CHAPTER 5 : THE MINIMUM ACCEPTABLE RATE OF RETURN (MARR) and the Cost of Capital. Capital is a necessary factor of production, of production, and like any other factor , it has a cost. The cost of each financial component or instrument is defined as the component cost of that of that particular financial component. The three major capital structure components are: debt(bonds and loans), equity(common stock, preferred stock), retained earnings. The MARR value used in engineering economic analysis is one of the of the most important parameters of such of such an analysis . The correct use and the value used for the MARR is of the of the utmost importance to achieve reliable decisions. The setting of the of the MARR for an engineering economic analysis is not an exact science. The financial structure of company is changing over time an therefore the debt to equity ratio will change and this change will influence the MARR value. The MARR value can also change between projects because of changes of changes in the risk profiles of projects. of projects. Management might decide to change the MARR value to increase the rate of return of return or because of identified of identified new risks in projects.
5.1. Capital Structure of a of a Firm. The debt part of the of the capital structure of a of a firm leverages the equity part by increasing the total funds available for capital projects as well as the potential wealth of a of a firm.
5.1.1. Debt Capital: Debt Capital involves both short term and long term borrowing of ‐
‐
funds. Interest must be paid to the suppliers of the of the capital, and debt must be repaid at a specified time.
The suppliers of debt of debt do not share in the profits resulting from the use of the of the capital.
Interest paid for the use of borrowed of borrowed funds is a tax deductible expense for the ‐
firm .
5.1.1.1 Loans: Loans are regarded as a short term financial instrument (n<5 years)
For simplicity assume that all interest payments on the loan as well as income
taxes are paid by a firm on an annual basis. The after tax cost of capital for a short term loan is: ‐
c L i L 1 t c L after tax cos t of capital for a loan. i L rate of int erest per year paid on the loan . t = effective (marginal) income tax rate ‐
Example: The required return to investors
c L
is not equal to the company` cost of debt since interest
payments are tax deductible. As a result , the cost of debt to the company is less than the rate of return required by debt holders. A project will be partially financed by loan of say R1 000 000 and the interest payable on the loan is 20% compounded annually. The tax rate of the company is 28%. The cost of capital for the company to use this loan would therefore be:
c L i L 1 t 20 1 0 . 28 14 . 4 %
5.1.1.2. Bonds.
Face value Fixed interest per period
0
1
n
i Selling price – flotation cost
m
i ieffective 1 1 m i = interest rate that will ensure equivalence between the net selling price ,the interest, and the face value.
ieffective
effective interest rate per period
m = frequency of compounding of the interest per period(one year)
t company tax rate After tax cost of a bond = ieffective
1 t
Example: A company offers bonds to investors to finance a capital project. The maturity date is 30 years and the coupon rate will be 12% payable semi annually. The bond is offered to investors at R1 000 par ‐
value. The tax rate for the company is 28%.
i effective
i 1 m
m
2
0 . 12 1 1 1 0 . 1236 12 . 36 % 2
1 t 12.361 0.28 8.899%
After tax cost of a bond = ieffective
5.1.2. Equity Capital: Equity capital is supplied and used by its owners in the expectation that a profit will be earned.
Equity capital cannot be obtained, however, unless the expected rate of return is high enough, at an acceptable risk, to be attractive to potential investors.
5.1.2.1. Common Stock/Shares. The owner of a share of common stock in a corporation is entitled to receive cash dividends declared by the company, as well as the price of the stock at the time it is sold.
P0
Div1
Div 2
1 ea 1 ea 2
.....
Div n
1 ea N
P N
1 ea N
e a rate of return per year(required by common stockholders(after tax cost of equity to the corporation).
P0 current value of a share of common stock. P N selling price of a share of common stock at the end of N years. If we now assume that dividends stay constant over an infinite period of time and P0
P0 Div( P / A, ea , )
PN :
Div ea
Thus, if the current selling price of a share of common stock is known and the annual dividend for the past year is also known, the after tax cost of equity(common stock) is conservatively estimated ‐
to be:
ea
Div P0
Note:
1 i n 1 P A n i1 i
If n
∞
then :
P
A i
therefore i
A P
Example: If some of the earnings are retained, then the company`s stockholders will incur an opportunity cost because the earnings could have been paid as dividends , in which case stockholders could have reinvested the money .The firm should earn on its reinvested earnings at least as much as its stockholders could earn on alternative investments of equivalent risk If a company would finance a project by issuing common stock or by retained earnings at the market price of R100, the company`s common shares at present. The anticipated dividend is R5 per share and the investors expect a growth rate of 10%. The investors also anticipate a share price of R120 after 3 years.
