# 202E13

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```					Problem 13-16                 Basic Net Present Value Analysis
Given:
Renfree Mines, Inc., owns the mining rights to a large tract of land in a mountainous area. The
tract contains a mineral deposit that the company believes might be commercially attractive to
mine and sell. An engineering and cost analysis has been made, and it is expected that the
following cash flows would be associated with opening and operating a mine in the area:

Cost of equipment required                                             \$850,000                \$804,920.93
Net annual cash receipts                                               \$230,000 ***            Cost (NPV = 0)
Working capital required                                               \$100,000                \$804,920.93
Cost of road repairs in three years                                     \$60,000
Salvage value of equipment in five years                               \$200,000

*** Receipts from sales of ore, less out-of-pocket costs for salaries, utilities, insurance,
and so forth.

It is estimated that the mineral deposit would be exhausted after five years of mining. At that
point, the working capital would be released for reinvestment elsewhere. The Company's
required rate of return is 14%.

Required:    Determine the net present value of the proposed mining project. Should the project be accepted?
Ignore income taxes.
Timing of       Cash          14%            PV of
Cash          Flow        PV Table         Cash
Relevant Items:                                      Flows      Amounts         Factor          Flows
Cost of equipment required                            Now         (\$850,000)      1.000000 (\$850,000.00)
Working capital required                              Now         (\$100,000)      1.000000 (\$100,000.00)
Net annual cash receipts                         End of Ys 1-5     \$230,000       3.433081 \$789,608.62
Cost of road repairs in three years              End of Year 3     (\$60,000)      0.674972    (\$40,498.29)
Salvage value of equipment in 5 years            End of Year 5     \$200,000       0.519369 \$103,873.73
Working capital released                         End of Year 5     \$100,000       0.519369     \$51,936.87
Net Present Value                                                                          (\$45,079.07)

No, the project should not be accepted; it has a negative net present value. This means that the
rate of return on the investment is less than the company's required rate of return of 14%
Explain.
0.12246555
Timing of     Yearly Cash          14%           PV of
Cash           Flow           PV Table         Cash
Flows        Amounts           Factor          Flows
Now         (\$950,000.00)       1.000000   (\$950,000.00)
End of Y1       \$230,000.00        0.877193    \$201,754.39
End of Y2       \$230,000.00        0.769468    \$176,977.53
End of Y3       \$170,000.00        0.674972    \$114,745.16
End of Y4       \$230,000.00        0.592080    \$136,178.46
End of Y5       \$530,000.00        0.519369    \$275,265.39
3.433081    (\$45,079.07)
3.433081

12.246555%          IRR

(\$39,543.04)
Note: Wrong NPV
Excel formula is wrong
(\$45,079.07)
Corrected NPV
Exercise 13-10           Internal Rate of Return and Net Present Value
Given:
Scalia's Cleaning Service is investigating the purchase of an ultrasound machine for cleaning window
blinds. The machine would cost \$136,700, including invoice cost, freight, and training of employees
to operate it. Scalia's has estimated that the new machine would increase the company's cash flows,
net of expenses, by \$25,000 per year. The machine would have a 14-year useful life with no expected
salvage value.

Required:  Ignore income taxes
1. Compute the machine's internal rate of return to the nearest whole percent.

IRR = the interest rate that yields a NPV = 0
Annual cash inflows X Table Value ( Y%, 14 years) from PV of an Annuity Table - Cost = 0
\$25,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table - \$136,700 = 0
\$25,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table = \$136,700
Table Value (Y%, 14 years) from PV of an Annuity Table = \$136,700/\$25,000                      5.468

From PV of an Annuity Table, scanning along the row for 14 periods yields 5.468 for an IRR equal to 16%

2. Compute the machine's net present value. Use a discount rate of 16% and the format shown in
Exhibit 14-5. Why do you have a zero net present value?
Amount of      16%          Present
Item                            Year(s)    Cash flow Table Factor       Value
Initial Investment               Now        (\$136,700)      1.00000 (\$136,700)
Net annual cash inflows          1-14         \$25,000          5.468  \$136,700
Net present value                                                         \$0

The NPV is equal to zero because the discount rate used (16%) is also the IRR.

3. Suppose that the new machine would increase the company's annual cash flows, net of expenses,
by only \$20,000 per year. Under these conditions, compute the internal rate of return to the nearest
whole percent.

