Investment decisions and the cost of capital

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MANAGERIAL ECONOMICS

An Analysis of Business Issues

Howard Davies and Pun-Lee Lam

Capital and Capital Budgeting

Capital:

is the stock of assets that will generate a

flow of income in the future.

Capital budgeting:

is the planning process for allocating all

expenditures that will have an expected

4 Investments for complying with government or

insurance-company safety or environmental

Question for Discussion:

What are the factors you would consider when making a choice among different investment

projects?

1.

2.

3.

Question for Discussion:

What are the factors you would consider when making a choice among different investment

projects?

1.

2.

3.

Simple Technique for Appraisal of

Investment

Simple Technique for Appraisal of

Investment

Payback-period criterion:

Payback period is the amount of time

sufficient to cover the initial cost of an

investment

But it ignores any returns accrue after the

pay-back period; ignores the pattern of

returns; ignores the time value (time cost)

of money.

Payback-period criterion:

Payback period is the amount of time

sufficient to cover the initial cost of an

investment

But it ignores any returns accrue after the

pay-back period; ignores the pattern of

returns; ignores the time value (time cost)

of money.

Initial investment: $10 million

Payback-period?

If cash flow : $4 million per year

Payback-period?

On the other hand, the process of discounting

or capitalization is to turn a future stream of

services or income into its equivalent present value When an expected future sum is turned into its equivalent present value, we say that it

is discounted or capitalized.

On the other hand, the process of discounting

or capitalization is to turn a future stream of

services or income into its equivalent present value When an expected future sum is turned into its equivalent present value, we say that it

is discounted or capitalized.

The present value of a single future amount

In general, present value (PV) refers to the value

now of payments to be received in the future (I) The present value of I after n year at r is:

PV=

I (1+r) n

Suppose we try to find the present value of a

single future amount of $121, to be received

after two years Since goods available in the

future are worth less than the same goods

available now, the future amount of $121 is

worth less than $121 at present Given the

market rate of interest of 10%, its present

value is: $121

(1+0.1) 2 = $100

This means that the future amount of $121 (to

be received after two years) is equivalent to a

value of $100 at present.

Simple Technique for Appraisal of

Investment

Simple Technique for Appraisal of

Investment

Net-present-value technique:

Net present value (NPV) is the difference

between the present value of a future cash

flow and the initial cost of the investment

project; a firm should adopt a project if the expected NPV is positive.

Net-present-value technique:

Net present value (NPV) is the difference

between the present value of a future cash

flow and the initial cost of the investment

project; a firm should adopt a project if the expected NPV is positive.

NPV = -P + I 0 + I 1

(1+r)

I 2 (1+r) 2 + … + + (1+r) I n n

NPV = -P + I

r

where:

P: =capital cost, accruing in full at the

beginning of the project

I 1,2,…n =net cash flows arising from the project

in years 1 to n

or

Simple Technique for Appraisal of

Investment

Simple Technique for Appraisal of

Investment

Internal-rate-of-return method:

Internal rate of return (IRR) is the rate of

return that will equate the present value of

a multi-year cash flow with the cost of

investing in a project

Internal-rate-of-return method:

Internal rate of return (IRR) is the rate of

return that will equate the present value of

a multi-year cash flow with the cost of

investing in a project

P, n and the expected future cash returns (I) are known, we try to find IRR.

If the IRR is greater than the market rate of

interest r, it implies that the present value of the capital good (PV) is greater than its purchase

price (P) and the firm should invest Conversely,

if IRR is smaller than r, it implies that PV is

smaller than P and the firm should not invest.

P, n and the expected future cash returns (I) are known, we try to find IRR.

If the IRR is greater than the market rate of

interest r, it implies that the present value of the capital good (PV) is greater than its purchase

price (P) and the firm should invest Conversely,

if IRR is smaller than r, it implies that PV is

smaller than P and the firm should not invest.

What are the differences between NPV

technique and IRR method?

