Practice Problems Ch12

Foundations of Fin. Mgt. 8/E Cdn. • Block, Hirt, Short S-364

Practice Problems Chapter 12 Problems 12-1. Corporate cash flow

Earnings before amortization and taxes $ 90,000 Amortization – 40,000 Earnings before taxes 50,000 Taxes @ 30% 15,000 Earnings aftertaxes 35,000 Amortization + 40,000 Cash flow $ 75,000

Alternative cash flow calculation: $90,000 15,000 (taxes) $75,000 cash flow 12-2. Corporate cash flow

a. Earnings before amortization and taxes $ 90,000 Amortization – 10,000 Earnings before taxes 80,000 Taxes @ 30% 24,000 Earnings aftertaxes 56,000 Amortization + 10,000 Cash flow $ 66,000

b. Cash flow (problem 1) $75,000 or [$40,000 – $10,000](T) Cash flow (problem 2a) 66,000 = 30,000 (.3) Difference in cash flow $ 9,000 = $9,000


12-3. Blink 281 Corporation

a. ( )value book Averageaftertax earnings AverageAAR return accounting Average =

Year EBAT Amortization EBT Taxes EAT 1 $35,000 $16,000 $19,000 $7,600 $11,400 2 37,000 16,000 21,000 8,400 12,600 3 41,000 16,000 25,000 10,000 15,000 4 45,000 16,000 29,000 11,600 17,400 5 50,000 16,000 34,000 13,600 20,400 76,800 Average earnings aftertax $15,360

( ) %4.383840.02/000,80$

360,15$===AAR return accounting Average

b. Seems like a pretty good return, but we need a criteria for

acceptance of projects. What AAR is enough?

c. AAR does not use the time value of money, cash flows or the market value of assets.

12-4. Pluto Corporation

Year EBAT Amortization EBT Taxes EAT 1 $110,000 $70,000 $40,000 $16,000 $24,000 2 120,000 70,000 50,000 20,000 30,000 3 150,000 70,000 80,000 32,000 48,000 102,000 Average earnings aftertax $34,000

( ) %38.323238.02/000,210$

000,34$===AAR return accounting Average


12-5. Al Quick Being short term oriented, he may make the mistake of turning down the project even though it will increase cash flow because of his fear of investors’ negative reaction to the more widely reported quarterly decline in earnings per share. Even though this decline will be temporary, investors might interpret it as a negative signal.

12-6. Pluto Corporation

Year EBAT Amortization EBT Taxes EAT 1 $110,000 $70,000 $40,000 $16,000 $24,000 2 120,000 70,000 50,000 20,000 30,000 3 150,000 70,000 80,000 32,000 48,000 102,000 Average earnings aftertax $34,000

( ) %38.323238.02/)0000,210($

000,34$AARreturn accounting Average ==+

=

12-7. Payback

Payback for Investment X Payback for Investment Y

$40,000 – $ 6,000 1 year $40,000 – $15,000 1 year 34,000 – 8,000 2 years 25,000 – 20,000 2 years 26,000 – 9,000 3 years 5,000/ 10,000 2.5 years 17,000 – 17,000 4 years

Payback: Investment X = 4.00 years

Payback: Investment Y = 2.5 years

Investment Y would be selected because of the faster payback.


12-8. Payback Revisited

The $20,000,000 inflow would still leave the payback period for Investment X at 4 years. It would remain inferior to Investment Y under the payback method. 12-9. Payback versus NPV

NPV for Investment X

Year Cash flow Present value @ 15% 1 $ 6,000 $ 5,217 2 8,000 6,049 3 9,000 5,918 4 17,000 9,720 5 20,000 9,944 Present value of inflows $36,848 Initial investment 40,000 NPV (net present value) $(3,152)

NPV for Investment Y

Year Cash flow Present value @ 15% 1 $15,000 $13,043 2 20,000 15,123 3 10,000 6,575 Present value of inflows $34,741 Initial investment 40,000 NPV (net present value) $(5,259)

Neither project is attractive, with investment Y less attractive.


12-10. Boardwalk Company

a. Payback for Reading Railway Payback for St. Charles Place

$90,000 – $60,000 1 year $90,000 – $10,000 1 year 30,000 – 10,000 2 years 80,000 – 10,000 2 years 20,000 – 10,000 3 years 70,000 – 10,000 3 years 10,000 – 10,000 4 years 60,000 – 60,000 4 years

Both projects have equal payback = 4.00 years

b. Reading Railway with a $60,000 payback in year 1 is preferred to St. Charles with its $60,000 payback in year 4, when we consider the time value of money.

12-11. Diaz Camera Company

a. Payback for Project A Payback for Project B

$10,000 – $6,000 1 year $10,000 – $5,000 1 year 4,000 – 4,000 2 years 5,000 – 3,000 2 years 2,000 / 8,000 2.25 years

Choose project A

b. NPV for Project A Year Cash flow Present value @ 10% 1 $6,000 $5,455 2 4,000 3,306 3 3,000 2,254 Present value of inflows $11,015 Initial investment 10,000 NPV (net present value) $ 1,015


NPV for Project B Year Cash flow Present value @ 10% 1 $5,000 $4,545 2 3,000 2,479 3 8,000 6,011 Present value of inflows $13,035 Initial investment 10,000 NPV (net present value) $ 3,035

Both projects are attractive, but project B adds the most value to the firm. It has the higher NPV.

c. The NPV is preferred and gives more confidence because it incorporates the time value of money and considers all the cash flows.

12-12. Hand Salsa

D) Appendix A

PVPVIFA (889.5000,2$778,11$

===

For N = 10, we find 5.889 under the 11% column. Therefore IRR = 11%

Calculator: PV = $11,778 FV = 0 PMT = $2,000 N = 10 %i =? Compute: %i = 11.00%


12-13. Generation Thumbs

D) Appendix A

PVPVIFA (660.5000,3$980,16$

===


Calculator: PV = $16,980 FV = 0 PMT = $3,000 N = 12 %i =? Compute: %i = 14.00%

12-14. Warner Business Products

D) Appendix A

PVPVIFA (535.5000,2$070,11$

===


Calculator: PV = $11,070 FV = 0 PMT = $2,000 N = 8 %i =? Compute: %i= 9.00%

The machine should not be purchased since its return is under 13%.

