Solutions to assigned problems in Ch 21 Capital

Solutions to assigned problems in Ch. 21: Capital Budgeting ACCT 7310 Bailey

Exercises 18 & 19, Ch. 21

Pr. 21 -18 • The NPV using Table 4 values The table for the present value of annuities (Appendix A, Table 4) shows: 10 periods at 14% = 5. 216 1 a. Net present value = $28, 000 (5. 216) – $110, 000 = $146, 048 – $110, 000 = $36, 048 …or spreadsheet, using formula from Table 4:

Pr. 21 -19 cont’d • The payback period is straightforward with these equal cash flows: • Finding the IRR: Still positive NPV @ 18% so try higher rate, etc. • Note that Solver can find this exactly; we will probably do more with Solver, but see next slide.

Solver requires choosing the Solver add-in, then… Set NPV = 0 …by changing rate

IRR Cont’d • You also could “back in” to the table (Table 4) • NPV = $28, 000*[Table Factor, ? %, 10 yrs. ]-$110, 000=0 So, Factor = 110, 000/28000 = 3. 93. • Now, in Table 4, go across the 10 -year row and find the factor closest to 3. 93. It is 22% (3. 923) • If the factor fell between the table values, one coould “interpolate” to estimate the percentage • Interpolation was how it was done in the pre-computer age. Not needed with spreadsheets available.

21 -18 Accrual rate of Return • What does this project do to our GAAP-reported income?

21 -18—Other factors? Factors City Hospital should consider include: Quantitative financial aspects. Qualitative factors, such as the benefits to its customers of a better eyetesting machine and the employee-morale advantages of having up-todate equipment. Financing factors, such as the availability of cash to purchase the new equipment.

Pr. 21 -19 1 a. Net after-tax initial investment = $110, 000 (No immediate tax effect) Annual after-tax cash flow from operations (excluding the depreciation effect): Annual cash flow from operation with new machine Deduct income tax payments (30% of $28, 000) Annual after-tax cash flow from operations Income tax cash savings from annual depreciation deductions 30% $11, 000 Net initial investment; $110, 000 1. 00 10 -year annuity of annual after-tax cash flows from operations; $19, 600 5. 216 10 -year annuity of income tax cash savings from annual depreciation deductions; $3, 300 5. 216 Net present value $28, 000 8, 400 $19, 600 $3, 300 $(110, 000) 102, 234 17, 213 $ 9, 447

21 -19 --Payback Nothing different but the cash flows. Takes longer (than 3. 93) given lower after-tax cash flows…

21 -19 IRR • Same methods, different cash flows: – For a $110, 000 initial outflow, the project now generates $22, 900 in after-tax 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 16. 17%.

21 -19—Accounting ROR • Income now is reduced by taxes and depreciation, so…

21 -19: Effects of $10 K terminal disposal value? a. Increase in NPV. Note that from Table 2, the present value factor for 10 periods at 14% is 0. 270. Thus, the $10 K terminal disposal price at the end of 10 years would have an after-tax NPV of: $10, 000 (1 0. 30) 0. 270 = $1, 890 b. No change in the payback period of 4. 80 years. The cash inflow occurs at the end of yr 10. c. Increase in internal rate of return. The $10, 000 terminal disposal price would raise the IRR because of the additional inflow. (The new IRR is 16. 54%. ) d. The AARR on net initial investment would increase because accrual accounting income in year 10 would increase by the $7, 000 ($10, 000 gain from disposal, less 30% $10, 000) after-tax gain on disposal of equipment. This increase in year 10 income would result in higher average annual accounting income in the numerator of the AARR formula. e. The AARR on average investment would also increase, for the same reasons given in the previous answer. Note that the denominator is unaffected because the investment is still depreciated down to zero terminal disposal value, and so the average investment remains $55, 000.

21 -22—Payback & NPV, no income taxes Project A Net initial investment Project B Project C PV Factor Project A Project B =1/(1+$C$12)^B 7 $ 3, 000. 00 $ 1, 500, 000. 00 $ 4, 000. 00 Project C $ (3, 000) $ (1, 500, 000) $ (4, 000) Projected inflows: Year 1 $ 1, 000. 00 $ 400, 000. 00 $ 2, 000. 00 0. 9091 $ 909, 091 $ 363, 636 $ 1, 818, 182 Year 2 $ 1, 000. 00 $ 900, 000. 00 $ 2, 000. 00 0. 8264 $ 826, 446 $ 743, 802 $ 1, 652, 893 Year 3 $ 1, 000. 00 $ 800, 000. 00 $ 200, 000. 00 0. 7513 $ 751, 315 $ 601, 052 $ 150, 263 Year 4 $ 1, 000. 00 0. 6830 $ 683, 013 $ - $ 68, 301 $ 100, 000. 00 NPV: $ 169, 865 $ 208, 490 $ (310, 361) RRR Payback years: 10% 10% 3. 00 2. 25 2. 00 $ 200, 000. 00 remains after 2 years, and that's 25% of year 3

21 -22 summary & conclusion • Using NPV rankings, Projects B and A, which require a total investment of $3, 000 + $1, 500, 000 = $4, 500, 000 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. – Are there differential worker safety issues across the projects? – Differences in the extent of learning that can benefit other projects? – Differences in the customer relationships established with different projects that can benefit Andrews Construction in future projects?