IRR = the interest rate that yields a NPV = 0
Annual cash inflows X Table Value ( Y%, 14 years) from PV of an Annuity Table - Cost = 0
\$20,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table - \$136,700 = 0
\$20,000 X Table Value ( Y%, 14 years) from PV of an Annuity Table = \$136,700
Table Value (Y%, 14 years) from PV of an Annuity Table = \$136,700/\$20,000                      6.835

From PV of an Annuity Table, scanning along the row for 14 periods yields:

Interpolation
12%               6.628       6.628168
X                     ?%               6.835       6.835000   (0.206832)
0.01                   11%               6.982       6.981865   (0.353697)

X            =               0.206832
0.01                       0.353697001

0.353697 (X) = (0.01)(.206832)
0.353697 (X) =              0.00206832
X =              0.00584771
X =            0.584771%

?% = 12% - 0.5848% =         11.4152%
Rounded to nearest whole % = 11%        IRR
NPV
(pg. 678)

RR equal to 16%

(136,700)   (136,700)
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000      25,000
20,000    25,000
20,000    25,000

11.405%   15.998%
0.000     0.000
Exercise 13-3           Uncertain Future Cash Flows
Given:
Union Bay Plastics is investigating the purchase of automated equipment that would save
\$100,000 each year in direct labor and inventory carrying costs. This equipment costs \$750,000
and is expected to have a 10-year useful life with no salvage value. The company requires a
minimum 15% rate of return on all equipment purchases. This equipment would provide
intangible benefits such as greater flexibility and higher-quality output that are difficult to
estimate and yet are quite significant.

Required:
1. What dollar value per year would the intangible benefits have to be worth in order to make
the equipment an acceptable investment? (Ignore income taxes).

If Union Bay Plastics uses a discount rate of 15% to calculate the NPV and the resulting NPV
equals zero, then the investment would be earning a return of exactly 15%; the IRR = 15%.

Therefore:

Annual cash inflows X Table Value (15%, 10 years) from PV of an Annuity Table - Cost = 0
(Annual cash inflows X 5.019) - \$750,000 = 0
5.019 (Annual cash inflows) = \$750,000
Annual cash inflows = \$750,000/5.019
Annual cash inflows =                          \$149,432.16    \$149,439.05

Thus the dollar value per year of the intangible benefits must be worth at least:

Annual cash inflows required                      \$149,432.16    \$149,439.05
Less known yearly savings                          100,000.00     100,000.00
Minimum yearly intangible benefits                 \$49,432.16     \$49,439.05

Proof               (\$750,000.00)   (\$750,000.00)
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05
\$149,432.16     \$149,439.05

NPV =                    (\$34.57)          \$0.00
IRR =                14.998790%      15.000000%
Exercise 13-7            Payback Period and Simple Rate of Return
Given:
The Heritage Amusement Park would like to construct a new ride called the Sonic Boom, which
the park management feels would be very popular. The ride would cost \$450,000 to construct,
and it would have a 10% salvage value at the end of its 15-year useful life. The company
estimates that the following annual costs and revenues would be associated with the ride:

Ticket revenues                                             \$250,000
Less operating expenses:
Maintenance                                \$40,000
Salaries                                    90,000
Depreciation                                27,000
Insurance                                   30,000
Total Operating Expenses                                     187,000
Net Operating Income                                         \$63,000     \$945,000

Required:    Ignore income taxes
1. Assume that the Heritage Amusement Park will not construct a new ride unless the ride
provides a payback period of six years or less. Does the Sonic Boom ride satisfy this
requirement?

Payback period =     Investment Required / Net Uniform Annual Cash Inflow

Net Uniform Annual Cash Inflow
Net Operating Income                       \$63,000
Depreciation                                27,000
Net Uniform Annual Cash Inflow          \$90,000

Payback period =      \$450,000       /        \$90,000

Payback period =        5.00     years

The Sonic Boom has a payback less than the maximum 6-year limit.
The Sonic Boom satisfies the payback criterion.

2. Compute the simple accounting rate of return promised by the new ride. If Heritage Amusement
Park requires a simple rate of return of at least 12%, does the Sonic Boom ride meet this
criterion?

Simple accounting rate of return =          AROR

AROR = Annualized incremental NOI               /       Initial Investment Required

AROR =     \$63,000       /       \$450,000

AROR =      14.00%

The Sonic Boom has an AROR greater than the minimum 12% requirement.
The Sonic Boom satisfies the simple accounting rate or return criterion.
e Amusement
(\$450,000)
90000
90000
90000
90000
90000
90000
90000
90000
90000
90000
90000
90000
90000
90000
135000
18.595% IRR
Exercise 13-5:   Payback Method
Given:
The management of Weimar Inc., a civil engineering design company, is considering
an investment in a high-quality blueprint printer with the following cash flows:

Investment
Cash         Cash
Year            Outflow      Inflow
1               \$38,000       \$2,000
2                \$6,000       \$4,000
3                             \$8,000
4                             \$9,000
5                           \$12,000
6                           \$10,000
7                             \$8,000
8                             \$6,000
9                             \$5,000
10                             \$5,000

Required:
1. Determine the payback period of the investment.

