CHAPTER 9

Capital Budgeting

Techniques

9-3       LG 2, 3:  Choosing Between Two Projects with Acceptable Payback Periods

a.

 Project A Project B Year Cash Inflows Investment Balance Year Cash Inflows Investment Balance 0 -\$100,000 0 -\$100,000 1 \$10,000 -90,000 1 40,000 -60,000 2 20,000 -70,000 2 30,000 -30,000 3 30,000 -40,000 3 20,000 -10,000 4 40,000 0 4 10,000 0 5 20,000 5 20,000

Both project A and project B have payback periods of exactly 4 years.

b.         Based on the minimum payback acceptance criteria of 4 years set by John Shell both projects should be accepted.  However, since they are mutually exclusive projects John should accept project B.

c.                   Project B is preferred over A because the larger cash flows are in the early years of the project.  The quicker cash inflows occur the greater their value.

9-4       LG 3:  NPV

PVn = PMT x (PVIFA14%,20 yrs)

a.         PVn         =    \$2,000 x 6.623                     b.   PVn         =    \$3,000 x 6.623

PVn         =    \$13,246                                      PVn         =    \$19,869

NPV       =    PVn - Initial investment                 NPV       =    PVn - Initial investment

NPV       =    \$13,246 - \$10,000                      NPV       =    \$19,869 - \$25,000

NPV       =    \$3,246                                        NPV       =    -\$ 5,131

Calculator solution:  \$3,246.26                         Calculator solution:  - \$5,130.61

Accept                                                             Reject

c.         PVn         =    \$5,000 x 6.623

PVn         =    \$33,115

NPV       =    PVn - Initial investment

NPV       =    \$33,115 - \$30,000

NPV       =    \$3,115

Calculator solution:       \$3,115.65

Accept

9-5       LG 3:  NPV for Varying Required Returns

PVn   =    PMT x (PVIFAk%,8 yrs.)

a.                           10 %                                       b.                              12 %

PVn      =    \$5,000 x (5.335)                               PVn      =    \$5,000 x (4.968)

PVn      =    \$26,675                                            PVn      =    \$24,840

NPV    =    PVn - Initial investment              NPV =          PVn - Initial investment

NPV    =    \$26,675 - \$24,000                            NPV    =    \$24,840 - \$24,000

NPV    =    \$2,675                                              NPV    =    \$840

Calculator solution:  \$2,674.63                            Calculator solution:  \$838.19

Accept; positive NPV                                          Accept; positive NPV

c.                           14%

PVn      =    \$5,000 x (4.639)

PVn      =    \$23,195

NPV    =    PVn - Initial investment

NPV    =    \$23,195 - \$24,000

NPV    =    - \$805

Calculator solution:  - \$805.68

Reject; negative NPV

9-6       LG 2:  NPV-Independent Projects

Project A

PVn      =    PMT x (PVIFA14%,10 yrs.)

PVn      =    \$4,000 x (5.216)

PVn      =    \$20,864

NPV    =    \$20,864 - \$26,000

NPV    =    - \$5,136

Calculator solution: - \$5,135.54

Reject

Project B-PV of Cash Inflows

Year                 CF                      PVIF14%,n                  PV

1          \$100,000                       .877                    \$ 87,700

2            120,000                       .769                       92,280

3            140,000                       .675                       94,500

4            160,000                       .592                       94,720

5            180,000                       .519                       93,420

6            200,000                       .456                       91,200

\$553,820

NPV    =       PV of cash inflows - Initial investment = \$553,820 - \$500,000

NPV    =       \$53,820

Calculator solution:  \$53,887.93

Accept

Project C-PV of Cash Inflows

Year                 CF                      PVIF14%,n                  PV

1            \$20,000                       .877                    \$ 17,540

2              19,000                       .769                       14,611

3              18,000                       .675                       12,150

4              17,000                       .592                       10,064

5              16,000                       .519                         8,304

6              15,000                       .456                         6,840

7              14,000                       .400                         5,600

8              13,000                       .351                         4,563

9              12,000                       .308                         3,696

10            11,000                       .270                         2,970

\$86,338

NPV    =    PV of cash inflows - Initial investment = \$86,338 - \$170,000

NPV    =    - \$83,662

Calculator solution:  - \$83,668.24

Reject

Project D

PVn      =    PMT x (PVIFA14%,8 yrs.)