12-15. Home Security Systems

a. Year Cash flow PV @ 14% @15% 1 $20,000 $17,544 17,391 2 18,000 13,850 13,611 3 13,000 8,775 8,548 Present value of inflows $40,169 $39,550 Initial investment 40,000 40,000 NPV (net present value) $ 169 $ (450)

IRR is the discount rate at which the NPV = 0. This is a trial and error process. In this case IRR is between 14% and 15% (14% + 169/ 619 × 1% = 14.27%)


b. Year Cash flow Present value @ 12% 1 $20,000 $17,857 2 18,000 14,349 3 13,000 9,253 Present value of inflows $41,459 Initial investment 40,000 NPV (net present value) $ 1,459

The machine should be purchased as the NPV is positive.

c. 04.1000,40$459,41$

===outflows of PVinflows of PVindexity Profitabil

12-16. Aerospace Dynamics

Year Cash flow Present value @ 11% 1 $36,000 $32,432 2 44,000 35,711 3 38,000 27,785 4 (44,000) (28,984) 5 81,000 48,070 Present value of inflows $115,014 Present value of outflows 110,000 NPV(net present value) $ 5,014

The NPV is positive and the project should be undertaken.


12-17. Horizon Corporation Year Cash flow Present value @ 10% 1 $15,000 $13,636 2 25,000 20,661 3 40,000 30,053 3 (10,000) (7,513) Present value of inflows $56,837 Present value of time zero outflow 60,000 Net present value $(3,163)

The NPV is negative. The project should not be undertaken. Note, the $10,000 outflow could have been subtracted out of the $40,000 inflow in the third year and the same answer would result.

12-18. Skyline Corporation

Find the present value of a deferred annuity: PVA = A × PVIFA (n = 10, i = 12%) (Appendix D) PVA = $34,000 × 5.650 = $192,100

Calculator: PV =? FV = 0 PMT = $34,000 N = 10 %i = 12% Compute: PV = $192,108

Discount this value to PV from the beginning of the third period (end of 2nd). PV = FV × PVIF (n = 2, i = 12%) (Appendix B) PV = $192,100 × .797 = $153,104

Calculator: PV =? FV = $192,108 PMT = 0 N = 2 %i = 12% Compute: PV = $153,147

Present value of inflows $153,147 Present value of outflows 130,000 NPV (net present value) $ 23,147 Undertake project!


12-19. Ogden Corporation a. NPV

Year Cash flow Present value @ 9% 1 $ 5,000 $ 4,587 2 5,000 4,208 3 8,000 6,177 4 9,000 6,376 5 10,000 6,499 Present value of inflows $27,847 Present value of outflows (cost) 25,000 NPV (net present value) $ 2,847

b. IRR Since we have a positive net present value, the internal rate of return must be larger than 9%. Because of uneven cash flows, we need to use trial and error. Counting the net present value calculation as the first trial, we now try 11% for our second trial.

Year Cash flow Present value @ 11% 1 $ 5,000 $ 4,505 2 5,000 4,058 3 8,000 5,850 4 9,000 5,929 5 10,000 5,935 Present value of inflows $26,277

A two percent increase in the discount rate has eliminated over one-half of the net present value so another two percent should be close to the answer.

Year Cash flow Present value @13% 1 $ 5,000 $ 4,425 2 5,000 3,916 3 8,000 5,544 4 9,000 5,520 5 10,000 5,428 Present value of inflows $24,833


The correct answer must fall between 11% and 13%. We interpolate.

$26,277 PV @ 11% $26,277 PV @ 11% 24,833 PV @ 13% 25,000 (Cost) $ 1,444 $ 1,277

( ) ( ) ( )

%77.121277.00177.11.0

02.0884.011.002.0444,1$277,1$11.0

==+=

+=+=

einterpolat IRR

Calculator: Cfi = – 25,000; 5,000; 5,000; 8,000; 9,000; 10,000 n = 5 %i =? Compute: IRR = 12.76%

c. The project should be accepted because the NPV is positive and the IRR exceeds the cost of capital.


12-20. Adventures Club, Inc.

NPV for Project X (Disneyland) Year Cash flow Present value @ 12% 1 $4,000 $ 3,571 2 5,000 3,986 3 4,200 2,989 4 3,600 2,288 Present value of inflows 12,834 Present value of outflows (cost) 10,000 NPV (net present value) $ 2,834

2834.1000,10$834,12$


NPV for Project Y (Film Festivals) Year Cash flow Present value @ 12% 1 $10,800 $ 9,643 2 9,600 7,653 3 6,000 4,271 4 7,000 4,449 Present value of inflows $26,016 Present value of outflows (cost) 22,000 NPV (net present value) $ 4,016

1825.1000,22$016,26$


You should select Project X because it has the higher profitability index. This is true in spite of the fact that it has a lower net present value. The profitability index may be appropriate when you have different size investments. What can be earned on the differential investment of $12,000 (between projects) may be relevant.


12-21. Cablevision, Inc.

a. Reinvestment assumption of NPV

No. of Year Inflows Rate Periods Future value

1 $10,000 9% 4 $14,116 2 10,000 9% 3 12,950 3 16,000 9% 2 19,010 4 19,000 9% 1 20,710 5 20,000 – 0 20,000 $86,786

b. Reinvestment assumption of IRR

No. of Year Inflows Rate Periods Future value

1 $10,000 15% 4 $17,490 2 10,000 15% 3 15,209 3 16,000 15% 2 21,160 4 19,000 15% 1 21,850 5 20,000 – 0 20,000 $95,709

c. No. However, for investments with a very high IRR, it may be

unrealistic to assume that reinvestment can take place at an equally high rate. The net present value method makes the more conservative assumption of reinvestment at the cost of capital.


12-22. Last Century Corporation

a. Year Inflows Rate # of Periods Future value

1 $12,000 7% 2 $13,739 2 10,000 7% 1 10,700 3 7,200 7% 0 7,200 Terminal value $31,639

B)Appendix ( 790.0639,31$000,25$

FVPVPVIF ===

At 3 periods, appendix B suggests a modified IRR of 8%

Calculator: PV = $25,000 FV = $31,639 PMT = 0 N = 3 %i = ? Compute: %i = 8.17%

b.

Calculator: CFi = – 25,000; 12,000; 10,000; 7,200 %i = ? Compute: IRR = 8.96% The difference occurs because the traditional IRR assumes reinvestment at the IRR whereas the modified IRR (MIRR) assumes reinvestment at the lower cost of capital.


12-23. Music Box Rentals


1 $16,000 10% 2 $19,360 2 12,300 10% 1 13,530 3 15,100 10% 0 15,100 Terminal value $47,990

B)Appendix ( 813.0990,47$000,39$

FVPVPVIF ===



b.

Calculator: CFi = – 39,000; 16,000; 12,300; 15,100 %i = ? Compute: IRR = 5.6% The difference occurs because the traditional IRR assumes reinvestment at the IRR whereas the modified IRR (MIRR) assumes reinvestment at the higher cost of capital.