Investment
Cash         Cash      Unrecovered
Year            Outflow      Inflow      Investment
1              (\$38,000)      \$2,000        (\$36,000)
2               (\$6,000)      \$4,000        (\$38,000)
3                             \$8,000        (\$30,000)
4                             \$9,000        (\$21,000)
5 *****                     \$12,000          (\$9,000)
6 *****                     \$10,000           \$1,000
7                             \$8,000          \$9,000
8                             \$6,000         \$15,000
9                             \$5,000         \$20,000
10                             \$5,000         \$25,000

Payback =               5        0.90             5.9 years

2. Would the payback period be affected if the cash inflow in the last year
was several times larger?

Since 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.
Problem 13-17                Preference Ranking of Investment Projects

Given:
Austin Company is investigating four different investment opportunities. Information on the
four projects under study is given below:

Project Number                                            1           2         3          4
Investment required                                   (\$480,000) (\$360,000) (\$270,000) (\$450,000)
Present value of cash inflows (10%)                     567,270    433,400    336,140    522,970
Net present value                                       \$87,270    \$73,400    \$66,140    \$72,970
Life of Project (in years)                                6          12         6          3
Internal Rate of Return                                  16%        14%        18%        19%

Since the company's required rate of return is 10%, a 10% discount rate has been used tn the
NPV calculations above. Limited funds are available for investment, so the company can not
accept all of the available projects.

Required: Break-even point: 400                                       Fixed Expenses
Total Expenses
Total Sales
1. Compute the project profitability index for each investment project.

Project profitability index =               NPV          /        Investment Required

Project Number                                            1            2           3           4
Net present value                                       \$87,270      \$73,400    \$66,140      \$72,970
Investment required                                   \$480,000     \$360,000    \$270,000    \$450,000
Project profitability index                           0.1818125    0.2038889    0.244963   0.1621556

Present value of cash inflows (10%)/Investment Req.   1.1818125    1.2038889   1.244963    1.1621556

2. Rank the four projects according to preference, in terms of:
Project Number                                      1                 2          3            4
a. NPV                                             1                  2          4            3
b. PPI                                             3                  2          1            4
c. IRR                                             3                  4          2            1

3. Which ranking do you prefer? Why?

Which ranking is best depends on the company's opportunities for reinvesting funds
as they are released from a project.

IRR:    The internal rate of return method assumes that any released funds are reinvested
at the internal rate of return.

This means that funds released from project #4 would have to be reinvested at a
rate or return of 19%, but another project yielding such a high rate of return might
be difficult to find.

PPI:    The project profitability index approach assumes that funds released from a project
are reinvested at a rate of return equal to the discount rate, which in this case is only
10%. On balance, the PPI is generally regarded as the most dependable method of
ranking competing projects.
NPV: The net present value is inferior to the project profitability index as a ranking device
because it does not properly consider the amount of investment.

For example, it ranks project #3 fourth because of its low NPV; yet this project is
the best in terms of the amount of cash inflow generated per dollar invested.
(\$1,560,000)

(Not in text)

case is only
Problem 13C-6         Net Present Value Analysis Including Income Taxes
Given:
The Crescent Drilling Company owns the drilling rights to several tracts of land on which natural gas has been found. Th
on some of the tracts is somewhat marginal, and the company is unsure whether it would be profitable to extract and sell
these tracts contain. One such tract is tract 410, on which the following information has been gathered:

Investment in equipment needed for extraction work
Working capital investment needed
Annual cash receipts from sale of gas, net of related cash operating expenses (before taxes)
Cost of restoring the land at completion of extraction work

The natural gas in tract 410 would be exhausted after 10 years of extraction work. The equipment would have a useful life
it could be sold for only 15% of its original cost when extraction was completed. For tax purposes, the company would de
equipment over 10 years using straight-line depreciation and assuming zero salvage value. The tax rate is 30%, and the c
tax discount rate is 10%. The working capital would be released for use elsewhere at the completion of the project.

