# time value of money

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Cost of capital is Rate of return required to

maintain the market value of stock.

It can be rate of return required by suppliers of

capital to attract their funds to the firms.

It is expected average future cost of funds in the

long run

It decides for long term investment decisions.

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Long term Sources of capital

1) Stock holder’s equity – preferred stock and

common stock

1) Retained earnings

2) Long term debts

Optimal mix of debt and equity is required

and it is called Target capital structure.

Why???

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Sample Problem

A firm is currently faced with an investment opportunity.

Best project available today

Cost = $100,000

Life = 20 years

IRR = 7%

Cost of least-cost financing

source available

Debt = 6%

Decision:

The firm undertakes the

opportunity because it can earn

7% on the investment of funds

costing only 6%.

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Best project 1 week later

Cost = $100,000

Life = 20 years

IRR = 12%

Cost of least-cost financing

source available

equity = 14%

Decision:

The firm rejects the opportunity

because the 14% financing cost

is greater than the 12%

expected return.

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Net Proceeds

Net proceeds

funds actually received from the sale of security

Floatation costs

the total costs of issuing and selling a security-reduce

the net proceeds from the sale.

These costs apply to all public offerings of securities –

debt, preferred stock, and common stock.

(1) Underwriting costs –

compensation earned by

investment bankers for selling the

security

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(2) Administrative costs – issuer

expenses such as legal,

accounting, printing, and other

expenses

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Before-Tax Cost of Debt

Before-tax cost of debt(rd) for a bond can be obtained in

3 ways:

Using Cost Quotations

Calculating the Cost

When the net proceeds from

sale of a bond equal its par

value, the before-tax cost just

equals the coupon interest rate

.

This approach finds the beforetax cost of debt by calculating the IRR on the bond cash flows. This

value is the cost to maturity of

the cash flows associated with

the debt.

A bond with a 10% coupon

interest rate that nets proceeds

equal to the bond’s $1,000 par

value would have a before-tax

cost, rd, of 10%.

Calculated by: Financial

calculator, an electronic

calculator, or trial-and-error

technique. It represents the

annual before-tax percentages

cost

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Approximating the Cost

Can be calculated using the

formula

Par value - Nd

I +

rd =

n

Nd

+ Par value

2

Where:

I = annual interest

Nd = net proceeds from the

sale of debt (bond)

n = no. of years to the bond’s

maturity

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Before-Tax Cost of Debt..example

Calculating the Cost (IRR)

In the preceding example, the net proceeds of a $1,000, 9% coupon interest rate, 20-year bond were found to be $960. The calculation of the annual cost is quite simple. The cash flow pattern is exactly the opposite of a conventional pattern; it consists of an initial inflow (the net proceeds) followed by a series of annual outlays (the interest payments). In the final year, when the debt is retired, an outlay representing the repayment of the principal also occurs. The cash flows associated with Duchess Corp.’s bond issue are as follows; Spreadsheet Analysis

End of

year (s)

Cash

Flow

0

$960

($980-$20)

1-20

- $90

9% coupon int. rate X $1,000 par

value

20

-$1000

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(repayment of the principal)

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Before-Tax Cost of Debt..example

Approximating the Cost

The before-tax cost of debt, rd, for a bond with a

$1,000 par value can be approximated by using the

following equation:

Where:

I = annual interest = 90

Nd = net proceeds from the sale of debt

(bond) = 960

n = no. of years to the...

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