Fin323 Ch 10 Cost Of Capital

Front 1

cost of capital

Back 1

the rate of return that a firm must earn on the projects in which it invests to maintain its market value and attract funds

The cost of capital acts as a link between the firm’s long-term investment decisions and the
wealth of the owners as determined by investors in the marketplace.
• It is the “magic number” that is used to decide whether a proposed investment will increase or
decrease the firm’s stock price.

Formally, the cost of capital is the rate of return that a firm must earn on the projects in which it
invests to maintain the market value of its stock.

some assumption when looking at cost of captial:
business risk and financial risk assumed to be unchanged.

it is estimated at a given point in time. it reflects the expected avg. future cost of funds over the long run.

Front 2

target capital structure

Back 2

teh desired optimal mix of debt and equity financing that most firms attempt to maintain.

where firms want to have a desired mix of financing

debt = borrow money
equity = sold of stock

ex. if there are two investment opportunities...where one has a IRR =7% with a debt of 6%... a manager would take it.

now if there's another opportunity with an IRR = 12% and equity =14%. a manager would reject it.

however, if there's mix financing such as 50/50 of debt and equity... then the weighted cost will be 10% [(.05 x 6% debt) + (0.05 x 14% equity)]

note: long-term financing supports the firm's fixed-asset investments

Front 3

name four long-term funds for business firm

Back 3

long term debt
preferred stock
common stock
retained earnings

Front 4

cost of long-term debt, Ki

or after-tax cost of debt

Back 4

teh after-tax cost today of raising long-term funds through borrowing.

because interest on debt is tax deductible, it reduces the firm's taxable income...therefore, it can be found by multiplying the before-tax cost, kd, by 1 minus the tax rate, T

Ki=Kd x (1-T)

typically the cost of long term debt is less than the cost of any alternative forms of long-term financing, primarily because of the tax deductibility of interest

we typically assume that the funds are raised through the sale of bonds. and that the bonds pay annual interest

Front 5

net proceeds

Back 5

funds actually received from the sale of security.

sale of bond, or any security, are the fudns that are actually received from the sale

Duchess Corporation, a major hardware manufacturer, is contemplating selling $10
million worth of 20-year, 9% coupon bonds with a par value of $1,000. Because current
market interest rates are greater than 9%, the firm must sell the bonds at $980. Flotation
costs are 2% or $20. The net proceeds to the firm for each bond is therefore $960 ($980 -
$20).

net proceeds = $960

Front 6

flotation costs

Back 6

the total costs of issuing and selling a security.

they include two components: underwriting costs and administrative costs

Duchess Corporation, a major hardware manufacturer, is contemplating selling $10
million worth of 20-year, 9% coupon bonds with a par value of $1,000. Because current
market interest rates are greater than 9%, the firm must sell the bonds at $980. Flotation
costs are 2% or $20. The net proceeds to the firm for each bond is therefore $960 ($980 -
$20).

floation cost = 2%

Front 7

before-tax cost of debt, Kd

Back 7

when the net proceeds from sale fo a bond equal its par value, the before-tax cost just equals the coupon interest rate.

a second quotation sometimes used is the yield to maturity (YTM) on a similar-risk bond.

calculation cost:
find the internal RATE of return (IRR)...also called cost of maturity from a issuer's point of view.

Front 8

cost of preferred stock, Kp

Back 8

because preferred stock is a form of ownership, the proceeds from its sale are expected to be held for an infinited period of time. however, the one aspect of preferred sotck that required review is dividends.

the ratio of the preferred stock dividend to the firm's net proceeds from the sale of preferred stock; calculated by
Kp = Dp/Np

Dp= annual dividend

Np= preferred stock

because preferred stock dividents are paid out of the firm's after-tax cash flow, tax adjustment is not required

Duchess Corporation is contemplating the issuance of a 10% preferred stock that is expected to
sell for its $87-per share value. The cost of issuing and selling the stock is expected to be $5 per
share. The dividend is $8.70 (10% x $87). The net proceeds price (Np) is $82 ($87 - $5).
rP = DP/Np = $8.70/$82 = 10.6%

Front 9

cost of common stock equity, Ks

Back 9

the rate at which investors discount the expected dividends of the firm to determine its share value.

two forms of common stock financing
1. retained earnings
2. new issues of common stock

two ways to estimate cost of common equity

1. divident valuation model

using the constant-growth valuation model (Gordon model) to find Ks

Po= D1/(Ks-g)

D1=per-share dividend expected at the end of year 1
Ks = required return on common stock
g= constant rate of growth in dividends.
Po= value of common stock

therfore, Ks = D1/Po +g

2. capital asset pricing model (CAPM)

it describes the relationship btw required return, Ks, and the nondiversifiable risk of the firm as measured by the beta coefficient, b.

Ks = Rf+[bx(km-Rf)]

Rf = risk-free rate of return
km= market return; return on the market portfolio of assets

The CAPM differs from dividend valuation models in that it explicitly considers the
firm’s risk as reflected in beta.
• On the other hand, the dividend valuation model does not explicitly consider risk.
• Dividend valuation models use the market price (P0) as a reflection of the expected riskreturn
preference of investors in the marketplace.
• Although both are theoretically equivalent, dividend valuation models are often preferred
because the data required are more readily available.
• The two methods also differ in that the dividend valuation models (unlike the CAPM) can
easily be adjusted for flotation costs when estimating the cost of new equity.

For example,
assume a firm has just paid a dividend of $2.50 per share, expects dividends to grow at 10%
indefinitely, and is currently selling for $50.00 per share.
First, D1 = $2.50(1+.10) = $2.75, and
rS = ($2.75/$50.00) + .10 = 15.5%.

For example, if the 3-month T-bill rate is currently 5.0%, the market risk premium is 9%, and the
firm’s beta is 1.20, the firm’s cost of retained earnings will be:
rs = 5.0% + 1.2 (9.0%) = 15.8%.
Using some managerial judgement and preferring to err on the high side, we will use 15.8% as
the estimate of cost of retained earnings (rE)

Front 10

cost of new issues of common stock, Kn

Back 10

the cost of common stock, net of underpricing and associated flotation costs.

normally, for a new issue to sell, i has to be underpriced...sold at a price below its current market price, Po. because
1. additional demand for shares can be achieved only at a lower price
2. each share's percentage of ownership in the firm is diluted
3. many investor see that company uses common stock equity financing because it believes that the shares are currently overpriced.
4. flotation cost.

kn = D1/Nn +g

kn will always be greater than cost of existing issues, ks.

Front 11

The Weighted Average Cost of Capital

Back 11

WACC = Ka = (wi x ki) + (wp Kp) + (ws x Kr or Kn)

• Wi = % of debt = proportion of long-term debt in capital structure
• Wp = % of preferred = proportion of preferred stock in capital structure
• Ws = % of common = proportion of common stock equity in capital structure.
wi+wp+ws= 1.0

reflects the expected average future cost of funds over the long run.

reflects the expected avg. future cost of funds over the long run; found by weighting the cost of each specific type of captial by its proportion in the firm's capital structure.

For example, assume the market value of the firm’s debt is $40 million, the market value of the
firm’s preferred stock is $10 million, and the market value of the firm’s equity is $50 million.
Dividing each component by the total of $100 million gives us market value weights of 40%
debt, 10% preferred, and 50% common.
Using the costs previously calculated along with the market value weights, we may calculate the
weighted average cost of capital as follows:
WACC = ra = wiri + wprp + wsrr or n
WACC = .40(5.67%) + .10(9.62%) + .50(15.8%)
= 11.13%
This assumes the firm has sufficient retained earnings to fund any anticipated investment
projects.