12-24. Caffeine Coffee Company


1 $15,000 12% 2 $18,816 2 12,000 12% 1 13,440 3 9,000 12% 0 9,000 Terminal value $41,256

B)Appendix ( 654.0256,41$000,27$

FVPVPVIF ===



b.

Calculator: CFi = – 27,000; 15,000; 12,000; 9,000 %i = ? Compute: IRR = 17.5% The difference occurs because the traditional IRR assumes reinvestment at the IRR whereas the modified IRR (MIRR) assumes reinvestment at the lower cost of capital.


12-25. Oliver Stone and Rock Company

You should rank the investments in terms of IRR.

Project IRR Project Size Total Budget

E 21% $20,000 $ 20,000 B 19.0 25,000 45,000 G 18.0 25,000 70,000 H 17.5 10,000 80,000 D 16.5 25,000 105,000 A 14.0 15,000 120,000 F 11.0 15,000 135,000 C 10.0 30,000 165,000

a. Because of capital rationing, only $80,000 worth of projects can be accepted. The four projects to accept are E, B, G and H. Projects D and A provide positive benefits also, but cannot be undertaken under capital rationing.

b. If Projects B and G are mutually exclusive, you would select Project B in preference to G. In summary, you would accept E, B, H and D. The last project would replace G and is of the same $25,000 magnitude.

12-26. Miller Electronics

12-27. Software Systems

a. NPV @ 0% discount rate Inflows Outflow $5,800 = (11,000 + $9,000 + $5,800) – $20,000

b. 10% discount rate

Year Cash Flow Present Value @ 10% 1 $11,000 $10,000 2 9,000 7,438


3 5,800 4,358 Present value of inflows 21,796 Present value of outflows 20,000 NPV (net present value) $ 1,796

c. 20% discount rate

Year Cash Flow Present Value @ 20% 1 $11,000 $ 9,167 2 9,000 6,250 3 5,800 3,356 Present value of inflows 18,773 Present value of outflows 20,000 Net Present Value $(1,227)


d. Net present value profile

e. Interpolate between 15% and 16%:

Year Cash Flow Present Value @ 15% 1 $11,000 $ 9,565 2 9,000 6,805 3 5,800 3,814 Present value of inflows $20,184

Year Cash Flow Present Value @ 16% 1 $11,000 $ 9,483 2 9,000 6,688 3 5,800 3,716 Present value of inflows $19,887


$20,184 PV @ 15% $20,184 PV @ 15% 19,887 PV @ 16% 20,000 (Cost) $ 297 $ 184

( ) ( ) ( )

%62.151562.00062.15.0

01.062.015.001.0297$184$15.0

==+=

+=+=

ationinterpolat IRR

Calculator: Cfi = – 20,000; 11,000; 9,000; 5,800 N = 3 %i =? Compute: IRR = 15.62%


12-28. Zebra Corporation

a. The original cost of the building would be deducted from the Class 3 pool as the lower of sale price or original cost is used when disposing of an asset. The Class 3 UCC is:

$12,000,000 4,500,000 $ 7,500,000

The present value of the tax shield lost on disposal would be: Salvage × d Tc/ (d + r) = $4,500,000 × .05 × .40/ (.05 + .12) = $4,500,000 × .1176471 = $529,412

The $500,000 difference ($5,000,000 – $4,500,000) would be a capital gain for tax purposes. Fifty percent of a capital gain is taxable. Zebra’s tax on the taxable capital gain is:

0.50 × capital gain × T × PVIF (n = 1, i = 12%) = 0.50 × $500,000 × .4 × PVIF (n = 1, i = 12%) = $89,286

The total present value of tax consequences = $529,412 + $89,286 = $618,698

b. Class 3 UCC $4,000,000 4,500,000 $ (500,000)

The negative balance of $500,000 is recaptured amortization. This is added to income in the year of disposal thus increasing tax by:

Income increase × T × PVIF (n = 1, i = 12%) = $500,000 × 0.4 × PVIF (n = 1, i = 12%) = $178,571


The present value of the tax shield lost on disposal would be: Salvage × d Tc / (d + r) = $4,000,000 × .05 × .40 / (.05 + .12) = $4,000,000 × .1176471 = $470,588

Since there was only $4,000,000 in the pool, that is the basis for calculating the tax shield lost on disposal. The tax on the taxable capital gain is $89,286 (as in part a).

The total present value of tax consequences = $178,571 + $470,588 + $89,286 = $738,445

c. Class 3 UCC $6,000,000 4,500,000 $1,500,000

The $1,500,000 left over in the Class 3 pool is a terminal loss and can be written off against income in the year of disposal. The tax savings is:

Terminal loss × T × PVIF (n = 1, i = 12%) = $1,500,000 × .4 × PVIF (n = 1, i = 12%) = $535,714

The present value of the tax shield lost on disposal would be:

Amount in pool × d Tc/ (d + r) = $6,000,000 × .05 × .40 / (.05 + .12) = $6,000,000 × .1176471 = $705,882

The tax on the taxable capital gain is $89,286 (as in part a).

The total present value of tax consequences = $(535,714) + $705,882 + $89,286 = $259,454


12-29. Capital Cost Allowance

a. The assets will fall under Class 10 (auto equipment) with an allowable CCA rate of 30%.

b. Year 1 Increase in pool’s UCC = $95,000 Allowable CCA in 1st year = 1/2 ($95,000 × .30)

= $14,250 Year 2

Remaining increase in UCC = $95,000 – $14,250 = $80,750

Additional CCA allowable = $80,750 × .30 = $24,225

c. The assets would then fall under Class 8 (machinery): The allowable CCA rate would be 20%.

d. There would be no effects except to the extent of any dollar

amounts realized on disposal.


12-30. Coastal Shipping Corporation

a. The original cost of the vessel would be deducted from the Class 7 pool as the lower of sale price or original cost is used when disposing of an asset. The Class 7 UCC is:

$2,000,000 1,000,000 $1,000,000

The present value of the tax shield lost on disposal would be: Amount lost from pool (salvage) × dTc / (d + r)

= $1,000,000 × .15 × .40 / (.15 + .10) = $1,000,000 × .240 = $240,000

This is the extent of the tax consequences.

b. Class 3 UCC $ 800,000 1,000,000 $ (200,000)

The negative balance of $200,000 is recaptured amortization. This is added to income in the year of disposal increasing tax by:

Income increase × T × PVIF (n = 1, i = 10%) = $200,000 × .4 × PVIF (n = 1, i = 10%) = $72,727

The present value of the tax shield lost on disposal would be: Amount lost from pool (salvage) × dTc / (d + r)

= $800,000 × .15 × .40 / (.15 + .10) = $800,000 × .240 = $192,000

Since there was only $800,000 in the pool, that is the basis for calculating the tax shield lost on disposal.