P0
P0
Div1
Div2
1 ea 1 ea 2 5
.....
51 0.1
1 ea 1 ea 2
Div n
1 ea N
P N
1 ea N
51 0.1 120 2
1 ea 3
100
ea 11.44% This results implies that if the company is to finance the project by using retained earnings or sell common stock to investors , it will have to realize a rate of return of at least 11.44%.
5.1.2.2. Preferred Stock/Shares. Because ,like debt, preferred stock carries a fixed commitment on the part of the corporation to make periodic payments, and ,in the case of liquidation, the claims of the preferred stockholders take precedence over those of the common stockholders. Preferred stock is therefore
more risky to the firm than common stock, but it is less risky than bonds. Because the dividend rate is fixed , the market value of such stock is less likely to fluctuate. Therefore the after tax cost of capital for preference stock can be ‐
approximated by dividing the guaranteed dividend by the original par value of the stock.
eP
Div P PP
Example: The cost of preferred stock is the preferred dividend divided by the net issuing price. The preferred stock price is R100 and it pays dividend of R10.If there is an underwriting or flotation cost of 2.5% of the share price (R2 50) then the net issuing price for the company would be ‐
R97 50. The cost of preferred stock would then be: ‐
eP
Div P PP
10 100 2.50
10.3%
5.1.2.3. Retained Earnings/Owners capital. The after tax cost of retained earnings is normally assumed to be ‐
the same as for common stock(the rate of return expected by common stockholders).
These earnings, which are equity funds, do not belong to the corporation, but rather to the stockholders. They have been retained and reinvested in the firm for the purpose of enhancing future growth and revenues and increasing stockholders wealth. Thus, there is the same opportunity cost for these funds as would occur if the shareholders received them originally and then invested them in additional common shares of the corporation.
5.2.4. Effect of Leverage on the Cost of Capital. The higher the level of debt , the larger the fixed charges and the higher the probability of not being able to cover fixed charges. The inability to cover the fixed charges then leads to a host of negative impacts and perceptions on the corporation. The greater probability of not covering fixed charges, which also increases the probabilities of bankruptcy , will cause the relationship between leverage and the risk measures to curve up more rapidly than without the bankruptcy clause.
With bankruptcy clause Required rate
Without bankruptcy clause
of return
Premium for business risk Riskless rate of return
Debt/equity ratio
5.3. The Effect of Leverage on the Component Cost of Debt. The higher the leverage ratio , the higher the cost of debt. The cost of debt can be expected to rise at an increasing rate beyond a certain ratio of debt to equity.
After tax Cost of debt
Debt to equity ratio The cost of capital for a company will start to increase as the debt ratio increases if the company borrow large sums of money to finance projects. If a company has only a few projects that is not that capital intensive , it can finance the capital budget with only equity funds. In case the company have a large number of economically viable projects, the management will have to go to the financial market to acquire the necessary funds. Depending on the debt ratio and the financial standing of the company within the financial constituency, the required cost of capital can increase. All projects with a NPV>0 at the MARR value can be considered as long s the budget limit is not exceeded. Under conditions of capital rationing the company`s value will not be maximized. Maximization of the company`s value can only take place if management can move to the point where the marginal projects` NPV is zero and there is no capital rationing present.
5.4. Weighted Average Cost of Capital (WACC). The weighted average cost of capital (WACC) of the pool is estimated by the relative fractions from debt and equity sources. If known exactly, these fractions are used to estimate the WACC.
WACC = (Equity fraction) (cost of equity capital)
+ (Debt fraction)(cost of debt capital) = (Common stock fraction)(Cost of common stock capital)
+ (Preferred stock fraction)(Cost of preferred stock capital)
+ (Retained earnings fraction)(Cost of retained earnings capital)
+ (Loans fraction)(Cost of loans capital)
+ (Bonds fraction)(Cost of bonds capital)
Sullivan, Wicks, Luxhoj p599 Source of financing
Short term debt Bonds Common stock Preferred stock Retained earnings
Am ou nt R x 000
Proportion
After Tax Cost (Decimal)
3 600
0.0809
Weighted Cost (Proportion) (After tax cost) 0.0481 0.0039
10 000 24 600
0.2247 0.5528
0.0424 0.1000
0.0095 0.0553
2 000
0.0449
0.08000
0.0036
4 300
0.0967
0.1000
0.0097
44 500
1.0000
WACC =
0.0820
5.5. Diagram for illu stration of the compos iti on of the MARR value After tax MARR = Before tax MARR(1 – tax rate) Relationship between Cost of Capital and the MARR value:
Established MARR value
Risk factor added
Percentage added to compensate for the risk involved
Expected return
Percentage added to make it economically viable
Minimum MARR value
Cost of Capital
5.6. Minim um Attracti ve Rate of Return The minimum attractive rate of return (MARR) is a cut off rate representing a ‐
yield on investments that is considered minimally acceptable.
