Lecture No. 50 Chapter 15 Contemporary Engineering Economics Copyright © 2010 Contemporary Engineering Economics, 5th edition, © 2010

Lecture No. 50Chapter 15

Contemporary Engineering EconomicsCopyright © 2010

Contemporary Engineering Economics, 5th edition, © 2010

Cost of Capital (k)Cost of Equity (ie) –

Opportunity cost associated with using shareholders’ capital

Cost of Debt (id) – Cost associated with borrowing capital from creditors

Cost of Capital (k) – Weighted average of ie and id


Cost of Equity (ie)Cost of Retained Earnings

(kr)Cost of issuing New

Common Stock(ke)Cost of Preferred Stock

(kp)Cost of equity: weighted

average of kr ke, and kp


Method 1: Calculating the Cost of Equity based on Financing Sources Formula:

Where Cr = amount of equity financed from retained earnings, Cc = amount of equity financed from issuing new stock, Cp = amount of equity financed from issuing preferred stock, and

Ce = Cr + Cc + Cp


Example 15.4 Determining the Cost of Equity – Alpha Corporation

Given: Financing mix

Find: Cost of equity (ie)


Method 2: Calculating the Cost of Equity based on the Financial Markets

Expected return on risky asset:

Inflation risk: The possibility that the value of assets or income will decrease as inflation shrinks the purchasing power of a currency.

Risk premium: The return in excess of the risk-free rate of return that an investment is expected to yield


An Alternative Way of Determining the Cost of Equity

The following formula quantifies the cost of equity (ie).

where rf = risk free interest rate (commonly referenced to U.S. Treasury bond yield)rM = market rate of return (commonly referenced to average return on S&P 500 stock index funds)


The cost of equity is the risk-free cost of debt (20-year U.S. Treasury Bills around 7%) plus a premium for taking a risk as to whether a return will be received.

The premium is the average return on the market (12.5%) less the risk-free cost of debt. This premium is multiplied by Beta, a measure of stock price volatility.

Beta quantifies risk and is an approximate measure of stock price volatility. It measures one firm’s stock price compared (relative) with the market stock prices as a whole.

A number greater than one means that the stock is more volatile than the market on average; a number less than one means that the stock is less volatile than the market on average.

Example 15.5 – Determining the Cost of Equity by the Financial Market

Given:Alpha Corporation needs to raise $10 million for plant modernization.

Alpha’s target capital structure calls for a debt ratio of 0.4, indicating that $6 million has to be financed from equity. Alpha is planning to raise $6 million from the financial market Alpha’s Beta is known to be 1.99, which is greater than 1, indicating the firm’s stock is perceived more riskier than the market average. The risk free interest rate is 6%, and the average market return is 13%.

Find: The cost of equity to finance the plant modernization.

Solution:


6%

13%1.99

0.06 1.99 0.13 0.06

19.93%

f

M

e

r

r

i


( ) (1 ) ( ) (1 )s bd s m b m

d d

c ci k t k t

c c

where the amount of the term loan, the amount of bond financing, the before-tax interest rate on the term loan, the before-tax interest rate on the bond, the firm's marginal tax rate,

s

b

s

b

m

cckkt

and

d s bc c c

Example 15.6 Determining the Cost of DebtGiven: $4M to raise by debt, kb = 10%, ks = 12%, flotation cost = 6%, and tax rate = 38%

Find: A/T cost of debt

Step 1: Effective before-tax cost of issuing the bond

kb = 10.74%

Step 2: After-tax cost of debt



d d e ei c i ck

V V

cd= Total debt capital (such as bonds) in dollars,ce=Total equity capital in dollars,V = cd+ ce,

ie= Average equity interest rate per period considering all equity sources,id = After-tax average borrowing interest rate per period considering all debt sources, andk = Tax-adjusted weighted-average cost of capital.

Process of Calculating the Cost of Capital


Example 15.7 Calculating the Marginal Cost of Capital

Given: Cd = $4 million, Ce = $6 million, V= $10 million,

id= 6.85%, ie=19.93%

Find: k

Marginal cost of Capital:

• Comments: This 14.70% would be the marginal cost of capital that a company with this financial structure would expect to pay to raise $10 million.


0.0685(4) 0.1993(6)10 10

14.70%

k

Summary• Methods of financing:

1. Equity financing uses retained earnings or funds raised from an issuance of stock to

finance a capital investment.2. Debt financing uses money raised through

loans or by an issuance of bonds to finance a capital investment.

• Companies do not simply borrow all funds to finance projects. Well-managed firms usually establish a target capital structure and strive to maintain the debt ratio when individual projects are financed.


The cost of the capital formula is a composite index reflecting the cost of funds raised from different sources. The formula is

The marginal cost of capital is defined as the cost of obtaining another dollar of new capital. The marginal cost rises as more and more capital is raised during a given period.


, where d d e ed e

i c i ck V c c

V V

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Lecture No. 50 Chapter 15 Contemporary Engineering Economics Copyright © 2010 Contemporary Engineering Economics, 5th edition, © 2010