PVn      =    \$230,000 x 4.639

PVn      =    \$1,066,970

NPV    =    PVn - Initial investment

NPV    =    \$1,066,970 - \$950,000

NPV    =    \$116,970

Calculator solution:  \$116,938.70

Accept

Project E-PV of Cash Inflows

Year                 CF                      PVIF14%,n                  PV

4            \$20,000                       .592                    \$ 11,840

5              30,000                       .519                       15,570

6                       0                                                             0

7              50,000                       .400                       20,000

8              60,000                       .351                       21,060

9              70,000                       .308                       21,560

\$90,030

NPV    =    PV of cash inflows - Initial investment

NPV    =    \$90,030 - \$80,000

NPV    =    \$10,030

Calculator solution:  \$9,963.62

Accept

9-10     LG 2, 3:  Payback and NPV

a.         Project                                                Payback Period

A                              \$40,000 ¸ \$13,000            =    3.08 years

B                               3 + (\$10,000 ¸ \$16,000)   =    3.63 years

C                              2 + (\$5,000 ¸ \$13,000)     =    2.38 years

Project C, with the shortest payback period, is preferred.

b.         Project

A                  PVn      =    \$13,000 x 3.274

PVn      =    \$42,562

NPV    =    \$42,562 - \$40,000

NPV    =    \$2,562

Calculator solution:  \$2,565.82

B      Year                 CF               PVIF16%,n                 PV

1             \$ 7,000                 .862                    6,034

2              10,000                 .743                    7,430

3              13,000                 .641                    8,333

4              16,000                 .552                    8,832

5              19,000                 .476                    9,044

\$39,673

NPV    =    \$39,673 - \$40,000

=    - \$327

Calculator solution:  - \$322.53

C         Year               CF                PVIF16%,n                 PV

1            \$19,000                 .862                \$16,378

2              16,000                 .743                  11,888

3              13,000                 .641                    8,333

4              10,000                 .552                    5,520

5                7,000                 .476                    3,332

\$45,451

NPV    =    \$45,451 - \$40,000

NPV    =    \$ 5,451

Calculator   solution: \$5,454.17

Project C is preferred using the NPV as a decision criterion.

c.         At a cost of 16%, Project C has the highest NPV.  Because of Project C’s cash flow characteristics, high early-year cash inflows, it has the lowest payback period and the highest NPV.

9-11     LG 4:  Internal Rate of Return

IRR is found by solving:

It can be computed to the nearest whole percent by the estimation method as shown for Project A below or by using a financial calculator. (Subsequent IRR problems have been solved with a financial calculator and rounded to the nearest whole percent.)

Project A

Average Annuity     =    (\$20,000 + \$25,000 + 30,000 + \$35,000 + \$40,000) ¸ 5

Average Annuity     =    \$150,000 ¸ 5

Average Annuity     =    \$30,000

PVIFAk%,5yrs.          =  \$90,000 ¸ \$30,000    =    3.000

PVIFA19%,5 yrs.        =  3.0576

PVlFA20%,5 yrs.        =  2.991

However, try 17% and 18% since cash flows are greater in later years.

CFt                  PVIF17%,t       PV@17%           PVIF18%,t          PV@18%

[(1) x (2)]                                    [(1) x (4)]

Yeart             (1)                    (2)                    (3)                 (4)                 (5)

1            \$20,000              .855              \$17,100           .847           \$16,940

2              25,000              .731                18,275           .718             17,950

3              30,000              .624                18,720           .609             18,270

4              35,000              .534                18,690           .516             18,060

5              40,000              .456                 18,240           .437            11,480

\$91,025                             \$88,700

Initial investment                - 90,000                             - 90,000

NPV                                  \$ 1,025                            - \$ 1,300

NPV at 17% is closer to \$0, so IRR 17%, if the firm's cost of capital is below 17%, the project would be acceptable.

Calculator solution:  17.43%

Project B

PVn                    =    PMT x (PVIFAk%,4 yrs.)

