San José State University Department of Economics 

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The determination of the cost of capital for a firm can be considered a matter of confronting the firm's demand schedule for investment funds with its supply schedule of investment funds. The cost of capital is the discount rate which makes the quantity of funds it needs for investment projects equal to the quantity of funds it has available at that cost of capital. Again it is a matter of a price that balances supply and demand.
Consider first the construction of the demand for capital schedule. Suppose the firm has five projects with the Internal Rates of Return and initial investment fund requirements as shown below. These projects are presumed to be independent; i.e., not mutually exclusive.
Project  IRR  Funding Requirement 

A  12%  $2 million 
B  6%  $4 million 
C  14%  $3 million 
D  10%  $1 million 
E  8%  $5 million 
From this data one can determine at each level of the cost of capital which projects are worthwhile and how much capital is needed to fund them. This is shown in the table below:
Cost of Capital  Which Projects Should Be Undertaken  Funding Requirement 

16%  none  $0 
14%  C  $3 million 
12%  C & A  $5 million 
10%  C, A & D  $6 million 
8%  C, A, D & E  $11 million 
6%  C, A, D, E & B  $15 million 
The above data can be plotted in a graph as shown below:
There is an analogous procedure for constructing the supply schedule. Suppose the firm can borrow from various sources in the amounts and at the interest rates given below. For now the tax deductibility for interest will be ignored.
Capital Source  Interest Rate  Maximum Borrowing 

F  6%  $2 million 
G  8%  $1 million 
H  10%  $3 million 
I  12%  $1 million 
J  16%  $5 million 
Interest Rate  Sources Which Can Be Accessed  Funding Available 

4%  none  $0 
6%  F  $2 million 
8%  F & G  $3 million 
10%  F, G & H  $6 million 
12%  F, G, H & I  $7 million 
16%  F, G, H, I & J  $12 million 
This information can be put into a graph as below:
One way to search for the interest rate or cost of capital that balances the supply and demand for capital is to desplay the demand and supply schedule in the same table, as shown below:
Interest Rate Cost of Capital  Supply of Capital  Demand for Capital 

16%  $12 million  $0 
14%  $7 million  $3 million 
12%  $7 million  $5 million 
10%  $6 million  $6 million 
8%  $3 million  $11 million 
6%  $2 million  $15 million 
4%  $0 million  $15 million 
Fortunately it is easy to spot the cost of capital that balances the demand and supply of investment funds. It is 10 percent, at which the supply of capital is $6 million and the demand is $6 million.
The same balance can be seen in the graph below where the demand schedule is in red and the supply schedule is in green. The lines cross at 10 percent.
To take the tax deductibility into account the nominal interest rate is multiplied by (1t_{p}) where t_{p} is the tax rate on profits. The effect of the taxdeductibility of interest is to shift downward (outward) the supply of capital schedule thereby reducing the equilibrium cost of capital.
One crucial extension of the analysis is the determination of the the cost of capital raised from selling new stock. For material on this topic: The Cost of Equity Capital
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