www.izmirekonomi.edu.tr (c) 2001 contemporary engineering economics1 discount rate to be used in...

(c) 2001 Contemporary Engineering Economics

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Discount Rate to be Used in Project Analysis

ECON 320 Engineering EconomicsMahmut Ali GOKCEIndustrial Systems EngineeringComputer Sciences


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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 NPV.


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Methods of Financing

Equity Financing – Capital is coming from either retained earnings or funds raised from an issuance of stock

Debt Financing – Money raised through loans or by an issuance of bonds

Capital Structure – Well managed firms establish a target capital structure and strive to maintain the debt ratio

Capital Structure

Debt

Equity



Equity Financing

Flotation (discount) Costs: the expenses associated with issuing stock

Types of Equity Financing: Retained earnings Common stock Preferred stock

Retained earnings

Preferred stock

Common stock

+

+



Debt Financing Bond Financing:

Incur floatation cost Pay only interests at the end each

period (usually semi-annually) Pay the entire principal (face value)

in a lump sum when the bond matures

Term Loan: Involve an equal repayment

arrangement. May incur origination fee Allow terms to be negotiated

directly between the borrowing company and a financial institution

Bond Financing

Term Loans

+



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



1. Calculating the after-tax Cost of Debt

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, and

C

C

k

k

t

C C C

s

b

s

b

m

d s b

Interest payments on both bond and loan financing is tax deductible



Practice Problem

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 for the following condition. (The remaining funds would be raised through equity financing.)

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

Bond

$1.33M

$2.67M

0.333

0.667

12%

10.74%

id=0.33*0.12*(1-0.38)+

0.667*0.1074*(1-0.38)=6.92%



2. Calculating the Cost of Equity 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

Cost of RetianedEarnings

Cost of IssuingNew Stock

Cost of IssuingPreferred Stock



i c c k c c k

c c ke r e r c e e

p e p

( / ) ( / )

( / )

Method 1: Calculating Cost of Equity Based on Financing Sources

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



Determining the Cost of Equity

Source Amount Interest Rate

Fraction of Total Equity

Retained earnings

$1 M 20.50% 0.167

New common stock

$4 M 22.27% 0.666

Preferred stock

$1 M 10.08% 0.167

ie

( . )( . ) ( . )( . ) ( . )( . )

.

0167 0 205 0 666 0 2227 0167 01008

19 96%



Method 2: Calculating Cost of Equity based on CAPM

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 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.



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)

[ ]e f M fi r r r



Practice Problem – Cost 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.



Solution

Ie=0.06+1.8*(0.13-0.06)=18.60%

This means if this company finances a project totally from equity funds, the project should at least earn 18.60%



3. Calculating the Weighted after-tax Cost of Capital

ki C

V

i C

Vd d e e

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.



Marginal Cost of Capital

• Given: Cd = $4 million, Ce = $6 million, V= $10 millions, id= 6.92%, ie=19.96%• Find: k

k

0 0692 4

10

01996 6

1014 74%

. ( ) . ( )

.

Comments: This 14.74% would be the marginal cost of capital that a company with this financial structure would expect to pay to raise $10 million.

Same formula can be used with interest on new equity and new debt



Cost of Capital

Cost of Debt Cost of Equity

Cost of Equity = Risk free return + Risk Premium

= [ ]

where risk free return (U.S. Treasury Bills)

Average rate of return on market

= stock price volatility

f M f

f

M

R R R

R

R

Cost of debt = debt interest rate (1 - tax rate)

Cost of Capital = (cost of debt) x (% of capital from debt) + (cost of equity) x (% of capital from equity)



Summary

Identifying and estimating relevant project cash flows is perhaps the most challenging aspect of engineering economic analysis. All cash flows can be organized into one of the following three categories:

1. Operating activities.2. Investing activities3. Financing activities.



•Cash Items

1. New investment and disposal of existing assets

2. Salvage value (or net selling price)

3. Working capital

4. Working capital release

5. Cash revenues/savings

6. Manufacturing, operating, and maintenance costs.

7. Interest and loan payments

8. Taxes and tax credits



Non-cash items1. Depreciation expenses2. Amortization expenses

The income statement approach is typically used in organizing project cash flows. This approach groups cash flows according to whether they are operating, investing, or financing functions.



• Methods of financing: 1. Equity financing uses retained earnings

or funds raised from an issuance of stock to finance a capital.

2. Debt financing uses money raised through loans or by an issuance of bonds to finance a capital investment.

• 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.



• The selection of an appropriate MARR depends generally upon the cost of capital—the rate the firm must pay to various sources for the use of capital.

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

ki C

V

i C

VV C Cd d e e

d e , where



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.

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