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Depreciation on new equipment

($300,000 + 5 ) $60,000

Depreciation on existing equipment

($60,000 -+ 5 ) 12,000

Increased depreciation charge $48,000

Tax rate 0.4

19.200

$ 87,000

Recurring annual cash flows

The new equipment is capable of producing 20,000 units, but Wisconsin Products

a

can sell only 18,oOO units annually.

The sales manager made several errors in his calculations of required investment and

annual cash flows.

Concerning the required investment, the sales manager made two errors: First, the cost of the

market research study ($44,OOO) is a sunk cost because it was incurred last year and will not change

regardless of whether the investment is made or not. Second, the loss on the disposal of the existing

equipment does not result in an actual cash cost as shown by the sales manager. The loss on disposal

results in a reduction of taxes which reduces the cost of the new equipment.

In computing the annual cash flows, the sales manager made three errors: First, he considered only

the depreciation on the new equipment rather than just the additional depreciation which would result

from the acquisition of the new equipment. Second, he failed to consider that the depreciation is a

noncash expenditure which provides a tax shield. Third, the sales manager's use of the discount rate

(i.e., cost of capital) was incorrect. The discount rate should be used to reduce the value of future cash

flows to their current equivalent at time period zero.

= PV - I = cash flow (PVIFAlSJ)- I

NPV

= ($87,000 X 3.3522) - $276,000 = $291,641 - $276,000 = $15,641

Mutually Exclusive Investments. The Wan-Ki Manufacturing Company must decide between

8.19

investment projects A and B, which are mutually exclusive. The data on these projects are as

follows (in thousands of dollars):

Cash Flows,per Year

2

1

Project 4

0 3

(100) $120.00

A

(loo)

B $193.80

( a )For each project, compute the NPV at 12percent cost of capital, and the IRR. ( 6 )Explain

why the rankings conflict. Recommend which project should be chosen.

SOLUTION

The NPV at 12 percent is:

(a)

NPV (PV - I)

PV at $1"

Cash M o w

Project PV

A $120.00 0.8929 $107.15 $ 7.15

B $193.80 0.6355 $123.16 $23.16

PVIF12,1 A and PVIF12q4 B; both from Appendix C.

for for

a

235

CAPITAL BUDGETING (INCLUDING LEASING)

CHAP. 81

The IRR is:

IRR

Project Wash Flow PVIF

$100

- 0.8333 (at 1 year) 20%

A --

$120.00

18%

$loo 0.516 (at 4 years)

-=

B

93.80

$1

(b) The conflicting ranking results from different assumptions regarding the reinvestment rate on the cash

inflows released by the project. The NPV method assumes the cost of capital (12 percent in this

problem) as the rate for reinvestment, whereas the IRR method assumes the cash inflows are

reinvested at their own internal rate of return (20 percent in the case of project A). The use of NPV

for ranking mutually exclusive investments is recommended since the cost of capital is a more realistic

reinvestment rate. Therefore, project B should be chosen.

NPV, IRR, and Mutually Exclusive Investments. The Bitter Almond Company was confronted

8.20

with the two mutually exclusive investment projects, A and B, which have the following after-tax

cash flows:

Cash Flows, per Year ($)

1 2

Project 0 3 4

5,000 5,000 5,000

5,000

A (12,000)

B (12,OW 25,000

Based on these cash flows: ( a ) Calculate each projectâ€™s NPV and IRR. (Assume that the firmâ€™s

cost of capital after taxes is 10percent.) (6) Which of the two projects would be chosen according

to the IRR criterion? (c) How can you explain the differences in rankings given by the NPV and

IRR methods in this case?

SOLUTION

(a) The NPV for project A is:

Present Value of $1

Cash (Outflow) Net Present Value

of Cash Flow

or Inflow at 10%

Year

$(woq 1.Ooo $(12,ooo)

0

$5,Ooo

1-4 3.1699 15.850

$ 3,850

The NPV for project B is:

Cash (Outflow) Present Value of $1 Net Present Value

at 10%

Year or Inflow of Cash Flow

1.WO $( 12,000)

0.6830 17.075

$ 5,075

[CHAP. 8

236 CAPITAL BUDGETING (INCLUDING LEASING)

The IRR for project A is:

$12,000 = $5,000 (PVIFAr.4)

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