The minimum attractive rate of return can be viewed as a rate at which the firm can always invest, since it has a large number of opportunities that yield such a return. Whenever any money is committed to an investment proposal, an opportunity to invest that money at the MARR has been foregone. The MARR is sometimes considered to be an “opportunity cost”. The MARR should not be confused with the cost of capital. Normally the MARR is substantially higher than the cost of capital. This difference occurs because few firms are willing to invest in projects that are expected to earn slightly more than the cost of capital, owing the risk elements in most projects and because of uncertainty about the future. When the interest rate (MARR) used in econ omic analysis calculations is raised to adjust for risk or uncertainty, greater emphasis is placed on i mmediate or short-term results and less emphasis on longer-term results. The higher the interest rate or MARR value the less t he influence of any cash flow the further it is from t=0.(Time value of mo ney).
Minimum attractive rate of return should be equal to the largest of: cost of borrowed money ,cost of capital or opportunity cost.
5.6.1. Selecting a Minimum Attractive Rate of Return.
Risk –adjusted rates may not work well. When MARR used in economic analysis calculations is raised to adjust for risk or uncertainty, greater emphasis is placed on immediate or short – term results and less emphasis on longer-term results.
Example: 0
1
2
3
4
5
1000 2000 3000 4000 5000 Present Value: 0% 10% 15% 20% 30% -15000 -10652.4 -9127.55 -7897.2 -6065.8 -15000 -12093
0
1
-10985
2
-10049
-8550
3
4
5
1000 2000 3000 4000 5000
Opportunit y cost of Capital Approach.
% Return on Investment
Funds available for investment
Opportunity Cost of inv estment 1 3 Not taken
6
9
4
2
Cumulative Total Cost of Investment
Optimal Capital Budg et. Optimum capital budget % Return on Investment
WACC
1 3
6
9
4
2
Cumulative Total of new Investments
5.6.2. The effective MARR can vary f rom one pr oject to another and throug h tim e because of:
Project risk Where there is greater risk(perceived or actual) associated with proposed projects, the tendency is to set a higher MARR. This means that there is some concern that the project will not realize its projected revenue requirements.
Investment Opportunities If management is determined to expand in a certain area, the MARR may be lowered.
Tax Structure If corporate taxes are rising, pressure to increase the MARR is present.
Limited Capital As debt and equity capital become limited, the MARR is increased. If the demand for limited capital exceeds supply, the MARR may tend to be set even higher.
Market rate at other corporations These variations are often based on changes in interest rates for loans, which directly impact the cost of capital.
Efficient allocation of available funds between divisions inside the company.
Increasing the economical viability of a project by decreasing the required rate of return(MARR) for that specific project.
5.6.3. Factors that Affect the WACC.
The level of Interest Rate. If interest rates increase , the cost of debt will increase because investors will demand a higher rate of return on their investment. Investors will also expect increased dividends and this will increase the costs of common and preferred stock.
Tax Rates. Tax rates are applicable to calculate the after tax cost of capital. The interest payable on a loan is tax deductible and would therefore reduce the cost of capital for the company.
Capital Structure of the Company. The after tax cost of capital is lower for debt than for equity. A company can change its capital structure with the understanding that it will influence the proportions (weights) of each financial instrument in the structure and therefore the final value of the WACC.
The Dividend Policy. The percentage of earnings paid out in dividends may affect a stock`s required rate of return.
Investment Policy. The cost of capital is determined by the company`s investment profile. If this profile is going to change it will also affect the perceived risk of the company by investors. If the investors experience the change as an increase in the riskiness of the company, they will demand higher compensation for the increased risk in the form of higher dividends and interest rates on loans.
Revision Questions. 1. What is the cost of capital ? 2. Identify the different components that the cost of capital can be comprised of. 3. Describe the influence of the different financial components on the value of the cost of capital. 4. Describe the influence of the capital structure on the value of the cost of capital. 5. Suppose that basic business risks to all firms in any given industry are similar. a.
Would you expect all firms in each industry to have approximately the same cost of capital ?
b. How would the averages differ among industries ?. 6. What factors operate to cause the cost of capital to increase with financial leverage ?. 7. Explain the relationship between the required rate of return on the equity/ debt ratio. 8. How would the various components of cost of capital , and the average cost of capital, be likely to change if a firm expands its operations into a new, more risky venture ?.
