## Thursday, August 19, 2010

### What is a "debt constant?"

If you invest in an asset that loses its value after some period (like designing a new model that will become obsolete after 7 years), you can account for this loss in value by computing the Net Present Value of the investment over its lifetime.  For example, if your cost of capital is 10%, and a new model design requires a \$400 million initial investment, you would discount the future profit over the next seven years using a 10% cost of capital, and invest in the project if, and only if, the Net Present Value of the future profit is bigger than the \$400 million design cost.

If you want to use a break-even short cut, however, you can adjust your cost of  capital to account for the finite life of the investment by using a debt constant  = r/ (1 - (1 / (1 + r) ^ n)), where r is the cost of capital and n is the number of years before the investment loses its value.

For example, if the investment loses its value after one period, then the debt constant is 110%, which makes intuitive sense.  Only an investment that pays 110% next period will cover the initial investment plus the 10% cost of capital.

For an investment that loses its value after 7 years, the debt constant falls to 20.5%, which means that the investment has to return at least 20.5% each year to cover the 10% cost of capital.

For an investment that loses its value after 30 years, the debt constant falls to 10.6%, which means that the investment has to return at least 10.6% each year to cover the 10% cost of capital.

With a debt constant, you can use break-even analysis to determine whether you are going to sell enough to cover your cost of capital.  But use the debt constant, not the cost of capital, when computing your annual fixed costs.

#### 1 comment:

1. The cost of capital and n is the number of years before the investment loses its value. Uni-source