What is the BASE rule the instructor uses to verify the equity-method roll-forward?

BASE stands for Beginning $+$**A**dditions$-$**S**ubtractions$=$ Ending. It's a universal sanity check used in financial accounting for any account that rolls forward across periods.

For an equity-method investment:

• Beginning carrying value
• Additions: share of investee net income for the period (and for multi-year, summed across all years)
• Subtractions: share of investee dividends for the period (also summed for multi-year)
• Ending carrying value

For the lecture example (4 years, 30% stake, $500K initial, total William NI of $1.3M, total dividends of $260K):

Why BASE is exam-essential:

1. It catches arithmetic errors. If your year-by-year roll-forward gives $814K but the BASE summary gives $812K, you made an arithmetic slip in one of the four years. Find it before submitting.

1. It can replace the year-by-year roll-forward when only the ending value matters. On a multi-year question where the exam asks "what is the investment carrying value at year-end 4?", you can skip the four-year detail and compute it directly: $\text{Beginning} + \sum (\text{share of NI}) - \sum (\text{share of Div}) = \text{Ending}$.

1. It generalises to other accounts. BASE works for any balance: PP&E ($\text{beginning} + \text{capex} - \text{depreciation} - \text{disposals} = \text{ending}$), debt ($\text{beginning} + \text{new issuances} - \text{repayments} = \text{ending}$), retained earnings ($\text{beginning} + \text{NI} - \text{dividends} = \text{ending}$), inventory ($\text{beginning} + \text{purchases} - \text{COGS} = \text{ending}$). Use it everywhere.

A worked example:

If you own 25% of an investee. Year-1 NI = $200K, divs = $40K. Year-2 NI = $250K, divs = $50K. Year-3 NI = $300K, divs = $60K. Initial investment $1,000K.

Year-by-year:

• Year 1 end: $1,000 + 0.25 × 200 − 0.25 × 40 = $1,000 + 50 − 10 = $1,040
• Year 2 end: $1,040 + 0.25 × 250 − 0.25 × 50 = $1,040 + 62.5 − 12.5 = $1,090
• Year 3 end: $1,090 + 0.25 × 300 − 0.25 × 60 = $1,090 + 75 − 15 = $1,150

BASE check:

• $B = \$1{,}000$
• $A = 0.25 \times \$750 \text{ (total NI)} = \$187.5$
• $S = 0.25 \times \$150 \text{ (total divs)} = \$37.5$
• $E = \$1{,}000 + 187.5 - 37.5 = \$1{,}150 \checkmark$

Match. Both methods give $1,150.

What if amortisation is in play?

If the excess purchase price attributed to depreciable assets must be amortised, BASE expands to:

For the lecture, if amortisation were $6,000/year for 4 years $= \$24{,}000$, the ending would shift by $-\$24\text{K}$.

Bottom line: BASE is one of the highest-leverage techniques in CFA Level II FSA. Use it on every multi-step roll-forward question.