\$490,000      =    \$150,000 x (PVIFAk%,4 yrs.)

\$490,000      ¸    \$150,000   =    (PVIFAk%,4 yrs.)

3.27              =    PVIFAk%,4

8% < IRR < 9%

Calculator solution:  IRR = 8.62%

The firm's maximum cost of capital for project acceptability would be 8% (8.62%).

Project C

PVn               =    PMT x (PVIFAk%,5 yrs.)

\$20,000        =    \$7,500 x (PVIFAk%,5 yrs.)

\$20,000        ¸    \$7,500    =    (PVIFAk%,5 yrs.)

2.67              =    PVIFAk%,5 yrs.

25% < IRR < 26%

Calculator solution:  IRR = 25.41%

The firm's maximum cost of capital for project acceptability would be 25% (25.41%).

Project D

IRR = 21%;  Calculator solution:  IRR = 21.16%

9-12     LG 4:  IRR-Mutually Exclusive Projects

a. and b.

Project X

IRR = 16%; since IRR > cost of capital, accept.

Calculator solution:  15.67%

Project Y

IRR = 17%; since IRR > cost of capital, accept.

Calculator solution:  17.29%

c.         Project Y, with the higher IRR, is preferred, although both are acceptable.

9-13     LG 2:  IRR, Investment Life, and Cash Inflows

a.         PVn            =    PMT x (PVIFAk%,n)

\$61,450     =    \$10,000 x (PVIFA k%,10 yrs.)

\$61,450     ¸    \$10,000 = PVIFAk%,10 Yrs.

6.145         =    PVIFAk%,10 yrs.

k                =    IRR = 10% (calculator solution: 10.0%)

The IRR < cost of capital; reject the project.

b.         PVn            =    PMT x (PVIFA5%,n)

\$61,450     =    \$10,000 x (PVIFA5%,n)

\$61,450     ¸    \$10,000 = PVIFA15%,n

6.145         =    PVIFA5%,n

18 yrs. < n < 19 yrs.

Calculator solution:  18.23 years

c.         PVn            =    PMT x (PVIFA15%,10)

\$61,450     =    PMT x (5.019)

\$61,450     ¸    5.019 = PMT

\$12,243.48 = PMT

Calculator solution: \$12,244.04

9-14     LG 2:  NPV and IRR

a.         PVn      =    PMT x (PVIFA10%,7 yrs.)

PVn      =    \$4,000 x (4.868)

PVn      =    \$19,472

NPV    =    PVn - Initial investment

NPV    =    \$19,472 - \$18,250

NPV    =    \$1,222

Calculator solution:  \$1,223.68

b.         PVn            =    PMT x (PVIFAk%,n)

\$18,250     =    \$4,000 x (PVIFAk%,7yrs.)

\$18,250     ¸    \$4,000 = (PVIFAk%,7 yrs.)

4.563         =    PVIFAk%,7 yrs.

IRR            =    12%

Calculator solution:  12.01%

c.         The project should be accepted since the NPV > 0 and the IRR > the cost of capital.

9-15     LG 3:  NPV, with Rankings

a.         NPVA = \$20,000(PVIFA15%,3) - \$50,000

NPVA = \$20,000(2.283) - \$50,000

NPVA = \$45,660 - \$50,000 = - \$4,340

Calculator solution:  - \$4,335.50

Reject

NPVB = \$35,000(PVIF15%,1) + \$50,000(PVIFA15%,2)(PVIF15%,1) - \$100,000

NPVB = \$35,000(.870) + \$50,000(1.626)(.870) - \$100,000

NPVB = \$30,450 + \$70,731- \$100,000 = \$1,181

Calculator solution:  \$1,117.78

Accept

NPVC = \$20,000(PVIF15%,1) + \$40,000(PVIF15%,2) + \$60,000(PVIF15%,3) - \$80,000

NPVC = \$20,000(.870) + \$40,000(.756) + \$60,000(.658) - \$80,000

NPVC = \$17,400 + \$30,240 + 39,480 - \$80,000 = \$7,120

Calculator solution:  \$7,088.02

Accept

NPVD = \$100,000(PVIF15%,1) + \$80,000(PVIF15%,2) + \$60,000(PVIF15%,3)

