Why is the overall cost of capital used for investment decisions even when only one source of capital will be used (e.g., debt)?

Why is the overall cost of capital used for investment decisions even when only one source of capital will be used (e.g., debt)?
In computing the cost of capital, are the historical costs of existing debt and equity or the current costs as determined in the market used? Why?
Why is the cost of retained earnings equal to the firm’s required rate of return on its common stock (Ke)?
If the company has the opportunity to earn a rate of return less than its cost of capital, but it will still generate a profit, should it make the investment? Why or why not?
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