Solutions to assigned problems in Ch. 21: Capital Budgeting
ACCT 7310 Bailey
Slide 3
Exercises 18 & 19, Ch. 21
Slide 4
Pr. 21-18 The NPV using Table 4 values or spreadsheet, using
formula from Table 4: The table for the present value of annuities
(Appendix A, Table 4) shows: 10 periods at 14% = 5.216 1a.Net
present value= $28,000 (5.216) $110,000 = $146,048 $110,000 =
$36,048
Slide 5
Pr. 21-19 contd 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.
Slide 6
Solver requires choosing the Solver add-in, then Set NPV = 0 by
changing rate
Slide 7
IRR Contd 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.
Slide 8
21-18 Accrual rate of Return What does this project do to our
GAAP-reported income?
Slide 9
21-18Other factors? Factors City Hospital should consider
include: Quantitative financial aspects. 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.
Financing factors, such as the availability of cash to purchase the
new equipment.
Slide 10
Pr. 21-19 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 1a. Net
after-tax initial investment = $110,000 (No immediate tax effect)
Annual after-tax cash flow from operations (excluding the
depreciation effect): Net initial investment; $110,000 1.00
$(110,000) 10-year annuity of annual after-tax cash flows from
operations; $19,600 5.216 102,234 10-year annuity of income tax
cash savings from annual depreciation deductions; $3,300 5.216
17,213 Net present value$ 9,447
Slide 11
21-19--Payback Nothing different but the cash flows. Takes
longer (than 3.93) given lower after-tax cash flows
Slide 12
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%.
Slide 13
21-19Accounting ROR Income now is reduced by taxes and
depreciation, so
Slide 14
21-19: Effects of $10K 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 $10K 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 summary & conclusion Using NPV rankings, Projects B
and A, which require a total investment of $3,000,000 + $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?
Slide 17
Pr. 21-27--Eqpt replacement, no income tax ModernizeReplaceRRR:
(1)(2) Contributions 12.00%Present Value of YearUnits Sold=units
$18,000*=units $24,000**PV FactorModernizeReplace 1/1/2012 0 $
(33,600,000) $ (55,200,000)1.000 ($33,600,000)($55,200,000)
1/31/20121552 $ 9,936,000 $ 13,248,0000.893 $8,871,429$11,828,571
1/31/2013 2 612 $ 11,016,000 $ 14,688,0000.797
$8,781,888$11,709,184 1/31/20143672 $ 12,096,000 $ 16,128,0000.712
$8,609,694$11,479,592 1/31/2015 4 732 $ 13,176,000 $
17,568,0000.636 $8,373,586$11,164,782 1/31/20165792 $ 14,256,000 $
19,008,0000.567 $8,089,237$10,785,650 1/31/2017 6 852 $ 15,336,000
$ 20,448,0000.507 $7,769,695$10,359,593 1/31/20187912 $ 16,416,000
$ 21,888,0000.452 $7,425,765$9,901,020 Salvage7 $ 6,000,000 $
14,400,0000.452 $2,714,095$6,513,829 NPV: $27,035,389$28,542,220 *
$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.
Slide 18
Pr. 21-27--Eqpt replacement, no income tax ModernizeReplaceRRR:
(1)(2) Contributions 12.00%Present Value of YearUnits Sold=units
$18,000*=units $24,000**PV FactorModernizeReplace 1/1/2012 0 $
(33,600,000) $ (55,200,000)1.000 ($33,600,000)($55,200,000)
1/31/20121552 $ 9,936,000 $ 13,248,0000.893 $8,871,429$11,828,571
1/31/2013 2 612 $ 11,016,000 $ 14,688,0000.797
$8,781,888$11,709,184 1/31/20143672 $ 12,096,000 $ 16,128,0000.712
$8,609,694$11,479,592 1/31/2015 4 732 $ 13,176,000 $
17,568,0000.636 $8,373,586$11,164,782 1/31/20165792 $ 14,256,000 $
19,008,0000.567 $8,089,237$10,785,650 1/31/2017 6 852 $ 15,336,000
$ 20,448,0000.507 $7,769,695$10,359,593 1/31/20187912 $ 16,416,000
$ 21,888,0000.452 $7,425,765$9,901,020 Salvage7 $ 6,000,000 $
14,400,0000.452 $2,714,095$6,513,829 NPV: $27,035,389$28,542,220 *
$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.
Slide 19
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
= $6 000 000. After-tax cash flow from disposal: $6 000 000 0.70 =
$4,200 000.
Slide 20
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
Slide 21
Pr 21-28: Same problem, with tax implications
ModernizeReplaceRRR: (1)(2) Contributions 12.00%Present Value of
YearUnits Sold =units $18,000* =units $24,000**PV
FactorModernizeReplace 1/1/2012 0(33,600,000)(56,280,000)1.000
(33,600,000)(56,280,000) 1/31/20121552 $ 6,955,200 $ 9,273,6000.893
$6,210,000$8,280,000 1/31/2013 2 612 $ 7,711,200 $ 10,281,6000.797
$6,147,321$8,196,429 1/31/20143672 $ 8,467,200 $ 11,289,6000.712
$6,026,786$8,035,714 1/31/2015 4 732 $ 9,223,200 $ 12,297,6000.636
$5,861,510$7,815,347 1/31/20165792 $ 9,979,200 $ 13,305,6000.567
$5,662,466$7,549,955 1/31/2017 6 852 $ 10,735,200 $ 14,313,6000.507
$5,438,786$7,251,715 1/31/20187912 $ 11,491,200 $ 15,321,6000.452
$5,198,035$6,930,714 Salvage7 $ 4,200,000 $ 10,080,0000.452
$1,899,867$4,559,680 Depreciation tax
benefit:NPV:$8,844,772$2,339,554 Modernize $ 1,440,0004.564 $
6,572,160 Replace $ 2,520,000 $ 11,501,280 $15,416,932$13,840,834
7yrs, 12% annuity factor 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.