- \$180,000

NPVD = \$100,000(.870) + \$80,000(.756) + \$60,000(.658) - \$180,000

NPVD = \$17,400 + \$60,480 + 39,480 - \$180,000 = \$6,640

Calculator solution:  \$6,898.99

Accept

b.         Rank                Press              NPV

1                      C                \$7,120

2                      D                  6,640

3                      B                   1,181

c.         Using the calculator the IRRs of the projects are:

Project                         IRR

A                              9.70%

B                            15.63%

C                            19.44%

D                            17.51%

Since the lowest IRR is 9.7% all of the projects would be acceptable if the cost of capital was approximately 10%.

NOTE:  Since project A was the only reject project from the 4 projects all that was needed to find the minimum acceptable cost of capital was to find the IRR of A.

9-16     LG 2, 3, 4:  All Techniques, Conflicting Rankings

a.

 Project A Project B Year Cash Inflows Investment Balance Year Cash Inflows Investment Balance 0 -\$150,000 0 -\$150,000 1 \$45,000 -105,000 1 \$75,000 -75,000 2 45,000 -60,000 2 60,000 -15,000 3 45,000 -15,000 3 30,000 +15,000 4 45,000 +30,000 4 30,000 0 5 45,000 30,000 6 45,000 30,000

b.         NPVA = \$45,000(PVIFA0%,6) - \$150,000

NPVA = \$45,000(6) - \$150,000

NPVA = \$270,000 - \$150,000 = \$120,000

Calculator solution:  \$120,000

NPVB = \$75,000(PVIF0%,1) + \$60,000(PVIF0%,2) + \$30,000(PVIFA0%,4)(PVIF0%,2)

-\$150,000

NPVB = \$75,000 + \$60,000 + \$30,000(4) - \$150,000

NPVB = \$75,000 + \$60,000 + \$120,000 - \$150,000 = \$105,000

Calculator solution:  \$105,000

c.         NPVA = \$45,000(PVIFA9%,6) - \$150,000

NPVA = \$45,000(4.486) - \$150,000

NPVA = \$201,870 - \$150,000 = \$51,870

Calculator solution:  \$51,886.34

NPVB = \$75,000(PVIF9%,1) + \$60,000(PVIF9%,2) + \$30,000(PVIFA9%,4)(PVIF9%,2)

-\$150,000

NPVB = \$75,000(.917) + \$60,000(.842) + \$30,000(3.24)(.842) - \$150,000

NPVB = \$68,775 + \$50,520 + \$81,842 - \$150,000 = \$51,137

Calculator solution:  \$51,112.36

d.         Using a financial calculator:

IRRA = 19.91%

IRRB = 22.71%

e.

 Rank Project Payback NPV IRR A 2 1 2 B 1 2 1

The project that should be selected is A.  The conflict between NPV and IRR is due partially to the reinvestment rate assumption.  The assumed reinvestment rate of project B is 22.71%, the project's IRR.  The reinvestment rate assumption of A is 9%, the firm's cost of capital.

9-17     LG 2, 3:  Payback, NPV, and IRR

a.         Payback period

3 + (\$20,000 ¸ \$35,000) = 3.57 years

b.         PV of cash inflows

Year                 CF                   PVIF12%,n         PV

1               \$20,000                 .893          \$ 17,860

2                 25,000                 .797             19,925

3                 30,000                 .712             21,360

4                 35,000                 .636             22,260

5                 40,000                 .567             22,680

\$104,085

NPV    =    PV of cash inflows - Initial investment

NPV    =    \$104,085 - \$95,000

NPV    =    \$9,085

Calculator solution:  \$9,080.61

c.

IRR = 15%

Calculator solution:  15.36%

d.         NPV    =    \$9,085; since NPV > 0; accept

IRR      =    15%; since IRR > 12% cost of capital; accept

The project should be implemented since it meets the decision criteria for both NPV and IRR.

9-18     LG 3, 4, 5:  NPV, IRR, and NPV Profiles

a. and b.