The total present value of tax consequences = $72,727 + $192,000 = $264,727

c. Class 3 UCC $ 600,000

1,000,000 $(400,000)

The negative balance of $400,000 is recaptured amortization. This is added to income in the year of disposal thus increasing tax by:

Income increase × T × PVIF (n = 1, i = 10%) = $400,000 × .4 × PVIF (n = 1, i = 10%) = $145,454

The present value of the tax shield lost on disposal would be:

Amount lost from pool (salvage) × dTc / (d + r) = $600,000 × .15 × .40 / (.15 + .10) = $600,000 × .240 = $144,000

Since there was only $600,000 in the pool, that is the basis for calculating the tax shield lost on disposal.

The total present value of tax consequences

= $145,454 + $144,000 = $289,454


12-31. Nexus Corp.

a. The CCA class for aircraft is Class 9, with a CCA rate of 25%.

b. CCA allowable in 1st year $1,500,000 × 25% × .5 = $187,500 CCA allowable in 2nd year [$1,500,000 − $187,500] × 25% = $328,125

c. The CCA class for hangars is class 6, with a CCA rate of 10%.

d. After 10 years the UCC of Class 9 will be(including CCA for the

10th year):

$1,500,000[1 − (.25/2) (1 − .25)10 – 1] = $1,500,000 [(.875) (.75)9] = $1,500,000 [.0656991] = $98,549

If the plane is scrapped after the 10th year the consequences are: Recapture of $200,000 98,549 $101,451

Thus $101,451 will be added to taxable income in the eleventh year. To determine the taxes payable: multiple by Nexus’ tax rate.


12-32. Thorpe Corporation

Increased sales $80,000 Increased costs 45,000 Earnings before amortization and taxes 35,000 Amortization ($50,000 × .20 × 1/2) 5,000 Earnings before taxes 30,000 Taxes @ 38% 11,400 Earnings aftertax 18,600 Amortization 5,000 Net cash flow $23,600

12-33. Cellular Spacephones Ltd.

a. The investment qualifies for a 35% ITC. $1,700,000 × .35 = $595,000

b. The original cost base is: $1,700,000 – $595,000 = $1,105,000

c. The effects of ITC and CCA are realized at year-end. Therefore: PV (ITC) = ITC × PVIF (n = 1, i = 10%)

= $595,000 × PVIF (n = 1, i = 10%) = $540,909

( ) [ ]

[ ] 700,154$10.1

10.5.120.10.22.20.000,105,1$

15.1

=

+×+

+×

=

++

+=

rr

drdTS-CCCA PV C

PV

Total combined present value of tax benefits is:

= $540,909 + $154,700 = $695,609


12-34. Medicine Hat Enterprises

a. (Beginning) Tax shield Year UCC Purchases Sales Rate CCA @ 43% 0 0 $250,000 – (.10)(.50) $12,500 $ 5,375 1 $237,500 – – (.10) 23,750 10,213 2 213,750 – – (.10) 21,375 300,000 – (.10)(.50) 15,000 36,375 15,641 3 477,375 – – (.10) 47,738 20,527 4 429,637 – – (.10) 42,964 400,000 – (.10)(.50) 20,000 62,964 27,075 This year 766,673 400,000 Remaining UCC 366,673 This is a Terminal loss Resulting in a tax savings of $366,673 × 0.43 = 157,669

b. As in (a) only no terminal loss.

c. CCA lost from this year forward on $400,000, but $366,673 remains in the pool.

Year Tax shield Present value @ 13% 1 $ 5,375 $ 4,757 2 10,213 7,998 3 15,641 10,840 4 20,527 12,590 5 27,075 14,695 Present value of tax shields $50,880 (without terminal loss) Terminal loss 157,669 85,576 $166,456


With formula: PV of impacts on pool: Year Purchase/ sell PV @ 13% 0 $250,000 $250,000 2 300,000 234,944 4 400,000 245,327 5 (400,000) (217,104) $513,167

( ) [ ]

[ ]

[ ]( ) ( ) 421,90$942478.01869565.0167,513$13.1

13.5.110.013.043.010.0167,513$

15.1

==

+×+

+×

=

++

+=

rr

drdTS-CCCA PV C

PV

Difference between formula and year by year calculation: = $90,421 – $50,880 = $39,541

Without formula $766,673 remains in the pool before $400,000 sale.

( ) [ ] [ ]

[ ]( ) ( )854,72$481,70$335,143$

17620239.0000,400$1869565.673,766$13.1

13.5.110.013.043.010.0000,400$

10.013.043.010.0673,766$

=−=−=

+×+

+×

−

+×

=

CCA PV

PV = $72,854 × PVIF (n = 5, %i = 13) = $39,542 (rounding difference)

Calculator: PV =? FV = $72,854 PMT = 0 N = 5 %i = 13% Compute: PV = $39,542

Note: The half year rule has already been applied to arrive at the $766,673.


12-35. Elite Car Rental Corporation

n = 2 T = 40% r = 12% d = 40% (class 16) Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 12%

0 Investment $(900,000) – $(900,000) 0 Working capital (10,000) – ( 10,000) 1-2 Revenue $10,500 × 30 = 315,000 189,000 319,420 1-2 Expenses $0.14(40,000) × 30 = 168,000 100,800 (170,357) 2 Sale (.60) (900,000) = 540,000 – 430,485 2 WC recovery 10,000 – 7,972 0 CCA pool

( ) [ ]

[ ]

[ ]( ) ( ) 727,1369464286.03076923.0515,469$12.1

12.5.140.012.040.040.0485,430$000,900$

15.1

==

+×+

+×

−=

++

+=

rr

drdTS-CCCA PV C

PV

NPV = $(185,753)

Elite Car Rental Corporation should not purchase the autos as the firm’s value will decrease by $185,753.


12-36. Albert I. Stein Ltd.

n = 9 T = 23% r = 13% d = 20% (class 8) ITC = 20%


12-37. Pierce Labs

n = 5 T = 44% r = 12% d = 20% (class 8) ITC = 15%

Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 12%

0 Investment $(390,000) – $(390,000) 0 Trade- in 85,000 – 85,000 1 ITC .15(390,000) = 58,500 – 52,232 1 Cost savings 99,000 55,440 49,500 2 Cost savings 88,000 49,280 39,286 3 Cost savings 77,000 43,120 30,692 4 Cost savings 66,000 36,960 23,489 5 Cost savings 55,000 30,800 17,477 0 CCA pool

( ) [ ]

[ ]

[ ]( ) ( ) 382,7994642857.02750.0000,305$12.1

12.5.120.012.044.020.0000,85$000,390$

15.1

==

+×+

+×

−=

++

+=

rr

drdTS-CCCA PV C

PV

1 ITC from CCA pool

( ) [ ] [ ]

[ ]( ) ( ) ( )364,14088,16$2750.0500,58$20.012.044.020.0500,58$

dr

dTITC-CCA PV CPV

=−=

+×

−=

+=

NPV = $(27,306) Pierce Labs should not purchase the new machine.


