ñòð. 94 |

$968.29 3.5231

1.OoOo

The duration of the bond is 3.52 years.

7.32 Interest Rate Sensitivity. What is the interest rate elasticity of the bond in Problem 7.31? What

does that mean?

SOLUTION

The formula is:

YTM

(-1)E = D

(1 + YTM)

(-1) E = 3.5231 (O.lO/l.lO) = 0.3203, which means that the bond will lose or gain 32.03% of principal

value for each 1percentage point move in interest rates.

Chapter 8

Capital Budgeting

(Including Leasing)

8.1 CAPITAL BUDGETING DECISIONS DEFINED

Capital budgeting is the process of making long-term planning decisions for investments. There are

typically two types of investment decisions: (1) selection decisions concerning proposed projects (for

example, investments in long-term assets such as property, plant, and equipment, or resource

commitments in the form of new product development, market research, re-funding of long-term debt,

introduction of a computer, etc.); and (2) replacement decisions (for example, replacement of existing

facilities with new facilities).

8.2 MEASURING CASH FLOWS

The incremental (or relevant) after-tax cash flows that occur with an investment project are the ones

that are measured. In general the cash flows of a project fall into the following three categories: (1)the

initial investment; (2) the incremental (relevant) cash inflows over the life of the project; and (3) the

terminal cash flow.

Initial Investment

The initial investment ( I ) is the initial cash outlay necessary to purchase the asset and put it in

operating order. It is determined as follows:

cost of asset + installation cost - proceeds from taxes on sale

+

Initial investment =

+ working capital investments sale of old asset - of old asset

The proceeds from the sale of old assets are subject to some type of tax. There are three

possibilities:

1. The asset is sold for more than its book value.

2. The asset is sold for its book value.

3. The asset is sold for less than its book value,

Additional working capital (in the form of increased inventory, cash, and receivables) is usually

required to support a new investment project. This should be included in the projectâ€™s initial outlay. At

the end of the projectâ€™s life, it should be recaptured as part of the projectâ€™s terminal cash flow.

EXAMPLE 8.1 Assume that an asset has a book value of $60,000 and initially cost $l00,OOO. Assume further that

the firmâ€™s ordinary marginal tax rate is 34 percent. Consider each of the three possible tax situations dealing with

the sale of the old asset.

1. The old asset is sold for $80,000. In this case, the total gain is simply recapture of depreciation and taxed

at the ordinary rate. Therefore,

($80,000 - $60,000)(0.34)= $6,800

2. The old asset is sold for $60,000. In this case, no taxes result since there is neither a gain nor a loss on

the sale.

3. The old asset is sold for $50,000. In this case there is a loss, which results in tax savings. The tax savings

are as follows:

($60,000- $50,000)(0.34) = $3,400

201

CHAP. 81 CAPITAL BUDGETING (INCLUDING LEASING)

Taxes on the gain from the sale of an old asset or the tax savings on a loss must be considered when

determining the amount of the initial investment of a new asset.

EXAMPLE 8.2 XYZ Corporation is considering the purchase of a new machine for $25O,OOO, which will be

depreciated on a straight-line basis over 5 years with no salvage value. In order to put this machine in operating

order, it is necessary to pay installation charges of $50,000. The new machine will replace an existing machine,

purchased 3 years ago at a cost of $240,000, that is depreciated on a straight-line basis (with no salvage value) over

its 8-year life (i.e., $30,000 per year depreciation). The old machine can be sold for $255,000 to a scrap dealer. The

company is in the 34 percent tax bracket. The machine will require an increase in w/p inventory of $5,000.

The key calculation of the initial investment is the taxes on the sale of the old machine. The total gain, which

is the difference between the selling price and the book value, is $105,000 ($255,000 - $150,000). The tax on this

$105,000 total gain is $35,700 (34% X $105,000). Therefore, the amount of initial investment is:

Purchase price of the machine $250,000

+ Installation cost 50,000

+ Increased investment in inventory 5,000

- Proceeds from sales of old machine 255,000

+ Taxes on sale of old machine 35,700

Initial investment $ 85,700

Incremental (Relevant) Cash Inflows

The relevant cash inflows over a projectâ€™s expected life involve the incremental after-tax cash flows

resulting from increased revenues and/or savings in cash operating costs. Cash flows are not the same

as accounting income, which is not usually available for paying the firmâ€™s bills The differences between

accounting income and cash flows are such noncash charges as depreciation expense and amortization

expense.

The computation of relevant or incremental cash inflows after taxes involves the following two

steps:

1. Compute the after-tax cash flows of each proposal by adding back any noncash charges, which

are deducted as expenses on the firmâ€™s income statement, to net profits (earnings) after taxes;

that is:

After-tax cash inflows = net profits (or earnings) after taxes + depreciation

2. Subtract the cash inflows after taxes resulting from use of the old asset from the cash inflows

generated by the new asset to obtain the relevant (incremental) cash inflows after taxes.

EXAMPLE 8 3 XYZ Corporation has provided its revenues and cash operating costs (excluding depreciation)

.

for the old and the new machine, as follows:

AnnUd

Net Profits before

Cash Operating Costs

Revenue Depreciation and Taxes

Old machine $150,000 $70,000 $ 80,000

New machine $˜,OOo

$180,000 $120,000

Recall from Example 8.2 that the annual depreciation of the old machine and the new machine will be $30,000

and $50,000, respectively.

202 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP 8

To arrive at net profits after taxes, we first have to deduct depreciation expenses from the net profits before

depreciation and taxes, as follows:

AftepTax

Net Profits after Taxes Add Depreciation Cash Mows

$57,000

$30,000

Old machine ($80,000- $30,000)(1- 0.46) = $27,000

($120,000 - $50,000)(1- 0.46) = $37,800 $87,800

$50,000

New machine

Subtracting the after-tax cash inflows of the old machine from the cash inflows of the new machine results in

the relevant, or incremental, cash inflows for each year.

Therefore, in this example, the relevant or incremental cash inflows for each year are $87,800 - $57,000 =

$30,800.

Alternatively, the incremental cash inflows after taxes can be computed, using the following simple

formula:

After-tax incremental cash inflows = (increase in revenues)(l - tax rate)

-(increase in cash charges)(l - tax rate)

+(increase in depreciation expenses)(tax rate)

EXAMPLE 8.4 Using the data in Example 8.3, after-tax incremental cash inflows for each year are:

ñòð. 94 |