Project A

PV of cash inflows:

Year                 CF                   PVIF12%,n         PV

1               \$25,000                 .893          \$ 22,325

2                 35,000                 .797             27,895

3                 45,000                 .712             32,040

4                 50,000                 .636             31,800

5                 55,000                 .567             31,185

\$145,245

NPV    =    PV of cash inflows - Initial investment

NPV    =    \$145,245 - \$130,000

NPV    =    \$15,245

Calculator solution:  \$15,237.71

IRR      =    16%

Calculator solution:  16.06%

Project B

PV of cash inflows:

Year                 CF                   PVIF15%,n         PV

1               \$40,000                 .893          \$ 35,720

2                 35,000                 .797             27,895

3                 30,000                 .712             21,360

4                 10,000                 .636               6,360

5                   5,000                 .567               2,835

\$ 94,170

NPV    =    \$94,170 - \$85,000

NPV    =    \$9,170

Calculator solution:  \$9,161.79

IRR      =    18%

Calculator solution:  17.75%

c.

 Net Present Value Profile
 Net Present Value (\$)
 Discount Rate (%)

Data for NPV Profiles

Discount Rate                                    NPV

A                  B

0%                              \$ 80,000         \$ 35,000

12%                            \$ 15,245                     -

15%                                         -           \$ 9,170

16%                                        0                     -

18%                                         -                     0

d.         The net present value profile indicates that there are conflicting rankings at a discount rate lower than the intersection point of the two profiles (approximately 15%).  The conflict in rankings is caused by the relative cash flow pattern of the two projects.  At discount rates above 15%, Project B is preferable; below 15%, Project A is better.

e.         Project A has an increasing cash flow from year 1 through year 5, whereas Project B has a decreasing cash flow from year 1 through year 5.  Cash flows moving in opposite directions often cause conflicting rankings.

9-19     LG 2, 3, 4, 5, 6:  All Techniques-Mutually Exclusive Investment Decision

Project

A                       B                    C

Cash inflows (years 1 - 5)              \$20,000           \$31,500           \$32,500

a.   Payback*                                  3 years          3.2 years          3.4 years

b.   NPV*                                     \$10,340           \$10,786            \$ 4,303

c.   IRR*                                             20%                 17%                 15%

*  Supporting calculations shown below:

a.         Payback Period:         Project A:        \$60,000   ¸   \$20,000   =    3 years

Project B:      \$100,000   ¸   \$31,500   =    3.2 years

Project C:      \$110,000   ¸   \$32,500   =    3.4 years

b.         NPV                                                                c.      IRR

Project A                                                                  Project, A

PVn      = PMT x (PVIFA13%,5 Yrs.)                              NPV at 19% =      \$1,152.70

PVn      =   \$20,000   x   3.517                                   NPV at 20% =     - \$ 187.76

PVn      =     70,340                                                   Since NPV is closer to zero

at 20%, IRR = 20%

NPV    =   \$70,340   -   \$60,000                               Calculator solution:  19.86%

NPV    =   \$10,340

Calculator solution: \$10,344.63

Project B                                                                  Project B

PVn      =       \$31,500.00   x   3.517                          NPV at 17% =          \$779.40

PVn      =     \$110,785.50                                          NPV at 18% =     -\$1,494.11

Since NPV is closer to zero

NPV    =     \$110,785.50   -   \$100,000                    at 17%, IRR = 17%

NPV    =       \$10,785.50                                          Calculator solution:  17.34%

Calculator solution:  \$10,792.78

Project C                                                                  Project C

PVn      =      \$32,500.00    x    3.517                        NPV at 14% =      \$1,575.13

PVn      =    \$114,302.50                                           NPV at 15% =    - \$1,054.96

Since NPV is closer to zero at

NPV    =    \$114,302.50   -   \$110,000                     15%, IRR = 15%

NPV    =    \$4,302.50                                               Calculator solution:  14.59%

Calculator solution:  \$4,310.02

d.

