash inflow of $340,000 over the 20year period ($14,000 × 20 = $280,000; $280,000 + $60,000 = $340,000), whereas the first option promises a cash inflow of only $150,000 However, the cash inflows under the second option are spread out over 20 years, causing the present value to be far less © The McGraw-Hill Companies, Inc., 2010 All rights reserved 81 Managerial Accounting, 13th Edition Exercise 14A-4 (10 minutes) From Exhibit 14B-2, the factor for 16% for periods is 4.344 The computer system should be purchased only if its net present value is positive This will occur only if the purchase price is less: $7,000 × 4.344 = $30,408 From Exhibit 14B-2, the factor for 20% for periods is 3.837 Therefore, the maximum purchase price would be: $7,000 ì 3.837 = $26,859 â The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14A 82 Exercise 14A-5 (10 minutes) From Exhibit 14B-2, the factor for 12% for 20 periods is 7.469 Thus, the present value of Mr Ormsby’s winnings is: $80,000 × 7.469 = $597,520 Whether or not it is correct to say that Mr Ormsby is the state’s newest millionaire depends on your point of view He will receive more than a million dollars over the next 20 years; however, he is not a millionaire as shown by the present value computation above, nor will he ever be a millionaire if he spends his winnings rather than investing them © The McGraw-Hill Companies, Inc., 2010 All rights reserved 83 Managerial Accounting, 13th Edition Exercise 14A-6 (10 minutes) From Exhibit 14B-1, the factor for 10% for periods is 0.621 Therefore, the company must invest: $500,000 × 0.621 = $310,500 From Exhibit 14B-1, the factor for 14% for periods is 0.519 Therefore, the company must invest: $500,000 × 0.519 = $259,500 © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14A 84 Appendix 14C Income Taxes in Capital Budgeting Decisions Exercise 14C-1 (10 minutes) Management development program cost $100,000 Multiply by – 0.30 × 70% After-tax cost $ 70,000 Increased contribution margin Multiply by – 0.30 After-tax cash flow (benefit) $40,000 ì70% $28,000 The depreciation deduction is $210,000 ữ years = $30,000 per year, which has the effect of reducing taxes by 30% of that amount, or $9,000 per year © The McGraw-Hill Companies, Inc., 2010 All rights reserved 85 Managerial Accounting, 13th Edition Exercise 14C-2 (20 minutes) Annual cost of operating the present equipment $85,000 Annual cost of the new dishwashing machine: Cost for wages of operators $48,000 Cost for maintenance 2,000 50,000 Annual net cost savings (cash inflow) $35,000 The net present value analysis would be as follows: Year(s ) (2) Tax Effect (1) Items and Computations Amount Cost of the new dishwashing $(140,00 machine Now 0) — Annual net cost savings (above) 1-12 $35,000 – 0.30 Depreciation deductions* 1-7 $20,000 0.30 Cost of the new water jets $(15,000) – 0.30 Salvage value of the new machine 12 $9,000 – 0.30 Net present value (1) × (2) After-Tax Cash Flows $(140,000 ) $24,500 $6,000 $(10,500) 14% Facto r 1.000 5.660 4.288 0.456 $6,300 0.208 Present Value of Cash Flows $(140,000 ) 138,670 25,728 (4,788) 1,310 $ 20,920 *$140,000 ÷ years = $20,000 per year Yes, the new dishwashing machine should be purchased © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14C 86 Exercise 14C-3 (20 minutes) Items and Computations Project A: Year(s ) Investment in heavy trucks Now Annual net cash inflows 1-9 Depreciation deductions* 1-5 Salvage value of the trucks Net present value (1) Amount (2) Tax Effect (1) × (2) After-Tax Cash 12% Flows Factor Present Value of Cash Flows $(130,00 0) — $(130,000) 1.000 $(130,000) $25,000 – 0.30 $17,500 5.328 93,240 $26,000 0.30 $7,800 3.605 28,119 $15,000 – 0.30 $10,500 0.361 3,791 $ (4,850) Project B: Investment in working $(130,00 capital Now 0) — $(130,000) 1.000 $(130,000) Annual net cash inflows 1-9 $25,000 – 0.30 $17,500 5.328 93,240 Release of working capital $130,000 — $130,000 0.361 46,930 Net present value $ 10,170 *$130,000 ữ years = $26,000 per year â The McGraw-Hill Companies, Inc., 2010 All rights reserved 87 Managerial Accounting, 13th Edition Problem 14C-4 (20 minutes) (1) Items and Computations Year(s) Amount $(350,00 Investment in the new trucks Now 0) Salvage from sale of the old trucks Now $16,000 Annual net cash receipts 1-7 $105,000 Depreciation deductions* 1-5 $70,000 Replacement of motors $(45,000) Salvage from the new trucks $18,000 Net present value (2) Tax Effect — – 0.30 – 0.30 0.30 – 0.30 – 0.30 (1) × (2) Present After-Tax Value of Cash 16% Cash Flows Factor Flows $(350,000 $(350,000 ) 1.000 ) $11,200 $73,500 $21,000 $(31,500) $12,600 1.000 4.039 3.274 0.552 0.354 11,200 296,867 68,754 (17,388) 4,460 $ 13,893 *$350,000 ÷ years = $70,000 per year Because the project has a positive net present value, the contract should be accepted © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14C 88 Problem 14C-5 (60 minutes) Items Buy the new trucks: Year(s ) Investment in the trucks Cash from