Pr. 21 -27 --Eqpt replacement, no income tax (1) 1/1/2012 Year 0 (2) Modernize Replace Contributions RRR: 12. 00% Present Value of Units Sold =units × $18, 000* =units × $24, 000** PV Factor Modernize $ (33, 600, 000) $ (55, 200, 000) 1. 000 ($33, 600, 000) 552 $ 9, 936, 000 $ 13, 248, 000 0. 893 $8, 871, 429 Replace ($55, 200, 000) 1/31/2012 1 1/31/2013 2 3 612 $ 11, 016, 000 $ 14, 688, 000 0. 797 $8, 781, 888 $11, 709, 184 672 $ 12, 096, 000 $ 16, 128, 000 0. 712 $8, 609, 694 $11, 479, 592 4 5 732 $ 13, 176, 000 $ 17, 568, 000 0. 636 $8, 373, 586 $11, 164, 782 792 $ 14, 256, 000 $ 19, 008, 000 0. 567 $8, 089, 237 $10, 785, 650 852 $ 15, 336, 000 $ 20, 448, 000 0. 507 $7, 769, 695 $10, 359, 593 1/31/2018 6 7 912 $ 16, 416, 000 $ 21, 888, 000 0. 452 $7, 425, 765 $9, 901, 020 Salvage 7 $ 6, 000 $ 14, 400, 000 0. 452 $2, 714, 095 $6, 513, 829 $27, 035, 389 $28, 542, 220 1/31/2014 1/31/2015 1/31/2016 1/31/2017 NPV: $11, 828, 571 *$80, 000 – $62, 000 = $18, 000 cash contribution per prototype. **$80, 000 – $56, 000 = $24, 000 cash contribution per prototype. I also am providing the Excel file.

Pr 21 -28: Same problem, with tax implications Modernize Alternative Annual depreciation: $33, 600 000 7 years = $4 800 000 a year. Income tax cash savings from annual depreciation deductions: $4 800 000 0. 30 = $1 440 000 a year. Terminal disposal of equipment = $6 000. After-tax cash flow from disposal: $6 000 0. 70 = $4, 200 000.

Pr 21 -28: Same problem, with tax implications Replace alternative (tax implications) After-tax cash flow from sale of old equipment: $3, 600, 000 0. 70 = $2, 520, 000. [Tax on recovery of depreciation taken] Annual depreciation: $58, 800, 000 7 years = $8, 400, 000 a year Income-tax cash savings from annual depreciation: $8, 400, 000 0. 30 = $2, 520, 000 After-tax cash flow from terminal disposal of equipment: $14, 400, 000 0. 70 = $10, 080, 000

Pr 21 -28: Same problem, with tax implications (1) 1/1/2012 1/31/2013 1/31/2014 1/31/2015 1/31/2016 1/31/2017 1/31/2018 Salvage Year 0 1 2 3 4 5 6 7 7 (2) Units Sold 552 612 672 732 792 852 912 Modernize Replace Contributions RRR: 12. 00% Present Value of =units × $18, 000* (33, 600, 000) $ 6, 955, 200 $ 7, 711, 200 $ 8, 467, 200 $ 9, 223, 200 $ 9, 979, 200 $ 10, 735, 200 $ 11, 491, 200 $ 4, 200, 000 Depreciation tax benefit: Modernize Replace =units × PV Factor Modernize $24, 000** (56, 280, 000) 1. 000 (33, 600, 000) $ 9, 273, 600 0. 893 $6, 210, 000 $ 10, 281, 600 0. 797 $6, 147, 321 $ 11, 289, 600 0. 712 $6, 026, 786 $ 12, 297, 600 0. 636 $5, 861, 510 $ 13, 305, 600 0. 567 $5, 662, 466 $ 14, 313, 600 0. 507 $5, 438, 786 $ 15, 321, 600 0. 452 $5, 198, 035 $ 10, 080, 000 0. 452 $1, 899, 867 NPV: $8, 844, 772 $ 1, 440, 000 4. 564 $ 6, 572, 160 $ 2, 520, 000 Replace (56, 280, 000) $8, 280, 000 $8, 196, 429 $8, 035, 714 $7, 815, 347 $7, 549, 955 $7, 251, 715 $6, 930, 714 $4, 559, 680 $2, 339, 554 $ 11, 501, 280 $15, 416, 932 7 yrs, 12% annuity factor $13, 840, 834 Cash flows are reduced by 30% because of tax. Because the salvage value recovers depreciated costs, it is taxable, as well. I also am providing the Excel file.

