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The question tells us that the expected rate of return on the new project is lower than the division’s overall return on investment, so the first part of this answer choice is incorrect. The second part of this answer choice is also incorrect. The expected rate of return on the new project cannot be lower than the firm’s cost of capital. If it were, the project would not increase the company’s residual income. Furthermore, the firm would lose money on the project because the financing for the project (the cost of capital) would cost more than the project would earn. The result would be that residual income would decrease, not increase.
The firm's cost of capital cannot be higher than the expected rate of return on the new project. If it were, the project would not increase the company’s residual income. Furthermore, the firm would lose money on the project because the financing for the project (the cost of capital) would cost more than the project would earn. The result would be that residual income would decrease, not increase.
The expected rate of return on the new project must be higher than the firm’s cost of capital. If it were not, the project would not increase the company’s residual income. If the expected rate of return were lower than the firm’s cost of capital, the firm would lose money on the project because the financing for the project (the cost of capital) would cost more than the project would earn. The result would be that residual income would decrease. Since we are told that the project will increase residual income, the project’s expected rate of return must be higher than the company’s cost of capital. We know the expected rate of return on the new project is lower than the division’s overall return on investment, because the question tells us it is.
The question tells us that the division is maintaining a positive residual income. If the division's return on investment were lower than the firm's cost of capital, then it would have a negative residual income. Since it does not, its return on investment must be higher than the firm's cost of capital, not lower.