Break-even point: 400
Required:
1. Compute the NPV of tract 410.
Timing of            Cash              After
Cash               Flow               Tax
Normal Acctg. Approach                                    Flows             Amounts            Effect
Investment in equipment                                    Now               (\$600,000)        None
Working capital required                                   Now                (\$85,000)        None
Net annual cash receipts                              End of Ys 1-10          \$110,000          70%
Tax Savings (Depreciation tax shield)                 End of Ys 1-10           \$60,000          30%
Restoration Expense                                   End of Year 10          (\$70,000)         70%
Salvage value of equipment in 10 years                End of Year 10           \$90,000         None
Tax Outflow from Salvage Gain                         End of Year 10           \$90,000          30%
Working capital released                              End of Year 10           \$85,000         None
Net Present Value

Normal Finance Approach                                Year 0 (Now)          Year 1            Year 2
Net annual cash receipts                                                      \$110,000          \$110,000
Less Depreciation Expense                                                      (60,000)          (60,000)
Less Restoration Expense
Taxable Salvage Gain
Income Before Taxes                                                             \$50,000          \$50,000
Less Income Taxes (30%)                                                         (15,000)         (15,000)
Net Income                                                                      \$35,000          \$35,000
Operating Cash Flow                                                             \$95,000          \$95,000
Working capital released
Cash Inflow                                                                     \$95,000           \$95,000
Table Factor 10% (PV of \$1 Table)                                              0.909091          0.826446
PV of cash inflows                  \$621,902.66           \$621,902.66        \$86,363.64        \$78,512.40
Initial Investment in equipment                           (600,000.00)
Initial Investment in Working Capital                      (85,000.00)
Net Present Value                                         (\$63,097.34)
Net Present Value (Adj. Excel Formula)                    (\$63,097.34)

2. Would you recommend that the investment project be undertaken?
No, the investment project should not be undertaken. The NPV is negative.

Calculation of Cash Inflow Y1       Finance         Acctg.        Net of Tax
Net annual cash receipts             \$110,000        \$110,000         \$77,000
Less Depreciation Expense              (60,000)                        18,000
Less Restoration Expense
Taxable Salvage Gain
Income Before Taxes                   \$50,000
Less Income Taxes (30%)               (15,000)         (15,000)
Net Income                            \$35,000
Operating Cash Flow                   \$95,000          \$95,000         \$95,000

Calculation of Cash Inflow Y10      Finance         Acctg.        Net of Tax
Net annual cash receipts             \$110,000        \$110,000         \$77,000
Less Depreciation Expense              (60,000)                         18,000
Less Restoration Expense               (70,000)        (70,000)        (49,000)
Taxable Salvage Gain                    90,000          90,000          63,000
Income Before Taxes                   \$70,000
Less Income Taxes (30%)                (21,000)        (21,000)
Net Income                            \$49,000
Operating Cash Flow                  \$109,000         \$109,000       \$109,000
ural gas has been found. The amount of gas
profitable to extract and sell the gas that
n gathered:

\$600,000
\$85,000
\$110,000
\$70,000

ment would have a useful life of 15 years, but
poses, the company would depreciate the
The tax rate is 30%, and the company's after-
mpletion of the project.

Fixed Expenses
Total Expenses
Total Sales
Cash           10%              PV of
Flow         PV Table           Cash
Amounts         Factor           Flows
(\$600,000)    1.000000         (\$600,000.00)
(\$85,000)    1.000000          (\$85,000.00)
\$77,000     6.144567          \$473,131.67
\$18,000     6.144567          \$110,602.21
(\$49,000)    0.385543          (\$18,891.62)
\$90,000     0.385543           \$34,698.90
(\$27,000)    0.385543          (\$10,409.67)
\$85,000     0.385543           \$32,771.18
(\$63,097.34)

Year 3        Year 4           Year 5           Year 6        Year 7       Year 8       Year 9
\$110,000      \$110,000           \$110,000       \$110,000      \$110,000     \$110,000     \$110,000
(60,000)       (60,000)           (60,000)       (60,000)     (60,000)     (60,000)     (60,000)

\$50,000        \$50,000             \$50,000      \$50,000       \$50,000      \$50,000      \$50,000
(15,000)       (15,000)            (15,000)     (15,000)      (15,000)     (15,000)     (15,000)
\$35,000        \$35,000             \$35,000      \$35,000       \$35,000      \$35,000      \$35,000
60,000         60,000              60,000       60,000        60,000       60,000       60,000
\$95,000        \$95,000             \$95,000      \$95,000       \$95,000      \$95,000      \$95,000