Pr. 21 -28 concluded • 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. In relocating/opening new plant, Pro Chips would prefer to: – have lower tax rates, – have revenue exempt from taxation, – recognize taxable revenues in later years rather than earlier years, – recognize taxable cost deductions greater than actual outlay costs, and – recognize cost deductions in earlier years rather than later years (including accelerated amounts in earlier years).

Pr. 21 -29: DCF, Sensitivity Analysis. No income taxes Basic model Revenues, $100 × 900, 000 $90, 000 Revenues@ $80 Variable cash costs, $50 × 900, 000 45, 000, 000 Cash contribution margin Fixed cash costs Cash inflow operations from $36, 000 Cash inflow from operations PV of Annuity, 7 yrs, 4. 868 10% $175, 248, 000 Net present value: Cash outflow for initial $ investment (120, 000) Net present value Variable cash costs, $50 × 900, 000 9, 000 Fixed cash costs PV of Annuity, 7 yrs, 10% Net present value: 20% increase in the variable cost per unit: 20% reduction in selling prices: $55, 248, 000 $ 72, 000 $90, 000 $ 45, 000 VC@1. 2*$50=$60 $54, 000 27, 000 Cash contribution margin 36, 000 $ 9, 000 Fixed cash costs $18, 000 Cash inflow from operations PV of Annuity, 7 4. 868 yrs, 10% $87, 624, 000 Net present value: $ (120, 000) ($32, 376, 000) 9, 000 $27, 000 4. 868 $131, 436, 000 $ (120, 000) $11, 436, 000

21 -29 Summarization • 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.

Pr. 21 -30: NPV, IRR, sensitivity analysis Period 0 Cash inflows Cash outflows 1 – 10 $ 28, 000. 00 $ (62, 000. 00) $ (18, 000. 00) Net cash flows $ (62, 000. 00) $ 10, 000. 00 Annual net cash inflows Present value factor for annuity, 10 periods, 8% Present value of net cash inflows Initial investment Net present value $ 10, 000. 00 from table 4 or see formula 6. 71 below cell H 16. $ 67, 100. 00 $(62, 000. 00) $ 5, 100. 00 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%. $ 10, 000. 00 times……. Initial inve stment…………… 0. 0979 Rate 6. 200393 $ 62, 003. 93 6. 200393 Factor $ (62, 000. 00) = $ 3. 93 =approx. zero at IRR

Pr. 21 -30: NPV, IRR, sensitivity analysis Period 0 Cash inflows Part 2: Revenues +/- 10% 1 – 10 $ 28, 000. 00 Plus 10% Minus 10% $ 30, 800 $ 25, 200 Cash outflows $ (62, 000) $(18, 000. 00) $ (18, 000. 00) Net cash flows $ (62, 000) $ 10, 000. 00 $ 12, 800. 00 $ 7, 200. 00 $ 10, 000 $ 12, 800 $ 7, 200 6. 71 Present value of net cash inflows $ 67, 100 $ 85, 888 $ 48, 312 Initial investment $ (62, 000) Net present value $ 5, 100 $ 23, 888 $ (13, 688) 9. 79% 15. 94% 2. 82% 6. 200392859 4. 844043618 8. 609100623 Annual net cash inflows Present value factor for annuity, 10 periods, 8% IRR (Adjust rate to make NPV =0) Factor PV of benefits $ 62, 003. 93 Initial investment…………… $ 62, 003. 76 $ 61, 985. 52 $ (62, 000. 00) $ 3. 93 $ 3. 76 $ (14. 48) =approx. zero at IRR

Pr. 21 -30: NPV, IRR, sensitivity analysis 1 – 10 Part 2: Revenues +/- 10% Part 3: both revenues and costs are +/- 10% Plus 10% Minus 10% $ 28, 000. 00 $ 30, 800 $ 25, 200 $ 30, 800 $ 25, 200 $(18, 000. 00) $ (19, 260. 00) $ (16, 200. 00) $ 10, 000. 00 $ 12, 800. 00 $ 7, 200. 00 $ 11, 540. 00 $ 9, 000. 00 $ 10, 000 $ 12, 800 $ 7, 200 $ 11, 540 $ 9, 000 6. 71 $ 67, 100 $ 85, 888 $ 48, 312 $ 77, 433 $ 60, 390 $ (62, 000) $ (62, 000) $ 5, 100 $ 23, 888 $ (13, 688) NPV $ 15, 433 $ (1, 610) 9. 79% 15. 94% 2. 82% 13. 25% 7. 42% 6. 200392859 4. 844043618 8. 609100623 5. 372456489 6. 889225111 IRR $ 62, 003. 93 $ 62, 003. 76 $ 61, 985. 52 $ 61, 998. 15 $ 62, 003. 03 $ (62, 000. 00) $ (62, 000. 00) $ (62, 000. 00) $ 3. 93 $ 3. 76 $ (14. 48) $ (1. 85) $ 3. 03