 Comparative Net Present Value Profiles
 Net Present Value (\$)
 Discount Rate (%)

Data for NPV Profiles

Discount Rate                                                         NPV

A                      B                     C

0%                                     \$ 40,000       \$ 57,500          \$ 52,500

13%                                     \$ 10,340          10,786               4,303

15%                                                  -                    -                      0

17%                                                  -                   0                       -

20%                                                 0                    -                       -

The difference in the magnitude of the cash flow for each project causes the NPV to compare favorably or unfavorably, depending on the discount rate.

e.         Even though A ranks higher in Payback and IRR, financial theorists would argue that B is superior since it has the highest NPV.  Adopting B adds \$445.50 more to the value of the firm than does A.

9-20     LG 2, 3, 4, 5, 6:  All Techniques with NPV Profile-Mutually Exclusive Projects

a.         Project A

Payback period

Year 1 + Year 2 + Year 3                  =        \$60,000

Year 4                                               =        \$20,000

Initial investment                                 =        \$80,000

Payback     =    3 years + (\$20,000 ¸ 30,000)

Payback     =    3.67 years

Project B

Payback period

\$50,000 ¸ \$15,000 = 3.33 years

b.         Project A

PV of cash inflows

Year                 CF                   PVIF13%,n         PV

1            \$15,000                    .885          \$ 13,275

2              20,000                    .783             15,660

3              25,000                    .693             17,325

4              30,000                    .613             18,390

5              35,000                    .543              19,005

\$83,655

NPV    =    PV of cash inflows - Initial investment

NPV    =    \$83,655 - \$80,000

NPV    =    \$3,655

Calculator solution:  \$3,659.68

Project B

NPV    =    PV of cash inflows - Initial investment

PVn      =    PMT x (PVIFA13%,n)

PVn      =    \$15,000 x 3.517

PVn      =    \$52,755

NPV    =    \$52,755 - \$50,000

=    \$2,755

Calculator solution:  \$2,758.47

c.         Project A

IRR   =  15%

Calculator solution:  14.61%

Project B

\$0     =    \$15,000 x (PVIFA k%,5) - \$50,000

IRR   =    15%

Calculator solution:  15.24%

 Net Present Value Profile

d.

 Net Present Value (\$)
 Discount Rate (%)

Data for NPV Profiles

Discount Rate                                     NPV

A                  B

0%                            \$ 45,000       \$ 25,000

13%                              \$ 3,655         \$ 2,755

14.6%                                        0                    -

15.2%                                         -                   0

Intersection -approximately 15%

If cost of capital is above 15%, conflicting rankings occur.

e.         Both projects are acceptable.  Both have positive NPVs and equivalent IRR's which are greater than the cost of capital.  Although Project B has a slightly higher IRR, the rates are very close.  Since Project A has a higher NPV, accept Project A.

9-21     LG 2, 3, 4:  Integrative--Complete Investment Decision

a.         Initial investment:

Installed cost of new press =

Cost of new press                                                                     \$2,200,000

-     After-tax proceeds from sale of old asset

Proceeds from sale of existing press               (1,200,000)

+    Taxes on sale of existing press *                          480,000

Total after-tax proceeds from sale                                          (720,000)

Initial investment                                                                                   \$1,480,000

*    Book value    =    \$0

\$1,200,000 - \$0 = \$1,200,000 capital gain

\$1,200,000 capital gain x (.40)       =          \$ 480,000 tax liability

b.

Calculation of Operating Cash Flows

Net Profits                     Net Profits   Cash

Year   Revenues     Expenses       Depreciation     before Taxes    Taxes     after Taxes   Flow

1   \$1,600,000      \$800,000         \$440,000      \$360,000   \$144,000   \$216,000  \$656,000

2     1,600,000        800,000           704,000          96,000       38,400       57,600    761,600

3     1,600,000        800,000           418,000        382,000     152,800     229,200    647,200

4     1,600,000        800,000           264,000        536,000     214,400     321,600    585,600

5     1,600,000        800,000           264,000        536,000     214,400     321,600    585,600

6                   0                   0           110,000       -110,000      -44,000      -66,000      44,000

c.         Payback period = 2 years + (\$62,400 ¸ \$647,200) = 2.1 years

d.         PV of cash inflows:

Year                 CF                   PVIF11%,n            PV

1             \$656,000                 .901            \$591,056

2               761,600                 .812              618,419

3               647,200                 .731              473,103

4               585,600                 .659              385,910

5               585,600                 .593              347,261

6                 44,000                 .535                23,540

\$2,439,289

NPV    =    PV of cash inflows - Initial investment

NPV    =    \$2,439,289 - \$1,480,000

NPV    =    \$959,289

Calculator solution:  \$959,152

IRR   =  35%

Calculator solution:  35.04%

e.         The NPV is a positive \$959,289 and the IRR of 35% is well above the cost of capital of 11%.  Based on both decision criteria, the project should be accepted.

