time value of money

Topics: Stock, Finance, Corporate finance Pages: 24 (2461 words) Published: November 29, 2013
Pratima Trivedi


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.
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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%
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%
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
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(2) Administrative costs – issuer
expenses such as legal,
accounting, printing, and other

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
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Approximating the Cost
Can be calculated using the
Par value - Nd

I +

rd =


+ Par value

I = annual interest
Nd = net proceeds from the
sale of debt (bond)
n = no. of years to the bond’s

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)






- $90

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



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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:

I = annual interest = 90
Nd = net proceeds from the sale of debt
(bond) = 960
n = no. of years to the...
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