Pr. 21 -30 part 4 Part 4: Original scenario but 2% higher RRR: 10. 00% 6. 144567 = factor All else the same 0 Cash inflows 1 – 10 $ 28, 000. 00 Cash outflows $ (62, 000) $(18, 000. 00) Net cash flows $ (62, 000) $ 10, 000. 00 Annual net cash inflows $ 10, 000 Present value factor for annuity, 10 periods, 8% 6. 144567106 Present value of net cash inflows $ 61, 446 Initial investment $ (62, 000) Net present value $ (554)

Pr. 21 -30 concluded 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.

Pr. 21 -31: Payback, even and uneven cash flows Annual revenue $140, 000 Annual costs Fixed $96, 000 Variable Net annual cash inflow 14, 000 110, 000 $30, 000

Pr 21 -31: Discounted Payback Period with even cash flows: Fixed Costs Variable Costs Discounted Cumulative Net Cash Disc Factor Unrecovered Cash Disc. Cash Inflows (12%) Investment Savings 0 1 $140, 000 $96, 000 $14, 000 $30, 000 0. 893 $26, 790 $132, 210 2 $140, 000 $96, 000 $14, 000 $30, 000 0. 797 $23, 910 $50, 700 $108, 300 3 $140, 000 $96, 000 $14, 000 $30, 000 0. 712 $21, 360 $72, 060 $86, 940 4 $140, 000 $96, 000 $14, 000 $30, 000 0. 636 $19, 080 $91, 140 $67, 860 5 $140, 000 $96, 000 $14, 000 $30, 000 0. 567 $17, 010 $108, 150 $50, 850 6 $140, 000 $96, 000 $14, 000 $30, 000 0. 507 $15, 210 $123, 360 $35, 640 7 $140, 000 $96, 000 $14, 000 $30, 000 0. 452 $13, 560 $136, 920 $22, 080 8 $140, 000 $96, 000 $14, 000 $30, 000 0. 404 $12, 120 $149, 040 $9, 960 9 $140, 000 $96, 000 $14, 000 $30, 000 0. 361 $10, 830 $159, 870 Cash Revenues Year $9, 960/$10, 830 =. 92 Discounted Payback Period = 8. 92 years $159, 000

Pr. 12 -31: Uneven cash flows Yr. 1 2 3 4 5 6 7 8 9 Cash Fixed Variable Cumulative Revenue Costs Net inflow Amounts Needed $90, 000 $96, 000 $9, 000 ($15, 000) $174, 000 115, 000 96, 000 11, 500 7, 500 -7, 500 $166, 500 130, 000 96, 000 13, 000 21, 000 13, 500 $145, 500 155, 000 96, 000 15, 500 43, 500 57, 000 $102, 000 170, 000 96, 000 17, 000 57, 000 114, 000 $45, 000 Need less than next year's 180, 000 96, 000 18, 000 66, 000 180, 000 ($21, 000) 140, 000 96, 000 14, 000 30, 000 210, 000 ($51, 000) 125, 000 96, 000 12, 500 16, 500 226, 500 ($67, 500) 110, 000 96, 000 11, 000 3, 000 229, 500 ($70, 500) 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, 000)/66, 000 = 5. 68 years

Pr. 12 -31: Discounted uneven cash flows Net Cash Inflows (same as before) Disc Factor (12%) Discounted Cash Savings Cumulative Disc. Cash Savings Unrecovered Investment $(15, 000) $ 7, 500 $ 21, 000 $ 43, 500 $ 57, 000 $ 66, 000 $ 30, 000 $ 16, 500 $ 3, 000 . 893. 797. 712. 636. 567. 507. 452. 404. 361 ($13, 395) $ 5, 978 $14, 952 $27, 666 $32, 319 $33, 462 $13, 560 $ 6, 666 $ 1, 083 ($13, 395) ($ 7, 417) $ 7, 535 $ 35, 201 $ 67, 520 $100, 982 $114, 542 $121, 208 $122, 291 $159, 000 $172, 395 $166, 417 $151, 465 $123, 799 $ 91, 480 $ 58, 018 $ 44, 458 $ 37, 792 $ 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.

The end