Comprehensive Problems 12-38. Ontario Corporation Tax Net Capital Cash *PV of Year EBIT - Interest = EBT (46%) = Income + Amort. - Investment = Flow Cash Flow 1 $650,000 $93,750 $556,250 $255,875 $300,375 $140,000 $200,000 $240,375 $ 212,721 2 $700,000 $93,750 $606,250 $278,875 $327,375 $140,000 $200,000 $267,375 $ 209,394 3 $720,000 $93,750 $626,250 $288,075 $338,175 $140,000 $200,000 $278,175 $ 192,789 4 $720,000 $93,750 $626,250 $288,075 $338,175 $140,000 $200,000 $278,175 $ 170,609 5 $690,000 $93,750 $596,250 $274,275 $321,975 $140,000 $200,000 $261,975 $ 142,190 6-10 $700,000 $93,750 $606,250 $278,875 $327,375 $140,000 $ 80,000 $387,375 $ 739,504 $1,667,207 *13% was used since this is an equity only investment. From the table we see that the present value of the cash flows estimates for the next ten years is $1,667,207. We must now calculate a value for the cash flows expected more than 10 years hence. To do this we will calculate a terminal value at the end of year 10 and discount that back to the present.

Terminal value = Annual cash flow/ discount rate = $387,375/ 0.13 = $2,979,808

Present value = $2,979,808 x PVIF (n = 10, i = 13%) = $877,817

Therefore, the present value of all future cash flow estimates is $1,667,207 + $877,817 = $2,545,024 Since the market value of the firm’s shares is $3,000,000 (2,000,000 × $1.50/share) there seems little point in Ontario pursuing Target Firm if management is reasonably confident in the assumptions underlying the analysis.


12-39. Signs For Fields Machinery Ltd.

n = 10 T = 39% r = 15% d = 20%

a. Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 15%

0 Purchase machine $(65,000) – $(65,000) 0 Installation (7,000) – ( 7,000) 1-10 Cost savings 17,500 10,675 53,575 10 Salvage 11,500 – 2,843 0 CCA pool

( ) [ ]

[ ]

[ ]( ) ( ) 407,149347826.022285714.0157,69$15.1

15.5.120.015.039.020.0843,2$7000$000,65$

15.1

==

+×+

+×

−+=

++

+=

rr

drdTS-CCCA PV C

PV

NPV = $( 1,175)

Signs For Fields Machinery should not purchase the new machine.

b. Sell old machine $ 9,000 Remove from CCA pool: – 9,000 (.208323) (1,875) Net increase in NPV 7,125 Overall the new NPV = $ 5,950

Signs For Fields Machinery should now purchase the new

machine.


c. Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 14%

0 Purchase machine $(65,000) – $(65,000) 0 Installation (7,000) – ( 7,000) 1-10 Cost savings 17,500 10,675 55,682 10 Salvage 11,500 – 3,102 0 CCA pool

( ) [ ]

[ ]

[ ]( ) ( ) 835,1493859649.022941176.0898,68$14.1

14.5.120.014.039.020.0102,3$7000$000,65$

15.1

==

+×+

+×

−+=

++

+=

rr

drdTS-CCCA PV C

PV

NPV = $ 1,619

$1,619 PV @ 14% $1,619 PV @ 14% – (1,175) PV @ 15% 0,000 (Cost) $2,794 $1,619

( ) ( ) ( )

%58.141458.00058.14.0

01.0579.014.001.0794,2$619,1$14.0

==+=

+=+=

ationinterpolat IRR

( ) 984.0000,72$825,70$

===outflows of PVinflows of PVPIindexity Profitabil


12-40. H. Improvements Ltd.

n = 7 T = 44% r = 14% d = 30%

OuOu Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 14%

0 Purchase machine $(50,000) – $(50,000) 1-7 Operating costs (19,500) (10,920) (46,828) 7 Salvage 6,000 – 2,398

( ) [ ]

[ ]( ) ( ) 404,1393859649.030.0602,47$14.1

14.5.130.014.044.030.0398,2$000,50$

==

+×+

+×

−=

CCA PV

NPV = $(81,026) Major OuOu Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 14%

0 Purchase machine $(69,000) – $(69,000) 1-7 Operating costs (13,000) (7,280) (31,219) 7 Salvage 8,000 – 3,197

( ) [ ]

[ ]( ) ( ) 529,1893859649.030.0803,65$14.1

14.5.130.014.044.030.0197,3$000,69$

==

+×+

+×

−=

CCA PV

NPV = $(78,493)

The salvage value of $4,500 for the old machine would be deducted from the CCA pool, but since it is common to both alternatives it is ignored for the analysis and decision making purposes.

The Major OuOu should be selected as its NPV is less costly. Our assumption is that the revenue stream is worthwhile and the least costly replacement is to be selected.


12-41. Jagged Pill Ltd.

n = 8 T = 39% r = 13% d = 20%


0 Purchase machine $(525,000) – $(525,000) 1-8 Cash flow 165,000 100,650 482,996 4 Capital upgrade (105,000) – (64,398) 8 Salvage 30,000 – 11,285 0 CCA pool (PV of tax savings)

[ ]

[ ]( ) ( ) 785,1289424779.02363636.0113,578$13.1

13.5.120.013.039.020.0285,11$398,64$000,525$

==

+×+

+×

−+=

NPV = $ 33,668

Note: The $60,000 deposit is a sunk cost and is irrelevant for this decision.

b. Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 15%

0 Purchase machine $(525,000) – $(525,000) 1-8 Cash flow 165,000 100,650 451,649 4 Capital upgrade (105,000) – (60,034) 8 Salvage 30,000 – 9,807 0 CCA pool (PV of tax savings)

[ ]

[ ]( ) ( ) 833,1199347826.022285714.0227,575$15.1

15.5.120.015.039.020.0807,9$034,60$000,525$

==

+×+

+×

−+=

NPV = ($3,745)


$33,668 PV @ 13% $33,668 PV @ 13% – (3,745) PV @ 15% 0,000 (Cost) $37,413 $33,668

( ) ( ) ( )

%80.141480.00180.13.0

02.08999.013.002.0413,37$668,33$13.0

==+=

+=+=

ationinterpolat IRR

This is an approximation.

c. ( ) 057.1398,589$066,623$


This is calculated @13%.

d. Jagged Pill should purchase the new machine. Value will increase by $33,668 (the NPV), the IRR exceeds the cost of capital and the PI exceeds 1.