9-22     LG 2, 3:  Integrative-Investment Decision

a.         Initial investment:

Installed cost of new asset =

Cost of the new machine                             \$1,200,000

+    Installation costs                                              150,000

Total cost of new machine                                                   \$1,350,000

-     After-tax proceeds from sale of old asset =

Proceeds from sale of existing machine          (185,000)

-     Tax on sale of existing machine*                       (79,600)

Total after-tax proceeds from sale                                         (264,600)

+    Increase in net working capital                                                               25,000

Initial investment                                                                             \$1,110,400

*    Book value                               =    \$384,000

\$384,000 -\$185,000                =    \$199,000 loss

\$199,000 x.40                         =    \$79,600 tax benefit

Calculation of Operating Cash Flows

New Machine

Reduction in                                Net Profits                        Net Profits         Cash

Year     Operating Costs    Depreciation      Before Taxes       Taxes     After Taxes        Flow

1          \$350,000            \$270,000          \$ 80,000        \$32,000    \$ 48,000      \$318,000

2            350,000              432,000           - 82,000        - 32,800     - 49,200        382,800

3            350,000              256,500             93,500          37,400       56,100        312,600

4            350,000              162,000           188,000          75,200     112,800        274,800

5            350,000              162,000           188,000          75,200     112,800        274,800

6                       0                67,500           - 67,500        - 27,000     - 40,500          27,000

Existing Machine

Net Profits                                Net Profits           Cash

Year              Depreciation              Before Taxes          Taxes         After Taxes         Flow

1                \$152,000                - \$152,000       - \$60,800          - \$91,200        \$60,800

2                    96,000                  -   96,000       -   38,400          -   57,600          38,400

3                    96,000                  -   96,000       -   38,400          -   57,600          38,400

4                    40,000                  -   40,000       -   16,000          -   24,000          16,000

5                             0                               0                     0                        0                   0

Incremental Operating Cash Flows

Incremental

Year                 New Machine               Existing Machine              Cash Flow

1                      \$318,000                          \$60,800                  \$257,200

2                        382,800                            38,400                    344,400

3                        312,600                            38,400                    274,200

4                        274,800                            16,000                    258,800

5                        274,800                                     0                    274,800

6                          27,000                                     0                      27,000

Terminal cash flow:

After-tax proceeds from sale of new asset =

Proceeds from sale of new asset                       \$200,000

-     Tax on sale of new asset *                                  (53,000)

Total proceeds-sale of new asset                                        \$147,000

-     After-tax proceeds from sale of old asset                                               0

+    Change in net working capital                                                        25,000

Terminal cash flow                                                                          \$172,000

*    Book value of new machine at the end of year 5 is \$67,500

\$200,000 - \$67,500                 =    \$132,500 recaptured depreciation

\$132,500 x.40                         =    \$53,000 tax liability

b.         Year                 CF                   PVIF9%,n             PV

1             \$257,200                   .917          \$ 235,852

2               344,400                   .842             289,985

3               274,200                   .772             211,682

4               258,800                   .708             183,230

5               274,800                   .650             178,620

Terminal

value            172,000                   .650             111,800

\$1,211,169

NPV    =    PV of cash inflows - Initial investment

NPV    =    \$1,211,169 - \$1,110,400

NPV    =    \$100,769

Calculator solution:  \$100,900

c.

IRR      =          12.2%

Calculator solution:  12.24%

d.         Since the NPV > 0 and the IRR > cost of capital, the new machine should be purchased.

e.         12.24%.  The criterion is that the IRR must equal or exceed the cost of capital; therefore, 12.24% is the lowest acceptable IRR.