1a. Net present value = $28,000 (5.216) $110,000 = $146,048 $110,000 = $36,048. = 3.93 years

Transcription

1 21-18 (25 min.) Capital budgeting methods, no income taxes. The table for the present value of annuities (Appendix A, Table 4) shows: 10 periods at 14% = a. Net present value = $28,000 (5.216) $110,000 = $146,048 $110,000 = $36,048 b. Payback period = $110,000 = 3.93 years $28,000 c. For a $110,000 initial outflow, the project generates $28,000 in cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 21.96%. d. Accrual accounting rate of return based on net initial investment: Net initial investment = $110,000 Estimated useful life = 10 years Annual straight-line depreciation = $110, = $11,000 Accrual accounting rate of return $ 28,000 $11,000 = $110,000 $17,000 = = 15.45% $110,000 e. Accrual accounting rate of return based on average investment: Average investment = ($110,000 + $0) / 2 = $55,000 Accrual accounting rate of return = $28,000 $11,000 $55,000 = 30.91%. 2. Factors City Hospital should consider include: a. Quantitative financial aspects. b. Qualitative factors, such as the benefits to its customers of a better eye-testing machine and the employee-morale advantages of having up-to-date equipment. c. Financing factors, such as the availability of cash to purchase the new equipment. 21-6

2 21-19 (35 min.) Capital budgeting, income taxes. 1a. Net after-tax initial investment = $110,000 Annual after-tax cash flow from operations (excluding the depreciation effect): Annual cash flow from operation with new machine $28,000 Deduct income tax payments (30% of $28,000) 8,400 Annual after-tax cash flow from operations $19,600 Income tax cash savings from annual depreciation deductions 30% $11,000 $3,300 These three amounts can be combined to determine the NPV: Net initial investment; $110, $(110,000) 10-year annuity of annual after-tax cash flows from operations; $19, , year annuity of income tax cash savings from annual depreciation deductions; $3, ,213 Net present value $ 9,447 b. Payback period = $110,000 ($19,600 + $3,300) = $110,000 $22,900 = 4.80 years 21-7

3 21-22 (30 min.) Payback and NPV methods, no income taxes. 1a. Payback measures the time it will take to recoup, in the form of expected future cash flows, the net initial investment in a project. Payback emphasizes the early recovery of cash as a key aspect of project ranking. Some managers argue that this emphasis on early recovery of cash is appropriate if there is a high level of uncertainty about future cash flows. Projects with shorter paybacks give the organization more flexibility because funds for other projects become available sooner. Strengths Easy to understand One way to capture uncertainty about expected cash flows in later years of a project (although sensitivity analysis is a more systematic way) Weaknesses Fails to incorporate the time value of money, unless discounted payback is used Does not consider a project s cash flows after the payback period 1b. Project A Outflow, $3,000,000 Inflow, $1,000,000 (Year 1) + $1,000,000 (Year 2) + $1,000,000 (Year 3) + $1,000,000 (Year 4) Payback = 3 years Project B Outflow, $1,500,000 Inflow, $400,000 (Year 1) + $900,000 (Year 2) + $800,000 (Year 3) Payback = 2 years + ($ 1,500,000 $400,000 $900,000) = 2.25 years $800,

4 Project C Outflow, $4,000,000 Inflow, $2,000,000 (Year 1) + $2,000,000 (Year 2) + $200,000 (Year 3) + $100,000 (Year 4) Payback = 2 years Payback Period 1. Project C 2 years 2. Project B 2.25 years 3. Project A 3 years If payback period is the deciding factor, Andrews will choose Project C (payback period = 2 years; investment = $4,000,000) and Project B (payback period = 2.25 years; investment = $1,500,000), for a total capital investment of $5,500,000. Assuming that each of the projects is an all-or-nothing investment, Andrews will have $500,000 left over in the capital budget, not enough to make the $3,000,000 investment in Project A. 2. Solution Exhibit shows the following ranking: NPV 1. Project B $ 207, Project A $ 169, Project C $(311,500) 3. Using NPV rankings, Projects B and A, which require a total investment of $3,000,000 + $1,500,000 = $4,500,000, which is less than the $6,000,000 capital budget, should be funded. This does not match the rankings based on payback period because Projects B and A have substantial cash flows after the payback period, cash flows that the payback period ignores. Nonfinancial qualitative factors should also be considered. For example, are there differential worker safety issues across the projects? Are there differences in the extent of learning that can benefit other projects? Are there differences in the customer relationships established with different projects that can benefit Andrews Construction in future projects? 21-13