12-42. Galaxydoughs Tea Ltd.

n = 12 T = 39% r = 14% d = 30%


0 Capital expenditure($1,000,000) – ($1,000,000) 0 Previously purchased equipment (opportunity cost of forgoing sale) (300,000) – (300,000) 0 Working capital ( 50,000) – ( 50,000) 1-6 Cash flow 355,000 216,550 842,091 7-12 Cash flow 425,000 259,250 1,008,137 459,294 1-12 Rent forgone (70,000) 42,700 (241,694) (opportunity cost) 12 Salvage 55,000 – 11,416 12 WC Recovery 50,000 – 10,378 0 CCA pool

( )

[ ]

[ ]( ) ( ) 607,3219385965.02659091.0584,288,1$14.1

14.5.130.014.039.030.0416,11$000,300$000,000,1$

==

+×+

+×

−+=

CCA PV

NPV = $ 53,092

Galaxydoughs Teas should proceed. Value will be added to the firm.

b. A changing cost of capital can be handled by discounting with multiple discount rates appropriate to each year.


12-43. Rinkydink Roller Rinks Ltd.

n = 7 T = 44% r = 20% d = 20%


0 Purchase land $(375,000) – $(375,000) 0 Working capital (65,000) – (65,000) 1-7 Cash flow 60,000 33,600 121,114 7 Sell land 900,000 – 251,173 7 WC recovery 65,000 – 18,140 8 Tax on taxable capital gain [900,000 – 375,000] × 0.50 × .44 = $115,500 (26,861)

NPV = $ (76,434)

Note: The tax is paid one year after the realization of the capital gain (year 8). This assumption is consistent with other treatments for analysis purposes.

Rinkydink should not purchase the vacant lot. Its purchase will decrease the value of the firm by $76,434.

If the tax on the capital gain is taken at year 7 its PV is negative $32,234 and the overall present value is a negative $81,807.


12-44. Clueless Company n = 15 T = 40% r = 12% (1 – .50) = 18% d = 30%


0 Investment $(375,000) – $(375,000) 0 Working capital 200,000 × 60/ 365 = (32,877) – (32,877) 1-15 Revenues 200,000 120,000 610,989 1-15 Expenses (85,000) (51,000) (259,670) 15 Salvage 15,000 – 1,253 15 WC Recovery 32,877 – 2,746 0 CCA pool

( )

[ ]

[ ]( ) ( ) 310,869237288.0250.0747,373$18.1

18.5.130.018.040.030.0253,1$000,375$

==

+×+

+×

−=

CCA PV

NPV =$ 33,751

Clueless should proceed. Value will be added to the firm. This analysis has used an adjusted discount rate to account for the higher risk that would be assumed if the project were undertaken.


12-45. Quixotic Enterprises

n = 10 T = 39% r = 20% d = 5%


0 Construct windmills$(400,000) – $(400,000) 0 Working capital (10,000) – (10,000) 1-10 Revenues 175,000 106,750 447,546 1-10 Big wind tax (7,500) (4,575) (19,181) 1-10 Rent forgone (opportunity cost) (5,000) (3,050) (12,787) 5 Capital upgrade (100,000) – (40,188) 10 Salvage 25,000 – 4,038 10 WC Recovery 10,000 – 1,615 0 CCA pool

( )

[ ]

[ ]( ) ( ) 185,319166667.0078.0150,436$20.1

20.5.105.020.039.005.0038,4$188,40$000,400$

==

+×+

+×

−+=

CCA PV

NPV = $ 2,228


b. IRR Expected Aftertax Present Value Year Event Cash Flow Cash Flow @ 21%

0 Construct windmills$(400,000) – $(400,000) 0 Working capital (10,000) – (10,000) 1-10 Revenues 175,000 106,750 432,773 1-10 Big wind tax (7,500) (4,575) (18,547) 1-10 Rent forgone (opportunity cost) (5,000) (3,050) (12,365) 5 Capital upgrade (100,000) – (38,554) 10 Salvage 25,000 – 3,716 10 WC Recovery 10,000 – 1,486 0 CCA pool

( )

[ ]

[ ]( ) ( ) 783,299132231.0075.0150,436$21.1

21.5.105.021.039.005.0716,3$554,38$000,400$

==

+×+

+×

−+=

CCA PV

NPV = ($11,708

$2,228 PV @ 20% $2,228 PV @ 20% – (11,708) PV @ 21% 0,000 (Cost) $13,936 $2,228

( ) ( ) ( )

%16.202016.00016.20.0

01.01599.020.001.0936,13$228,2$20.0

==+=

+=+=

ationinterpolat IRR

c. ( ) 005.1156,482$384,484$


Just above 1 indicating profitability. (Info from part (a))

d. Dream the impossible dream as it will add value to Quixotic Enterprises.


12-46. Blue Sky Ltd.

n = 10 T = 40% r = 15% d = 30%


0 Purchase machine $(150,000) – $(150,000) 0 Sell old machine 27,500 – 27,500 0 Deinvest WC 5,000 – 5,000 1-10 Incremental annual(50,000 – 20,000) cost savings 30,000 18,000 90,338 10 Incremental salvage(32,000 – 8,000) 24,000 – 5,932 10 Reinvest WC (5,000) – (1,236) 0 CCA pool

( )

[ ]

[ ]( ) ( ) 058,299347826.0266667.0568,116$15.1

15.5.130.015.040.030.0932,5$500,27$000,150$

==

+×+

+×

−−=

CCA PV

NPV = $ 6,592

Blue Sky Ltd. should proceed. Value will be added to the firm. Watch the complete differences between what essentially are two options.


12-47. Midnight Oil and Gas

n = 10 T = 42% r = 14% d (pipeline) = 20% d (buildings) = 4%


0 Construct pipeline$(1,000,000) – $(1,000,000) 0 Construct buildings (200,000) – (200,000) 0 Use land (opportunity cost) (2,000,000) – (2,000,000) 1-10 Cash flow 625,000 362,500 1,890,842 10 Enviro: cleanup (1,200,000) (696,000) (187,742) 10 Salvage 0 – 0 10 Sell land 4,500,000 – 1,213,847 11 Tax on capital gain (4,500,000 – 500,000) × .50 × .42 (840,000) (198,759) 1 Tax on capital gain forgone (2,000,000 – 500,000) × .50 × .42 315,000 276,316 0 CCA pool

( ) [ ]

[ ]( ) ( ) 520,1793859649.00933333.0000,200$14.1

14.5.104.014.042.004.0000,200$

==

+×+

+×

=

building

( ) [ ]

[ ]( ) ( ) 889,23193859649.02470588.0000,000,1$14.1

14.5.120.014.042.020.0000,000,1$

==

+×+

+×

=

pipeline

NPV = $ 43,913

Build the pipeline. Value will be added to the firm.


