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Discount Rate to be Used in Project Analysis

Lecture No. 24Chapter 9Fundamentals of Engineering EconomicsCopyright © 2008

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Cost of Capital – What is it? Cost of capital is the risk-adjusted discount

rate (k) to be used in computing a project’s NPW.

If we consider a project having a much greater risk than the normal project, the discount rate to be used in project selection could be higher than the cost of capital.

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Methods of Financing

Types of Financing: Equity financing uses retained earnings or funds raised

from an issuance of stock to finance a capital. Debt financing uses money raised through loans or by an

issuance of bonds to finance a capital investment.

Target Capital Structure:Companies do not simply borrow 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.

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Cost of Capital 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

Cost of Debt

Cos

t of

Cap

ital

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Calculating Cost of Equity 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, S&P 500, (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) to the market stock prices as a whole.

A number greater than one (β > 1) means that the stock is more volatile than the market on average; a number less than one (β < 1) means that the stock is less volatile than the market on average.

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Cost of Equity (ie) The following formula quantifies the cost of

equity (ie).

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)

[ ]e f M fi r r r

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Example 9.6 Determining the Cot of Equity 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 1.8, which is greater than 1, indicating the firm’s stock is perceived more riskier than market average.

The risk free interest rate is 6%, and the average market return is 13%.Determine the cost of equity to finance the plant modernization.

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Solution:

Given: rM = 15%, rf = 6%, and β = 1.8

Find: ie

0.06 1.8(0.13 0.06)

18.60%ei

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i c c k t c c k td s d s m b d b m ( / ) ( ) ( / ) ( )1 1

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

c

c

k

k

t

and

d s bc c c

Calculating the after-tax Cost of Debt

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Example 9.7 Determining the Cost of Debt Alpha Corporation needs to

raise $10 million and has decided to finance $4 million by securing a term loan and issuing 20‑year $1,000 par bonds.

Alpha’s marginal tax rate is 38%, and it is expected to remain constant in the future.

What is the after-tax cost of debt?

Source Amount Fraction Interest rate

Term Loan

Bonds

$1.33M

$2.67M

0.333

0.667

12%

10.74%

id = 0.333 0.12 1 0.38 + 0.667 0.1074 1 0.38a fa fa f a fa fa f

= 6.92%.

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Calculating the Weighted Average Cost of Capital

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.

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Illustration of Weighted Cost of Capital

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Marginal Cost of Capital

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.

Amount of Capital Borrowed ($)

Cos

t of

Cap

ital (k)

15%16%

16.5%

Marginal cost of capital

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Example 9.8 Calculating the Marginal Cost of Capital Given: Cd = $4 million, Ce = $6 million, V= $10 millions, id= 6.92%, ie=18.60% Find: k

0.0692(4) 0.1860(6)

10 1013.93%

k

Comments: This 13.93% would be the marginal cost of capital that a company with this financial structure would expect to pay to raise $10 million.