﻿ The Principles Determining the Cost of Capital
San José State University
Department of Economics

applet-magic.com
Thayer Watkins
Silicon Valley
USA

 The Principles Determining the Cost of Capital

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.

### The Demand Schedule for Capital

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.

ProjectIRRFunding Requirement
A12%\$2 million
B6%\$4 million
C14%\$3 million
D10%\$1 million
E8%\$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 CapitalWhich 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:

### The Supply Schedule for Capital

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 SourceInterest RateMaximum Borrowing
F6%\$2 million
G8%\$1 million
H10%\$3 million
I12%\$1 million
J16%\$5 million

Interest RateSources 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:

### The Supply and Demand for Capital by the Firm

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 CapitalDemand 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 (1-tp) where tp is the tax rate on profits. The effect of the tax-deductibility 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