Math Snap

STEP 1

1. Purple initially purchases 30% of Yellow's common stock for $150,000.
2. Yellow reports a net income of $50,000 on June 30.
3. Yellow declares dividends of $20,000 on June 30.
4. Purple purchases an additional 10% of Yellow's common stock for $50,000 on July 1.
5. Yellow reports a net income of $65,000 on December 31.
6. Yellow declares dividends of $20,000 on December 31.
7. We are calculating the Investment in Yellow account balance for Purple as of December 31, 2023.

STEP 2

1. Calculate the initial investment and its impact.
2. Adjust for income and dividends up to June 30.
3. Account for the additional purchase on July 1.
4. Adjust for income and dividends from July 1 to December 31.
5. Calculate the final balance in the Investment in Yellow account.

STEP 3

Calculate the initial investment and its impact.
The initial investment by Purple is 30% of Yellow's stock for $150,000.

STEP 4

Adjust for income and dividends up to June 30.
Purple's share of Yellow's net income up to June 30 is 30% of $50,000, which is:
$$0.30 \times 50,000 = 15,000$$ Purple's share of Yellow's dividends up to June 30 is 30% of $20,000, which is:
$$0.30 \times 20,000 = 6,000$$ The investment account is increased by the net income share and decreased by the dividends share:
$$150,000 + 15,000 - 6,000 = 159,000$$

STEP 5

Account for the additional purchase on July 1.
Purple purchases an additional 10% of Yellow's stock for $50,000, bringing the total investment to:
$$159,000 + 50,000 = 209,000$$

STEP 6

Adjust for income and dividends from July 1 to December 31.
Purple's share of Yellow's net income from July 1 to December 31 is 40% of $65,000, which is:
$$0.40 \times 65,000 = 26,000$$ Purple's share of Yellow's dividends from July 1 to December 31 is 40% of $20,000, which is:
$$0.40 \times 20,000 = 8,000$$ The investment account is increased by the net income share and decreased by the dividends share:
$$209,000 + 26,000 - 8,000 = 227,000$$

Calculate the final balance in the Investment in Yellow account.
The final balance in the Investment in Yellow account reported by Purple at December 31, 2023, is:
$$\boxed{227,000}$$