5 SOLUTION EXHIBIT Total Present Value Present Value Discount Factors at 10% PROJECT A Net initial invest. $(3,000,000) $(3,000,000) Sketch of Relevant Cash Flows Annual cash inflow 909, $1,000, , $1,000, , $1,000, , $1,000,000 Net present value $ 169,000 PROJECT B Net initial invest. $(1,500,000) $(1,500,000) Annual cash inflow 363, $ 400, , $ 900, , $ 800,000 Net present value $ 207,800 PROJECT C Net initial invest. $(4,000,000) $(4,000,000) Annual cash inflow 1,818, $2,000,000 1,652, $2,000, , $ 200,000 68, $ 100,000 Net present value $ (311,500) 21-14

6 21-27 (60 min.) Equipment replacement, no income taxes. 1. Cash flows for modernizing alternative: Net Cash Initial Sale of Equip. Year Units Sold Contributions Investments at Termination (1) (2) (3) = (2) $18,000 a (4) (5) Jan. 1, 2012 $(33,600,000) Dec. 31, $ 9, Dec. 31, , Dec. 31, , Dec. 31, , Dec. 31, , Dec. 31, , Dec. 31, , $ a $ $ = $ cash contribution per prototype. Cash flows for replacement alternative: Net Cash Initial Sale of Equip. Year Units Sold Contributions Investments (1) (2) (3) = (2) $24,000 b (4) (5) Jan. 1, 2012 $(58,800,000) $ Dec. 31, $13, Dec. 31, , Dec. 31, , Dec. 31, , Dec. 31, , Dec. 31, , Dec. 31, , $ b $ $ = $ cash contribution per prototype

7 2. Payback period calculations for modernizing alternative: Cumulative Net Initial Investment Year Cash Inflow Cash Inflow Unrecovered at End of Year (1) (2) (3) (4) Jan. 1, 2012 $33,600,000 Dec. 31, 2012 $ 9, $ 9, , Dec. 31, , , , Dec. 31, , , Dec. 31, , Payback = 3 + ($552,000 $13,176,000) = 3.04 years Payback period calculations for replace alternative: Cumulative Net Initial Investment Year Cash Inflow Cash Inflow Unrecovered at End of Year (1) (2) (3) (4) Jan. 1, 2012 $55,200,000 Dec. 31, 2013 $13, $13, , Dec. 31, , , , Dec. 31, , , , Dec. 31, , Payback = 3 + ($11,136,000 $17,568,000) = 3.63 years 21-26

8 3. Modernizing alternative: Present Value Discount Factors Net Cash Present Year At 12% Flow Value Jan. 1, $(33, ) $(33,600,000) Dec. 31, , , Dec. 31, , ,779,752 Dec. 31, , ,612,352 Dec. 31, , ,379,936 Dec. 31, , ,083,152 Dec. 31, , ,775,352 Dec. 31, , ,132,032 Total $27,035,424 Replace Alternative: Present Value Discount Factors Net Cash Present Year At 12% Flow Value Jan. 1, $(55, ) $(55,200,000) Dec. 31, , ,830,464 Dec. 31, , ,706,336 Dec. 31, , ,483,136 Dec. 31, , ,173,248 Dec. 31, , ,777,536 Dec. 31, , ,367,136 Dec. 31, ,288,000 16,402,176 Total $28,540, Using the payback period, the modernize alternative is preferred to the replace alternative. On the other hand, the replace alternative has a higher NPV than the modernize alternative and so should be preferred. However, the NPV amounts are based on best estimates. Pro Chips should examine the sensitivity of the NPV amounts to variations in the estimates. Nonfinancial qualitative factors should be considered. These could include the quality of the prototypes produced by the modernize and replace alternatives. These alternatives may differ in capacity and their ability to meet surges in demand beyond the estimated amounts. The alternatives may also differ in how workers increase their shop floor-capabilities. Such differences could provide labor force externalities that can be the source of future benefits to Pro Chips

