Chapter 9: The cost of capital
9.1 Overview of the cost of capital
Cost of capital – rate of return that a firm must earn on the projects in which it invests to maintain its
market value (of its shares) and attract funds from market supplier of capital
Link between firm’s long-term investment decisions and the wealth of the owners as determined by
investors in the marketplace
Project with a rate of return above cost of capital will increase the value of the firm
It is the ‘magic number’ that is used to decide whether a proposed investment will increase or decrease the
firm’s share price
Only invest if: NPV ≥ R0 or IRR ≥ cost of capital
Some key assumptions
Business risk: risk of firms being unable to cover operating cost – assume to be unchanged when new
project is accepted
o Acceptance will not affect ability to cover operating costs
Financial risk: risk of being unable to cover financial obligations – assume to be unchanged when new
project is accepted
o Acceptance will not affect ability to meet financing costs
After-tax basis: after-tax costs are considered relevant hence the cost of capital is measured on an after-tax
basis
o Assumed to be consistent with the after-tax framework used to make capital budgeting decisions
The basic concept
Positive relationship between risk and return ∴ therefore firm’s financing cost (cost of capital) will change if
the acceptance of a project changes firm’s business or financial risk
Cost of capital easily measured because assume new projects do not change these risks
Cost of capital estimated at given point in time – reflects future cost of funds over the long run – reflects the
interrelatedness of financing activities
Target capital structure – the desired optimal mix of debt and equity financing that most firms attempt to
maintain
o E.g. 40% debt + 60% equity
(Page 351 – 352 for example)
Specific sources of capital
Long-term sources of funds supply permanent financing
Long-term financing supports the firm’s fixed-asset investments
Four basic sources of long-term funds:
o Long-term debt
o Preference shares
o Ordinary shares
o Retained earnings
Specific cost of each source of financing is the after-tax cost of obtaining the financing today, not the
historically-based cost reflected by the existing financing on the firm’s books
Cost of capital values are rough approximates because numerous assumptions and forecasts underlie them
, 9.2 Cost of long-term debt
Cost of long-term debt, ri, is the after-tax cost today of raising long-term funds though borrowing
Assume that funds are raised through the sale of bonds (with annual interest)
Net proceeds received from the sale of a bond = funds actually received from sale (i.e. amount less flotations
cost)
Flotation cost: cost incurred to issue and sell a security
o Includes:
Underwriting costs – compensation earned by investment bankers for selling the security;
and
Administrative costs – issuer expenses (legal, accounting, printing and other expenses)
(Example page 353)
Before-tax cost of debt
Before-tax cost of debt, rd, for a bond can be obtained in any of three ways:
o Quotation
o Calculation
o Approximation
Using cost quotations
When net proceeds = par value, then before-tax cost = coupon interest rate
o E.g. Bond with 10% coupon interest rate that needs net proceeds equal to the bond’s R 1 000 par
value would have a before-tax cost of debt, rd, of 10%
Quotation sometimes used is the yield to maturity (YTM)
o Cost of debt = yield to maturity on the firm’s debt adjusted for floatation costs
o YTM – basically the IRR of a bond
o YTM depends on a number of factors:
Bond’s coupon ratee
Maturity date
Par value
Current market conditions and selling price
o Interest on debt is a tax-deductible expense
This will reduce cost of debt because we use after-tax costs
Calculating the cost
Find before-tax cost of debt by calculating the IRR on the bond cash flows
From issuers point of view, value = cost to maturity of cash flows associated with the debt
What is the cost of debt?
PV = - Net proceeds (selling price – flotation costs)
pmt = Annual interest payments (par value x coupon interest rate)
n = Number of years
FV = Par value
I = YIELD TO MATURITY
(example page 354)
9.1 Overview of the cost of capital
Cost of capital – rate of return that a firm must earn on the projects in which it invests to maintain its
market value (of its shares) and attract funds from market supplier of capital
Link between firm’s long-term investment decisions and the wealth of the owners as determined by
investors in the marketplace
Project with a rate of return above cost of capital will increase the value of the firm
It is the ‘magic number’ that is used to decide whether a proposed investment will increase or decrease the
firm’s share price
Only invest if: NPV ≥ R0 or IRR ≥ cost of capital
Some key assumptions
Business risk: risk of firms being unable to cover operating cost – assume to be unchanged when new
project is accepted
o Acceptance will not affect ability to cover operating costs
Financial risk: risk of being unable to cover financial obligations – assume to be unchanged when new
project is accepted
o Acceptance will not affect ability to meet financing costs
After-tax basis: after-tax costs are considered relevant hence the cost of capital is measured on an after-tax
basis
o Assumed to be consistent with the after-tax framework used to make capital budgeting decisions
The basic concept
Positive relationship between risk and return ∴ therefore firm’s financing cost (cost of capital) will change if
the acceptance of a project changes firm’s business or financial risk
Cost of capital easily measured because assume new projects do not change these risks
Cost of capital estimated at given point in time – reflects future cost of funds over the long run – reflects the
interrelatedness of financing activities
Target capital structure – the desired optimal mix of debt and equity financing that most firms attempt to
maintain
o E.g. 40% debt + 60% equity
(Page 351 – 352 for example)
Specific sources of capital
Long-term sources of funds supply permanent financing
Long-term financing supports the firm’s fixed-asset investments
Four basic sources of long-term funds:
o Long-term debt
o Preference shares
o Ordinary shares
o Retained earnings
Specific cost of each source of financing is the after-tax cost of obtaining the financing today, not the
historically-based cost reflected by the existing financing on the firm’s books
Cost of capital values are rough approximates because numerous assumptions and forecasts underlie them
, 9.2 Cost of long-term debt
Cost of long-term debt, ri, is the after-tax cost today of raising long-term funds though borrowing
Assume that funds are raised through the sale of bonds (with annual interest)
Net proceeds received from the sale of a bond = funds actually received from sale (i.e. amount less flotations
cost)
Flotation cost: cost incurred to issue and sell a security
o Includes:
Underwriting costs – compensation earned by investment bankers for selling the security;
and
Administrative costs – issuer expenses (legal, accounting, printing and other expenses)
(Example page 353)
Before-tax cost of debt
Before-tax cost of debt, rd, for a bond can be obtained in any of three ways:
o Quotation
o Calculation
o Approximation
Using cost quotations
When net proceeds = par value, then before-tax cost = coupon interest rate
o E.g. Bond with 10% coupon interest rate that needs net proceeds equal to the bond’s R 1 000 par
value would have a before-tax cost of debt, rd, of 10%
Quotation sometimes used is the yield to maturity (YTM)
o Cost of debt = yield to maturity on the firm’s debt adjusted for floatation costs
o YTM – basically the IRR of a bond
o YTM depends on a number of factors:
Bond’s coupon ratee
Maturity date
Par value
Current market conditions and selling price
o Interest on debt is a tax-deductible expense
This will reduce cost of debt because we use after-tax costs
Calculating the cost
Find before-tax cost of debt by calculating the IRR on the bond cash flows
From issuers point of view, value = cost to maturity of cash flows associated with the debt
What is the cost of debt?
PV = - Net proceeds (selling price – flotation costs)
pmt = Annual interest payments (par value x coupon interest rate)
n = Number of years
FV = Par value
I = YIELD TO MATURITY
(example page 354)