the sale of the old trucks: Sale price received Tax savings from loss on sale* Now Annual cash operating costs Depreciation deductions ($650,000 ÷ years = $130,000 per year) Salvage value of the new trucks 1-7 Now 1-5 Net present value * (1) Amount $(650,00 0) (2) Tax Effect — (1) × (2 Present ) After12% Value of Tax Cash Facto Cash Flows r Flows $(650,00 $(650,00 0) 1.000 0) $85,000 — $85,000 1.000 85,000 $35,000 0.30 $10,500 0.893 9,377 $(110,00 0) – 0.30 $(77,000) 4.564 (351,428) $130,000 0.30 $60,000 – 0.30 $39,000 3.605 140,595 $42,000 0.452 18,984 $(747,47 2) $120,00 Book value of old trucks 85,00 Less sale price (above) $ Loss on the sale 35,000 © The McGraw-Hill Companies, Inc., 2010 All rights reserved 89 Managerial Accounting, 13th Edition © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14C 90 Problem 14C-5 (continued) Items and Computations Keep the old trucks: Year(s ) Repairs needed Annual cash operating costs Depreciation deductions Salvage value of the old trucks 1-7 1-2 Net present value Net present value in favor of keeping the old trucks (1) Amount (2) Tax Effect $(170,00 0) – 0.30 $(200,00 0) – 0.30 $60,000 0.30 $15,000 – 0.30 (1) × (2 Present ) After12% Value of Tax Cash Facto Cash Flows r Flows $(119,00 0) $(140,00 0) $18,000 $10,500 $(106,26 0.893 7) 4.564 (638,960) 1.690 30,420 0.452 4,746 $(710,06 1) $ 37,41 © The McGraw-Hill Companies, Inc., 2010 All rights reserved 91 Managerial Accounting, 13th Edition Problem 14C-5 (continued) The solution by the incremental-cost approach below computes the net advantage (or disadvantage) of investing in the new trucks versus keeping the old trucks (1) × (2) Present (2) After-Tax Value of Year(s (1) Tax Cash 12% Cash Items and Computations ) Amount Effect Flows Factor Flows $(650,00 $(650,00 Investment in the new trucks Now 0) — $(650,000) 1.000 0) Repairs avoided on the old truck $170,000 – 0.30 $119,000 0.893 106,267 Cash from the sale of the old trucks: Sale price received Now $85,000 — $85,000 1.000 85,000 Tax savings from loss on sale $35,000 0.30 $10,500 0.893 9,377 Savings in annual cash operating costs ($200,000 – $110,000) 1-7 $90,000 – 0.30 $63,000 4.564 287,532 Depreciation deductions: Depreciation on new trucks 1-5 $130,000 0.30 $39,000 3.605 140,595 Depreciation forgone on old trucks 1-2 $(60,000) 0.30 $(18,000) 1.690 (30,420) Difference in salvage value in seven years ($60,000 – $15,000) $45,000 – 0.30 $31,500 0.452 14,238 $ Net present value (37,411) Because the net present value of investing in the new trucks rather than keeping the old trucks is negative, the new trucks should not be purchased © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14C 92 Problem 14C-6 (45 minutes) Items and Computations Alternative 1: Investment in the bonds Interest on the bonds (10% × $225,000) Maturity of the bonds (2) Tax Effect (1) × (2) After-Tax 8% Cash Facto Flows r Year(s) (1) Amount Now $(225,000 ) 1-12 12 $22,500 – 0.40 $13,500 $225,000 — $225,000 Net present value — Present Value of Cash Flows $(225,000 $(225,000 ) 1.000 ) 7.536 101,736 0.397 89,325 $ (33,939 ) © The McGraw-Hill Companies, Inc., 2010 All rights reserved 93 Managerial Accounting, 13th Edition Problem 14C-6 (continued) Items and Computations Alternative 2: Year(s ) Investment in the business Now Annual net cash receipts ($850,000 – $780,000 = $70,000) 1-12 Depreciation deductions: Year 1: 14.3% of $80,000 Year 2: 24.5% of $80,000 Year 3: 17.5% of $80,000 Year 4: 12.5% of $80,000 Year 5: 8.9% of $80,000 Year 6: 8.9% of $80,000 Year 7: 8.9% of $80,000 Year 8: 4.5% of $80,000 Payment to break the lease Recovery of working capital ($225,000 – $80,000 = $145,000) Net present value Net present value in favor of alternative 12 12 (1) Amount $(225,00 0) $70,000 (1) × (2 Present (2) ) After8% Value of Tax Tax Cash Facto Cash Effect Flows r Flows $(225,00 $(225,00 0) 1.000 0) — 1– 0.40 $42,000 7.536 316,512 $11,440 $19,600 $14,000 $10,000 $7,120 $7,120 $7,120 $3,600 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 1– $(2,000) 0.40 $145,000 — $4,576 $7,840 $5,600 $4,000 $2,848 $2,848 $2,848 $1,440 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 $(1,200) 0.397 $145,000 0.397 4,237 6,719 4,446 2,940 1,939 1,794 1,660 778 (476) 57,565 $173,114 $207,053 © The McGraw-Hill Companies, Inc., 2010 All rights reserved Solutions Manual, Appendix 14C 94 ... provide the required 18% return, as shown by its negative net present value © The McGraw-Hill Companies, Inc., 2010 All rights reserved 29 Managerial Accounting, 13th Edition Exercise 14-9 (10 minutes)... payback period is within the year payback required by Mr Sharkey © The McGraw-Hill Companies, Inc., 2010 All rights reserved 47 Managerial Accounting, 13th Edition Problem 14-24 (30 minutes) Average... 0.303 15,835 2,765 $ © The McGraw-Hill Companies, Inc., 2010 All rights reserved 23 Managerial Accounting, 13th Edition Exercise 14-3 (15 minutes) The equipment’s net present value without considering