9 21-28 (40 min.) Equipment replacement, income taxes (continuation of 21-27). 1. & 2. Income tax rate = 30% Modernize Alternative Annual depreciation: $33, years = $ a year. Income tax cash savings from annual depreciation deductions: $ = $ a year. Terminal disposal of equipment = $ After-tax cash flow from terminal disposal of equipment: $ = $4, The NPV components are: a. Initial investment: NPV Jan. 1, 2012 $(33, ) $(33, ) b. Annual after-tax cash flow from operations (excluding depreciation): Dec. 31, , ,210, , ,145, ,096, ,028, , ,865, , ,658, , ,442, , ,194,022 c. Income tax cash savings from annual depreciation deductions ($1,440,000 each year for 7 years): $1,440, ,572,160 d. After-tax cash flow from terminal sale of equipment: $4,200, ,898,400 Net present value of modernize alternative $ 15,416,

10 Replace alternative Initial machine replacement = $58,800,000 Sale on Jan. 1, 2012, of equipment = $3,600,000 After-tax cash flow from sale of old equipment: $3,600, = $2,520,000 Net initial investment: $58,800,000 $2,520,000 = $56,280,000 Annual depreciation: $58,800,000 7 years = $8,400,000 a year Income-tax cash savings from annual depreciation deductions: $8,400, = $2,520,000 After-tax cash flow from terminal disposal of equipment: $14,400, = $10,080,000 The NPV components of the replace alternative are: a. Net initial investment Jan. 1, 2012 $(56,280,000) $(56,280,000) b. Annual after-tax cash flow from operations (excluding depreciation) Dec. 31, 2012 $13,248, ,281, ,688, ,194, ,128, ,038, ,568, ,821, ,008, ,544, ,448, ,256, ,888, ,925,363 c. Income tax cash savings from annual depreciation deductions ($2,520,000 each year for 7 years) $2,520, ,501,280 d. After-tax cash flow from terminal sale of equipment, $10,080, ,556,160 Net present value of replace alternative $13,839,302 On the basis of NPV, Pro Chips should modernize rather than replace the equipment. Note that absent taxes, the replace alternative had a higher NPV than the modernize alternative. In making decisions, companies should always consider after-tax amounts. 3. Pro Chips would prefer to: a. have lower tax rates, b. have revenue exempt from taxation, c. recognize taxable revenues in later years rather than earlier years, d. recognize taxable cost deductions greater than actual outlay costs, and e. recognize cost deductions in earlier years rather than later years (including accelerated amounts in earlier years)