\$95,000        \$95,000            \$95,000        \$95,000       \$95,000      \$95,000      \$95,000
0.751315       0.683013           0.620921       0.564474      0.513158     0.466507     0.424098
\$71,374.91     \$64,886.28         \$58,987.53     \$53,625.02    \$48,750.02   \$44,318.20   \$40,289.27
Year 10
\$110,000
(60,000)
(70,000)
90,000
\$70,000
(21,000)
\$49,000
60,000
\$109,000
85,000
\$194,000
0.385543
\$74,795.40
Problem 13-22         Net Present Value Analysis of a Lease or Buy Decision

Given:
Blinko Products wants an airplane for use by its corporate staff. The airplane that the company wishes to acquire, a Z

Purchase alternative.
If the Zephyr II is purchased, then the costs incurred by the company would be as follows:

Purchase cost of the plane                                      \$850,000
Annual cost of servicing, licenses, and taxes                     \$9,000
Repairs:
First 3 years (per year)                                       \$3,000
Fourth year                                                    \$5,000
Fifth year                                                    \$10,000

The plane would be sold after 5 years. Based on current resale values, the company would be able to sell it for abo
the five-year period.

Lease alternative.
If the Zephyr II is leased, then the company would have to make an immediate deposit of \$50,000 to cover any dam
years, a the end of which time the deposit would be refunded. The lease would require an annual rental payment o
of Year 1). As part of this lease cost, the manufacturer would provide all servicing and repairs, license the plane, a
plane would revert to the manufacturer, as owner.

Blinko Products' required rate of return is 18%

Break-even point: 400
Required: Ignore income taxes.                                           Total Expenses
Fixed Expenses
Total Sales
1. Use the total-cost approach to determine the present value of the cash flows associated
with each alternative.
Timing of      Amount of         PV Table
Purchase alternative.                       Cash Flows      Cash Flows      Factor (18%)
Purchase cost of the plane                     Now              (\$850,000)      1.000000
Annual cost of servicing, etc.             End of Ys 1-5           (\$9,000)     3.127171
Repairs:
First Three Years                       End of Ys 1-3           (\$3,000)     2.174273
Fourth Year                             End of Year 4           (\$5,000)     0.515789
Fifth Year                              End of Year 5          (\$10,000)     0.437109
Resale value of the plane                  End of Year 5         \$425,000       0.437109

Timing of     Amount of       PV Table
Lease alternative.                              Cash Flows     Cash Flows    Factor (18%)
Damage Deposit                                     Now             (\$50,000)     1.000000
Annual Lease Payments                          End of Ys 1-5      (\$200,000)     3.127171
Refund of Deposit                              End of Year 5        \$50,000      0.437109

Net present value in favor of the leasing option
2. Which alternative would you recommend that the company accept? Why?

The company should accept the leasing alternative. The present value of the cash outflows is less negative under
at the company wishes to acquire, a Zephyr II, can be either purchased or leased

e as follows:

mpany would be able to sell it for about one-half of its original cost at the end of

deposit of \$50,000 to cover any damage during use. The lease would run for five
d require an annual rental payment of \$200,000 (the first payment is due at the end
cing and repairs, license the plane, and pay all taxes. At the end of five-years, the

2.174273

PV of           Timing of      Amount of    PV Table              PV of
Cash Flow        Cash Flows      Cash Flows Factor (18%)          Cash Flow
(\$850,000.00)        Now            (\$850,000)   1.000000         (\$850,000.00)
(28,144.54)    End of Year 1        (12,000)   0.847458           (10,169.49)
End of Year 2        (12,000)   0.718184            (8,618.21)
(6,522.82)    End of Year 3        (12,000)   0.608631            (7,303.57)
(2,578.94)    End of Year 4        (14,000)   0.515789            (7,221.04)
(4,371.09)    End of Year 5        406,000    0.437109           177,466.34
185,771.42
(\$705,845.98)                     (\$705,845.98)       3.127171    (\$705,845.98)

PV of           Timing of       Amount of    PV Table             PV of
Cash Flow        Cash Flows      Cash Flows Factor (18%)          Cash Flow
(\$50,000.00)        Now              (\$50,000)   1.000000         (\$50,000.00)
(625,434.20)    End of Year 1        (200,000)   0.847458         (169,491.53)
21,855.46     End of Year 2        (200,000)   0.718184         (143,636.89)
(\$653,578.74)    End of Year 3        (200,000)   0.608631         (121,726.17)
End of Year 4        (200,000)   0.515789         (103,157.78)
End of Year 5        (150,000)   0.437109          (65,566.38)
(\$653,578.74)                   (\$653,578.74)

\$52,267.23                         \$52,267.23                         \$52,267.23
cash outflows is less negative under the leasing option.

```
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