- CFA Exams
- CFA Level I Exam
- Study Session 11. Equity Valuation (3)
- Reading 30. Residual Income Valuation
- Subject 1. Calculating residual income

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**CFA Practice Question**

An analyst gathers the following data for a company (all data in $MM):

- Total assets: $380.
- Debt: $114.
- Pretax cost of debt: 5%.
- Equity (26.6 million shares outstanding): $266.
- Cost of equity: 14%.
- EBIT: $45.
- Marginal tax rate: 40%

The residual income of the company using capital charge method is:

A. -$12.8.

B. -$13.6.

C. -$10.4.

**Explanation:**To use the capital charge method, we need to calculate WACC first. WACC = Equity share x cost of equity + Debt share x cost of debt x (1 - Tax rate) = (Equity / Total Assets) x cost of equity + (Debt / Total Assets) x cost of debt x (1 - Tax rate) = ($266/$380) x 0.14 + ($114/$380) x 0.05 x (1 - 0.4) = 0.107.

Note that in the calculation of WACC we used after-tax cost of debt, since interest expense is tax-deductible.

After-tax operating income = EBIT x (1 - Tax rate) = $45.0 x (1 - 0.4) = $27.0.

Residual income = After-tax operating income - (Total Assets x WACC) = $27.0 - ($380 x 0.107) = $(13.6).

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**User Contributed Comments**
7

User |
Comment |
---|---|

Mogensen |
I don't agree. I think RI should be NI - equity charge. I get -12.3 |

andrewevelyn |
The Capital Charge method seems to be what Schweser calls Economic Value Added (EVA): EVA = NOPAT - (WACC*invested capital) = EBIT (1-t) - Dollar WACC. Does anyone know if they are indeed the same? |

danlan2 |
Andrewevelyn: they are the same |

pao13 |
But Schweser uses another approach for invested capital {(net PP&E + net WC) or (long-term debt + stochholders' equity)}. According to AnalystNotes Invested capital equals Total Assets. Which approach should we use? |

volkovv |
There is a much easier way to solve it. Residual Income = Net Income - Equity Charge RI = (EBIT - Interest) * (1 - tax) - (Equity * Cost of Equity) RI = (45 - 114*.05)*(1 - .4) - (266 * .14) = -13.6 |

ljamieson |
I did it volkow's way. Makes more sense. But EVA is in the CFA book too. They don't mention Cap Charge. |

MattNYC |
Capital Charge in the CFA is NOPAT Less: Capital Charge (which is MVequity * Kequity) Be careful. I only took out the taxes part for this question and forgot the Interest. |