In most situations, the IRR method will yield

the same results as the NPV method But:

•there may be more than one value for the IRR that

satisfies the NPV equation; if the sign of cash flows

changes more than once in the life of the project,

there may be multiple solutions

•the NPV rule uses actual opportunity cost of capital

as the discount rate; the IRR rule assumes the

shareholders can invest at the IRR

•IRR is expressed in terms of a percentage rate of

In most situations, the IRR method will yield

the same results as the NPV method But:

•there may be more than one value for the IRR that

satisfies the NPV equation; if the sign of cash flows

changes more than once in the life of the project,

there may be multiple solutions

•the NPV rule uses actual opportunity cost of capital

as the discount rate; the IRR rule assumes the

shareholders can invest at the IRR

•IRR is expressed in terms of a percentage rate of

A firm will invest only if the expected rate

of return exceeds the cost of capital For a firm under rate-of-return regulation, if the permitted rate of return is set above the

cost of capital (or the required rate of

return), the firm will over-invest;

conversely, if the permitted rate is set

below the cost of capital, the firm will

under-invest.

A firm will invest only if the expected rate

of return exceeds the cost of capital For a firm under rate-of-return regulation, if the permitted rate of return is set above the

cost of capital (or the required rate of

return), the firm will over-invest;

conversely, if the permitted rate is set

below the cost of capital, the firm will

under-invest.

The Cost of Capital

Weighted Average Cost of Capital (WACC):

Cost of debt (rd): interest rate paid to creditors net of taxes

Cost of equity (re): rate of return to shareholders in order to induce them to invest in the firm

WACC : rd × + re D × E

•there are no taxes

•the capital market is efficient and competitive

•there are no transaction costs

•there are no costs associated with bankruptcy

•shareholders can borrow on the same terms as

corporations

•the cost of debt is constant, whatever the level of

•If they were not the same, investors could improve

their position by “arbitrage”, selling the shares of one and buying shares in the other, which would alter the relative prices of shars until the WACCs become equal

The Cost of Equity Capital

The Cost of Equity Capital

1 Dividend valuation approach DVA

(or dividend growth/discounted cash flow model ):

Rate of return = Dividend/Price + Expected

growth rate

re = D 1

P 0 + g The DVA relies on the equivalence of the market price of a stock, P 0 , with the present value of the dividends ( or cash flows) expected from the

stock The discount rate in finding the present

value is considered to be the cost of equity capital.

There are few assumptions behind the method:

(a) future dividends are expected to grow at a constant rate perpetually;

(b) future dividends can be discounted at a

constant cost of equity capital;

(c) future dividends remain a constant

proportion of earnings over time;

D 1 (1 + r) + (1 + r) 2 +

(1 + r) 3

D 1 (1+g) PV= D 1 (1+g)

2

+

D 1 (1 + r)

Let A = Let B = (1 + r) (1 + g)

PV = A(1 + B + B 2 + …) (1)

× B on both sides:

PV × B = A(B + B 2 + B 3 + …) (2) (2) - (1):

PV(1 - B) = A

A (1 - B)

= 1

-=

=

(1 + r) (1 + g)

1 - B

The Cost of Equity Capital

The Cost of Equity Capital

2 Capital asset pricing model (CAPM):

Cost of equity capital = risk-free rate +

beta (market rate - free rate)

Re = Rf + β (Rm - Rf)

Therefore, if we use the CAPM to estimate a

firm’s cost of equity capital (Re, or the required rate of return), we have to estimate a firm’s beta, the risk-free rate of return, and the market risk

premium (the difference between Rm and Rf).

In the CAPM, the measure of market risk is

known as beta (β)

For example, the returns from an asset with a beta

of 0.5 will fluctuate by 5% for each 10%

fluctuation in the market’s returns

It has been shown that the required risk premium for an asset is directly proportional to its beta

Therefore, the holder of an asset with a beta of 0.5 will require a risk premium only half as large as

that offered by the market as a whole