12-48. St. Bernard Venture

n = 12 T = 40% r = 15% d (machinery) = 30% d (buildings) = 4%


0 Acquire land $(600,000) – $(600,000) 1 Payment building (1,100,000) – (956,522) 2 Purchase machinery (175,000) – (132,325) 3-12 Revenues 5875,000 525,000 1,992,328 3-12 Expenses (325,000) (195,000) (740,007) 12 Sell building 225,000 – 42,054 12 Sell machinery 50,000 – 9,345 12 Sell land 600,000 (1.09)12 1,687,599 – 315,424 13 Tax on capital gain (1,687,599 – 600,000) × .50 × .40 (217,520) (35,353) 0 CCA pool

( ) [ ]

[ ]( ) ( ) 986,719347826.00842105.0468,914$15.1

15.5.104.015.040.004.0054,42$522,956$

==

+×+

+×

−=

building

( ) [ ]

[ ]( ) ( ) 656,309347826.02666667.0980,122$15.1

15.5.130.015.040.030.0345,9$325,132$

==

+×+

+×

−=

machinery

NPV = $(2,414)

St. Bernard should not proceed with the venture. Value will not be added to the firm.


12-49. Marceline Enterprises

n = 9 T = 40% r = 11% d = 15%


0 Expansion $(1,000,000) − $(1,000,000) 0 Working capital (50,000) − (50,000) 3 Additional capital (200,000) − (146,238) 3 Additional WC (10,000) − (7,312) 6 Additional capital (200,000) − (106,928) 6 Additional WC (10,000) − (5,346) 1-2 Revenues 250,000 150,000 256,879 3-5 Revenues 325,000 195,000 386,758 6-9 Revenues 375,000 225,000 414,259 9 Salvage 150,000 − 58,639 9 WC Recovery 70,000 − 27,365 0 CCA pool

[ ] ( )( ) ( )

++

+−++

11.111.5.1

15.11.40.15.639,58928,106238,146000,000,1 =

1,194,527 (.2307692) (.9504505) 262,001 NPV = $90,077

Marceline Enterprises should proceed with the amusement park expansion, as the NPV is positive.


MINI CASES Aerocomp Corporation (Methods of Investment Evaluation)

This case places emphasis on comparing the payback method, the internal rate of return, and the net present value approaches for a series of investments. As the student progresses through the calculations, the various advantages and disadvantages of the different approaches become evident. The reinvestment assumption of a high return project under the internal rate of return can be highlighted and evaluated. Capital rationing is also introduced into the case and plays a part in the analysis. Finally, the issue of reported earnings to shareholders versus sophisticated capital budgeting techniques is brought up and makes for interesting classroom discussion. Are shareholders more concerned with next quarter’s earnings or long-term benefits?

a. Total Reported Earnings increases for each projects:

Project A Project B Project C Project D Year 1: $(13,250) $ 29,313 $(60,000) $ 192,206 Year 2: $ (450) $ 87,938 $(16,000) $ 129,846 Year 3: $ 25,494 $146,563 $ 61,640 $ (43,350) Year 4: $101,003 $234,500 $162,140 $ (62,475) Year 5: $ 63,315 $322,438 $262,640 $ (94,350) Total: $176,112 $820,752 $410,420 $ 121,877

We are told in the case that Kay Marsh is sensitive to Aerocomp’s level of earnings. Therefore, Project B, with over $820,000 in reported earnings increases (twice as much as any of the other projects), will be the one that attracts Kay’s attention. (She may initially be swayed by the $192,206 that Project D brings in during the first year, but the losses in years three through five will probably cause her to reject that alternative quickly.)

Note: Projects A and C both produce earnings decreases for the first two years. We would suspect that if Emily thinks that either of these two should


be selected (on the basis of some other ranking method, such as NPV), she had better have some convincing arguments prepared!


b. Payback Period, IRR, and NPV of each alternative:

Project A Project B Project C Project D Payback Period: 4 years 5 Years 5 Years 2 Years

IRR: 14.08% 7.18% 11.95% 12.48% NPV @ 10%: $39,971 ($63,848) $52,192 $20,609

(Students may get slightly different values due to rounding.)

Note: A few students may question the fact that Project B’s cost has not been completely recovered in the five-year period shown, as the cost of the other projects has been. Therefore, they will claim, we are not using the proper time frame for our comparison of the projects. Of course, they are correct, and deserve extra points for their astute observation. In the case, Project B’s amortization, or depreciation, was limited on purpose to highlight the effect of amortization on reported income and cash flows.

c.

1. According to the Payback period, Project D should be selected. The initial investment of $510,000 is recovered in the second year.

2. The chief disadvantage of the Payback Period is obvious at once: the method ignores cash flows occurring after the payback period. In this case such an omission is disastrous, since Project D’s reported earnings and cash flows fall off significantly after the payback period and never recover. Another disadvantage of the Payback Period is that it does not consider the timing of cash flows during the payback period.

3. In general, the Payback Period should not be used. However, it is used from time to time because it is easy to understand, and because it favors projects that pay off quickly. This can be an important factor in some fast-paced industries where a quick return is important. The Payback Period may have some justification as a backup method, but not as the primary analytical tool.


d. 1. According to the IRR method, Project A should be chosen. It returns

nearly two percent more than the closest competing project.

2. Remember, that to achieve the IRR during a project’s life, the project’s cash inflows must be reinvested at the IRR rate. This may be difficult or impossible to accomplish when high IRR’s are involved. (Suppose you were Aerocomp’s financial manager, and you were getting the cash flows from Project A. What would you do with them: Pay dividends? Put them in a money market account at? You might encounter a great deal of difficulty locating an investment that would pay you back the IRR rate of 14.08%). As a matter of interest (no pun intended) if Project A’s cash flows were reinvested at 7% annually instead of the IRR rate of 14.08%, the project’s total return for the five-year period would drop to 11.84%.

3. Another disadvantage of the IRR method is that it does not give any consideration to project size. For example, the IRR method would select a project that returned $10 on a $1 investment over any of the projects in this case, even though the dollar return to the firm was only $9. This is not a problem when all projects with IRRs over the cost of capital can be selected, but when the projects are mutually exclusive, or when capital rationing is in effect (as it is in this case), the IRR method may lead the firm to make an incorrect choice.

(Note: It is important to avoid confusion on this point. The IRR and NPV methods will both accept and reject the same investments, but they will not give them the same ranking. In this case, projects A, C, and D are all acceptable per IRR and NPV. However, the IRR method would choose projects A, D, and C, in that order, while the NPV method would choose C, A, and D.)

