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

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**CFA Practice Question**

At the end of 2011, 40% of DIY Software, Inc.'s $1 million in total assets were debt-financed. The company's cost of debt was 6 percent, and its cost of equity was 12 percent.

2011 EBIT was $200,000, and is expected to remain constant. Income was taxed at 40 percent. The 50,000 shares of common stock outstanding had a year-end 2011 book value of $12.00 per share. The dividend payout ratio was 100%.

Calculate the intrinsic value of a share of stock.

Correct Answer: Interest Expense = Total Assets x Debt Percentage of Assets x Cost of Debt Capital = ($1,000,000 x 0.4 x 0.06) = $24,000.

Net Income = (EBIT - Interest Expense) x (1 - Tax Rate) = (200,000 - 24000) x (1 - 0.4) = $105,600.

Equity Capital = Total Assets x Equity Percentage of Assets = $1,000,000 X 0.6 = $600,000.

Equity Charge = Equity Capital x Cost of Equity Capital = $600,000 x 0.12 = $72,000.

Residual Income = Net Income - Equity Charge = $105,600 - 72,000 = $33,600.

Per-share RI = Residual Income / # Shares = $33,600 / 50,000 = $0.672.

RI is a perpetuity, so Intrinsic Value = Book Value + Present Value of Expected Residual Income = B

Net Income = (EBIT - Interest Expense) x (1 - Tax Rate) = (200,000 - 24000) x (1 - 0.4) = $105,600.

Equity Capital = Total Assets x Equity Percentage of Assets = $1,000,000 X 0.6 = $600,000.

Equity Charge = Equity Capital x Cost of Equity Capital = $600,000 x 0.12 = $72,000.

Residual Income = Net Income - Equity Charge = $105,600 - 72,000 = $33,600.

Per-share RI = Residual Income / # Shares = $33,600 / 50,000 = $0.672.

RI is a perpetuity, so Intrinsic Value = Book Value + Present Value of Expected Residual Income = B

_{0}+ (RI / r) = 12 + 0.672/0.12 = $17.6.###
**User Contributed Comments**
7

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

ikaneng |
alternatively: (capital charge) RI = EBIT(1-T) minus (WACC X Total assets) WACC = (40% x 6% x (1 - 40%)) + (60% x 12%) = 8.64% 200000 (1 - 40%) minus (8.64% x 1000000) RI = 33600 |

gaai |
Or just 105,600/12%/50,000 |

rhardin |
Or just take P/E = 1/r. Which is P/2.112 = 1/.12 and solve for Price. The 2.112 is just the earnings per share. |

davcer |
RI and Gordon are consistent |

Sp1993 |
To calculate rBVPS at t-1 (beginning BVPS), since all the earnings are paid out as dividends (dividend ratio 100%), the BVPS ending is the same as the BVPS beginning = 12.00. |

davidt876 |
note that rhardin's formula is just the per share equivalent of gaai's formula. and that the only reason they work here is because EBIT is unchanging and therefore the stock is a perpetuity. those formulas will not work for questions where EBIT is expected to change |

ashish100 |
Oooooh that felt good. Got it right. God bless you all |