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$ 2,680

which is about 7 percent in the 5-year line of Appendix D.

226 CAPITAL BUDGETING (INCLUDING LEASING) [CHAR 8

Supplying Missing Data. Fill in the blanks for each of the following independent cases. Assume

8.9

in all cases the investment has a useful life of 10 years.

Annual Cash cost of

NPV

IRR

Investment Capital

Ineow

(4

$449,400

$100,ooo 14% (b)

(4

14% 20Yo

(c)

$70,000

(f)

(4 14% $35,624

$200,000

(h)

$300,000 12% $39,000

(g)

SOLUTION

I = PV

$449,400 = $100,000 PVIFA,10

PVIFA,lo = - 4.494

$4497400 =

$100,000

From Appendix D, the present value factor of 4.494 at 10 years gives a rate of 18%.

PV - I

NPV =

(b)

= $100,000 PVIFA14.10 - $449,400

= $100,000(5.2161) - $449,400 = $521,610 - $449,400 = $72,210

I = PV

= $70,000 PVIFA20,l0 = $70,000(4.1925) = $293,475

NPV PV - I

(4 =

= $70,000 PVIFA14.1o- $293,475

= $70,000(5.2161) - $293,475 = $365,127 - $293,475 = $71,652

At IRR 14%, PV = I.

(e)

Cash inflow X PVIFA14s10 investment

=

investment -

_--$2007000- $38,343 (rounded)

Cash inflow =

PVIFAld+10 5.2161

NPV = PV - I

$35,624 = PV - $200,000

$35,624 + $200,000 = PV = cash inflow (PVIFA,,lO)

$235,624 = $38,343 PVIFA,,lo

$235,624

-= PVIFA,1"

$38,343

6.1451 = PVIFA,,l0

Since this is the present value factor for 10 percent at 10 years, the cost of capital is 10

percent.

PV = NPV + 1

(g)

$39,000 + $300,000 = $339,000

Cash inflow (PVIFA12,10)= NPV + I =

- $3397000 $59,998 (rounded)

Cash inflow = $3397000 --=

PVIFAlz, 10 5.6502

227

CAPITAL BUDGETING (INCLUDING LEASING)

CHAP. 81

I = PV

$300,000 = $59,998 PVIFA,lO

$300,000

PVIFA, 10 = - 5.0002 =

$59,998

Since this PVIFA value is about halfway between 15 percent and 16 percent at 10 years, IRR is

estimated at about 15.5 percent.

NPV Analysis. Kim Corporation invested in a 4-year project. KimвЂ™s cost of capital is 8 percent.

8.10

Additional information on the project follows:

Present Value

After-Tax Cash M o w of $1 at 8%

Year

0.926

1 $2,000

0.857

2 $2,200

0.794

3 $2,400

0.735

$2,600

4

Assuming an NPV of $700, what was the initial investment?

SOLUTlON

CashIdow PV Total PV

Year

0.926 $1,852

$2,000

1

1,885

$2,200 0.857

2

1,906

$2,400 0.794

3

1,911

$2,600 0.735

4

$7,554

= PV - I

NPV

I = PV - NPV

= $7,554 - $700 = $6,854

IRR. XYZ, Inc., invested in a machine with a useful life of 6 years and no salvage value. The

8.11

machine was depreciated using the straight-line method and it was expected to produce annual

cash inflow from operations, net of income taxes, of $2,000. The present value of an ordinary

annuity of $1 for six periods at 10 percent is 4.3553. The present value of $1 for six periods at 10

percent is 0.5645. Assuming that X Y Z used an internal rate of return of 10 percent, what was the

amount of the original investment?

SOLUTl0N

By definition, at IRR, PV = I or NPV = 0.

To obtain the amount of initial investment find the present value of $2,000 a year for 6 periods.

PV = $2,000 X 4.3553 = $8,710.60

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