11 21-29 (20 min.) DCF, sensitivity analysis, no income taxes. 1. Revenues, $ ,000 $90,000,000 Variable cash costs, $50 900,000 45,000,000 Cash contribution margin 45,000,000 Fixed cash costs 9,000,000 Cash inflow from operations $36,000,000 Net present value: Cash inflow from operations: $36,000, $175,248,000 Cash outflow for initial investment (120,000,000) Net present value $ 55,248,000 2a. 20% reduction in selling prices: Revenues, $80 900,000 $72,000,000 Variable cash costs, $50 900,000 45,000,000 Cash contribution margin 27,000,000 Fixed cash costs 9,000,000 Cash inflow from operation $18,000,000 Net present value: Cash inflow from operations: $18,000, $87,624,000 Cash outflow for initial investment (120,000,000) Net present value $(32,376,000) b. 20% increase in the variable cost per unit: Revenues, $ ,000 $90,000,000 Variable cash costs, $60 900,000 54,000,000 Cash contribution margin 36,000,000 Fixed cash costs 9,000,000 Cash inflow from operations $27,000,000 Net present value: Cash inflow from operations: $27,000, $131,436,000 Cash outflow for initial investment (120,000,000) Net present value $ 11,436, Sensitivity analysis enables management to see those assumptions for which input variations have sizable impact on NPV. Extra resources could be devoted to getting more informed estimates of those inputs with the greatest impact on NPV. Sensitivity analysis also enables management to have contingency plans in place if assumptions are not met. For example, if a 20% reduction in selling price is viewed as occurring with a reasonable probability, management may wish to line up bank loan facilities

12 21-30 (45 min.) NPV, IRR and sensitivity analysis. 1. Net Present Value of project: Period Cash inflows $28,000 Cash outflows $(62,000) (18,000) Net cash flows $(62,000) $ 10,000 Annual net cash inflows $ 10,000 Present value factor for annuity, 10 periods, 8% 6.71 Present value of net cash inflows $67,100 Initial investment (62,000) Net present value $ 5,100 For a $62,000 initial outflow, the project now generates $10,000 in cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 9.79%. 2. If revenues are 10% higher, the new Net Present Value will be: Period Cash inflows $30,800 Cash outflows $(62,000) (18,000) Net cash inflows $(62,000) $12,800 Annual net cash inflows $12,800 Present value factor for annuity, 10 periods, 8% 6.71 Present value of net cash inflows $85,888 Initial investment (62,000) Net present value $23,888 For a $62,000 initial outflow, the project now generates $12,800 in cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 15.94%

13 If revenues are 10% lower, the new net present value will be: Period Cash inflows $25,200 Cash outflows $(62,000) (18,000) Net cash inflows $(62,000) $ 7,200 Annual net cash inflows $ 7,200 Present value factor for annuity, 10 periods, 6% x 6.71 Present value of net cash inflows $ 48,312 Initial investment (62,000) Net present value $ (13,688) For a $62,000 initial outflow, the project now generates $7,200 in cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 2.82%. 3. If both revenues and costs are higher, the new Net Present Value will be: Period Cash inflows $30,800 Cash outflows $(62,000) (19,260) Net cash inflows $(62,000) $11,540 Annual net cash inflows $ 11,540 Present value factor for annuity, 10 periods, 6% 6.71 Present value of net cash inflows $77,433 Initial investment (62,000) Net present value $15,433 For a $62,000 initial outflow, the project now generates $11,540 in cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 13.25%

14 If both revenues and costs are lower, the new Net Present Value will be: Period Cash inflows $25,200 Cash outflows $(62,000) (16,200) Net cash inflows $(62,000) $ 9,000 Annual net cash inflows $ 9,000 Present value factor for annuity, 10 periods, 8% 6.71 Present value of net cash inflows $60,390 Initial investment (62,000) Net present value $ (1,610) For a $62,000 initial outflow, the project now generates $9,000 in cash flows at the end of each of years one through ten. Using either a calculator or Excel, the internal rate of return for this stream of cash flows is found to be 7.42%. 4. To find the NPV with a different rate of return, use the same cash flows but with a different discount rate, this time for ten periods at 10%. Annual net cash inflows $ 10,000 Present value factor for annuity, 10 periods, 10% Present value of net cash inflows $61,450 Initial investment (62,000) Net present value $ (550) 5. The sensitivity analysis shows that the return on the project is sensitive to changes in the projected revenues and costs. With the cost of capital (8%) as the discount rate, the NPV is positive and the IRR exceeds the required rate of return in most cases. The exceptions occur when the sales revenues are 10% lower than in the benchmark case, regardless of whether costs decline proportionately. Further, if Crumbly seeks to earn returns that exceed its cost of capital by 2%, then even the baseline scenario is unprofitable and should be rejected. Overall, the project appears to be a good one for Crumbly Cookie, provided that it is satisfied with earning its cost of capital, and if the likelihood of the scenario where revenues decline substantially is not too great