Slide 22
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).
Slide 23
Pr. 21-29: DCF, Sensitivity Analysis. No income taxes Basic
model 20% reduction in selling prices: 20% increase in the variable
cost per unit: Revenues, $100 900,000$90,000,000 Revenues@ $80 $
72,000,000$90,000,000 Variable cash costs, $50 900,000 45,000,000
Variable cash costs, $50 900,000 $
45,000,[email protected]*$50=$60$54,000,000 Cash contribution
margin45,000,000 Cash contribution margin 27,000,000 Cash
contribution margin 36,000,000 Fixed cash costs9,000,000 Fixed cash
costs $ 9,000,000Fixed cash costs 9,000,000 Cash inflow from
operations $36,000,000 Cash inflow from operations $18,000,000 Cash
inflow from operations $27,000,000 PV of Annuity, 7 yrs, 10% 4.868
PV of Annuity, 7 yrs, 10%4.868 PV of Annuity, 7 yrs, 10%4.868 Net
present value: $175,248,000Net present value:$87,624,000Net present
value:$131,436,000 Cash outflow for initial investment $
(120,000,000) Net present value
$55,248,000($32,376,000)$11,436,000
Slide 24
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.
Slide 25
Pr. 21-30: NPV, IRR, sensitivity analysis Period 0 1 10 Cash
inflows $ 28,000.00 Cash outflows $ (62,000.00) $ (18,000.00) Net
cash flows $ (62,000.00) $ 10,000.00 Annual net cash inflows $
10,000.00 Present value factor for annuity, 10 periods, 8%6.71 from
table 4 or see formula below cell H16. Present value of net cash
inflows $ 67,100.00 Initial investment $(62,000.00) Net present
value $ 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%.
0.0979 Rate $ 10,000.00times.6.200393 $ 62,003.936.200393 Factor
Initial inve stment $ (62,000.00) = $ 3.93=approx. zero at IRR
Slide 26
Pr. 21-30: NPV, IRR, sensitivity analysis Period Part 2:
Revenues +/- 10% 0 1 10 Plus 10% Minus 10% Cash inflows $ 28,000.00
$ 30,800 $ 25,200 Cash outflows $ (62,000) $(18,000.00) Net cash
flows $ (62,000) $ 10,000.00 $ 12,800.00 $ 7,200.00 Annual net cash
inflows $ 10,000 $ 12,800 $ 7,200 Present value factor for annuity,
10 periods, 8%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) IRR (Adjust rate to make NPV =0)
9.79%15.94%2.82% Factor6.2003928594.8440436188.609100623 PV of
benefits $ 62,003.93 $ 62,003.76 $ 61,985.52 Initial investment $
(62,000.00) $ 3.93 $ 3.76 $ (14.48) =approx. zero at IRR
Pr. 21-30 part 4 Part 4: Original scenario but 2% higher RRR:
10.00% 6.144567 = factor 0 1 10 All else the same Cash inflows $
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)
Slide 29
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.
Slide 30
Pr. 21-31: Payback, even and uneven cash flows Annual revenue
$140,000 Annual costs Fixed$96,000 Variable14,000110,000 Net annual
cash inflow$30,000
Slide 31
Pr 21-31: Discounted Payback Period with even cash flows:
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$30,0000.893$26,790
$132,210 2$140,000$96,000$14,000$30,0000.797$23,910$50,700$108,300
3$140,000$96,000$14,000$30,0000.712$21,360$72,060$86,940
4$140,000$96,000$14,000$30,0000.636$19,080$91,140$67,860
5$140,000$96,000$14,000$30,0000.567$17,010$108,150$50,850
6$140,000$96,000$14,000$30,0000.507$15,210$123,360$35,640
7$140,000$96,000$14,000$30,0000.452$13,560$136,920$22,080
8$140,000$96,000$14,000$30,0000.404$12,120$149,040$9,960
9$140,000$96,000$14,000$30,0000.361$10,830$159,870 $9,960/$10,830
=.92 Discounted Payback Period = 8.92 years
Slide 32
Pr. 12-31: Uneven cash flows Yr.Revenue Cash Fixed Costs
Variable CostsNet inflow Cumulative AmountsNeeded
1$90,000$96,000$9,000($15,000) $174,000
2115,00096,00011,5007,500-7,500 $166,500
3130,00096,00013,00021,00013,500 $145,500
4155,00096,00015,50043,50057,000 $102,000
5170,00096,00017,00057,000114,000 $45,000 Need less than next
year's 6180,00096,00018,00066,000180,000 ($21,000)
7140,00096,00014,00030,000210,000 ($51,000)
8125,00096,00012,50016,500226,500 ($67,500)
9110,00096,00011,0003,000229,500 ($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
Slide 33
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 $159,000
$(15,000).893($13,395) $172,395 $ 7,500.797 $ 5,978 ($
7,417)$166,417 $ 21,000.712 $14,952 $ 7,535$151,465 $ 43,500.636
$27,666 $ 35,201$123,799 $ 57,000.567 $32,319 $ 67,520$ 91,480 $
66,000.507 $33,462 $100,982$ 58,018 $ 30,000.452 $13,560 $114,542$
44,458 $ 16,500.404 $ 6,666 $121,208$ 37,792 $ 3,000.361 $ 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.