4. If the size of Aerocomp’s capital budget were not limited, the IRR method would accept projects A, C, and D. Project B, with an IRR of 7.18%, almost 3% less than the cost of capital, would be rejected.


e. 1. According to the NPV method, Project C, with an NPV of over

$52,000, will be chosen. It will add to the present value of the firm over $12,000 more than the next best project. Of course, under the IRR, Project A will be selected. Actually Project C is only a third place finisher under the IRR method.

2. If the size of Aerocomp’s capital budget were not limited, the NPV method would accept projects A, C, and D. Project B, with an NPV of negative $63,848, would be rejected anyway. Note that both the NPV and IRR methods rejected project B. The return is less than the cost of capital.

3. The likely selection is Project C because of its high net present value. This is partly attributable to the fact that only one project can be selected. Had there not been capital limitations, one might put more emphasis on the IRR or use a profitability index approach. Of course, some instructors might select Project A as being preferable using other criteria, and that is fine. There may be some interesting opportunities for a classroom debate or discussion on these points.

f. 1. Profitability index =

Project A [39,971 + 300,000]/ 300,000 = 1.133 Project B [- 63,848 + 700,000]/ 700,000 = 0.909

Project C [52,192 + 800,000]/ 800,000 = 1.065 Project D [20,609 + 510,000]/ 510,000 = 1.040

2. The profitability index suggests project A with the highest relative profitability. However, project A adds the most value to the firm. Notice that projects A and D together, at roughly the same initial investment as C, provide a higher combined NPV.


Galaxy Systems, Inc. (Divisional Cost of Capital)

Purpose: The case combines risk analysis with discount rate considerations. To emphasize how many multidivisional corporations operate, the case actually gets into the topic of divisional hurdle rates. The student is able to see how different divisions in a corporation might have different required rates of return based on their risk exposure. In this particular case, a key risk measure for the consideration is beta. (Only observe how they might be used). Calculations related to net present value and internal rate of return are purposely simple to emphasize more conceptual items. (IRRs can be found as exact values from Appendix D after only one calculation, if tables are preferred).

Emphasis can be made on how financial decisions are made in a corporate culture.

This case draws on material from many of the capital budgeting chapters. Proposal A

NPV (10% discount rate for the auto airbags production division) Cost $2,355,600

Calculator: PV =2,355,600 FV = 0 PMT = $400,000 n = 10 %i = ? Compute: %i = 11.00

11%IRR

10nD) (App. 5.889$400,000

$2,355,600Annuity

InvestmentIRR

=

====

PVA = A × PVIFA (n = 10, %i = 10) (Appendix D) PVA = $400,000 × 6.145 = $2,258,000

Calculator: PV =? FV = 0 PMT = $400,000 n = 10 %i = 10% Compute: PV = $2,457,827

Present value of inflows $2,457,827 Cost 2,355,600 Net present value $ 102,227


Proposal B

NPV (15% discount rate for the aerospace division) Cost $2,441,700


13%IRR

10nD) (App. 5.426$450,000

$2,441,700IRR

=

===

PMT = $450,000, n = 10, %i = 15 Present value of inflows = $450,000 × 5.019 = $2,258,550


Present value of inflows $2,258,446 Cost 2,441,700 Net present value ($ 183,254)

Proposal C

NPV (10% discount rate for the auto airbags production division) Cost $145,680

Calculator: PV =145,680 FV = 0 PMT = $15,000 n = 15 %i = ? Compute: %i = 6.00

6%IRR

15nD) 9.712(App.15,000$

$145,680IRR

=

===


PMT = $15,000, n = 15, %i = 10 Present value of inflows = $15,000 × 7.606 = $114,090

Calculator: PV =? FV = 0 PMT = $450,000 n = 15 %i = 10% Compute: PV = $114,091

Present value of inflows $ 114,091 Cost 145,680 Net present value ($ 31,589)

Proposal D

NPV (15% discount rate for the aerospace division) Cost $1,262,100


17%IRR

8nDApp$300,000

$1,262,100IRR

=

=== ).(207.4

PMT = $300,000, n = 8, %i = 15 Present value of inflows = $300,000 × 4.487 = $1,346,100


Present value of inflows $1,346,196 Cost 1,262,100 Net present value $ 84,096


a. Proposal A should be accepted IRR > discount rate (11% > 10%)

NPV is positive $102,227

Proposal B should be rejected IRR < discount rate (13% < 15%) NPV is negative ($183,254)

Proposal C should be rejected IRR < discount rate (6% < 10%) NPV is negative ($31,589)

Proposal D should be accepted IRR > discount rate (17% > 15%) NPV is positive $84,096 b. While the decisions related to Proposals A and B appear to be straightforward,

Proposals C and D require further discussion.

Proposal C has a negative net present value and the internal rate of return of 6% is well below the required rate of return of 10%. Nevertheless, it calls for the development of special equipment to be used in the disposal of environmentally harmful waste material created in the manufacturing process. Given tougher environmental laws, the project may have to be accepted. We are not told whether the installation is mandatory under the law, but there probably is adequate motivation to move forward with the project. Of course, if the installment of the equipment is required by law, then Galaxy must move forward regardless of the numbers.

Proposal D has a positive net present value and the internal rate of return of 17 percent is well above the required rate of return of 15 percent for the division. However, the proposal appears to have even greater risk than projects normally undertaken in the aerospace division. While the high required rate of return for this division is supposed to cover the risk exposure of dealing in U.S. government contracts, Project D calls for the development of a microelectric control system for fighter jets that are still in the design stage. Even if the microelectric systems are successfully developed, there may not be a need for them if the other aerospace company cannot successfully develop fighter jets. Furthermore, the target market for the jets is in underdeveloped countries, which increases the uncertainty associated with this project. In the final analysis, top management might require an anticipated return of 20 percent or more to take on this highly speculative project.


c. The $300,000 that has already been spent on the initial research for Proposal B (radar surveillance equipment) is a sunk cost. The money has already been spent and should have no influence on subsequent decisions. Sometimes in the real world, egos get in the way of corporate decisions, and division heads (or other executives) push hard for the continuance of projects that they spent funds on to explore; but that is not justification to continue on. This is somewhat like buying stock in an underperforming company in the stock market. Sometimes, you just have to take your losses.

Of course, even if we considered the $300,000 that had already been spent, it would raise the total cost of the project and make it even less economical.

Further overall comments: Companies that use divisional required rates of return often do have difficulties in finding betas for firms that produce products comparable to a division. That is, finding a “pure play” comparison is difficult. Therefore, using the average beta for an entire industry may be the next best alternative. For example, if a division produces machine tools, its beta may be inferred from the entire machine tool industry rather than from a given firm in the industry.

Documents

Practice Problems Ch12