15 21-31 (30 min.) Payback, even and uneven cash flows. Payback problem: 1. Annual revenue $140,000 Annual costs Fixed $96,000 Variable 14, ,000 Net annual cash inflow $ 30,000 Payback period = Investment net cash inflows = $159,000 $30,000 = 5.30 years Discounted Payback Period with even cash flows: Year Cash Revenues Fixed Costs Variable Costs Net Cash Inflows Disc Factor (12%) Discounted Cash Savings Cumulative Disc. Cash Savings Unrecovered Investment 0 $159,000 1 $140,000 $96,000 $14,000 $30, $26,790 $ 26,790 $132,210 2 $140,000 $96,000 $14,000 $30, $23,910 $ 50,700 $108,300 3 $140,000 $96,000 $14,000 $30, $21,360 $ 72,060 $ 86,940 4 $140,000 $96,000 $14,000 $30, $19,080 $ 91,140 $ 67,860 5 $140,000 $96,000 $14,000 $30, $17,010 $108,150 $ 50,850 6 $140,000 $96,000 $14,000 $30, $15,210 $123,360 $ 35,640 7 $140,000 $96,000 $14,000 $30, $13,560 $136,920 $ 22,080 8 $140,000 $96,000 $14,000 $30, $12,120 $149,040 $ 9,960 9 $140,000 $96,000 $14,000 $30, $10,830 $159,870 $9,960/$10,830 =.92 Discounted Payback Period = 8.92 years 21-34

16 Year 2. Cash Fixed Costs (2) Cash Variable Costs (3) Revenue (1) Net Cash Inflows (4) = (1) (2) (3) Cumulative Amounts 1 $ 90,000 $ 96,000 $ 9,000 $(15,000) $(15,000) 2 115,000 96,000 11,500 7,500 (7,500) 3 130,000 96,000 13,000 21,000 13, ,000 96,000 15,500 43,500 57, ,000 96,000 17,000 57, , ,000 96,000 18,000 66, , ,000 96,000 14,000 30, , ,000 96,000 12,500 16, , ,000 96,000 11,000 3, ,500 Year The cumulative amount exceeds the initial $159,000 investment for the first time at the end of year 6. So, payback happens in year 6. Using linear interpolation, a more precise measure is that payback happens at: 5 years + $159,000 - $114, years. $66,000 Discounted Payback Period with uneven cash flows: Cash Revenues Fixed Costs Variable Costs Net Cash Inflows Disc Factor (12%) Discounted Cash Savings Cumulative Disc. Cash Savings Unrecovered Investment 0 $159,000 1 $ 90,000 $96,000 $ 9,000 $(15,000).893 ($13,395) ($13,395) $172,395 2 $115,000 $96,000 $11,500 $ 7, $ 5,978 ($ 7,417) $166,417 3 $130,000 $96,000 $13,000 $ 21, $14,952 $ 7,535 $151,465 4 $155,000 $96,000 $15,500 $ 43, $27,666 $ 35,201 $123,799 5 $170,000 $96,000 $17,000 $ 57, $32,319 $ 67,520 $ 91,480 6 $180,000 $96,000 $18,000 $ 66, $33,462 $100,982 $ 58,018 7 $140,000 $96,000 $14,000 $ 30, $13,560 $114,542 $ 44,458 8 $125,000 $96,000 $12,500 $ 16, $ 6,666 $121,208 $ 37,792 9 $110,000 $96,000 $11,000 $ 3, $ 1,083 $122,291 $ 36,709 At a 12% rate of return, this project does not generate sufficient cash flows to ever recoup the investment under the discounted payback method