Calculation Review: Time Accounting Drills

Overview

• What you’ll learn: Calculation fluency across the four quantitative areas tested in the BIZ exam, with worked examples and practice problems at exam speed.
• Estimated reading time / practice time: 25 minutes

Area 1: Unit Time Profit

Formula: UTP = (Revenue − Expenses) ÷ Total Work Hours

Practice Problem 1: An amoeba has monthly revenue of ¥4,800,000, expenses of ¥3,200,000, and 320 person-hours of work. Calculate UTP.

Solution: UTP = (¥4,800,000 − ¥3,200,000) ÷ 320 = ¥1,600,000 ÷ 320 = ¥5,000/hour

Practice Problem 2: An amoeba targets UTP of ¥4,500/hour. In March, it worked 280 hours and earned revenue of ¥2,100,000 with expenses of ¥850,000. Did it meet its target?

Solution: UTP = (¥2,100,000 − ¥850,000) ÷ 280 = ¥1,250,000 ÷ 280 ≈ ¥4,464/hour. Below target.

Area 2: Hourly Efficiency Ratio

Formula: Efficiency Ratio = Actual UTP ÷ Target UTP

Practice Problem 3: Target UTP = ¥5,000/hour. Actual UTP = ¥5,750/hour. What is the efficiency ratio?

Solution: Efficiency Ratio = ¥5,750 ÷ ¥5,000 = 1.15 (115%)

Practice Problem 4: An amoeba’s efficiency ratio was 1.08 in Q1, 0.92 in Q2, 1.15 in Q3. What is the average quarterly efficiency ratio?

Solution: Average = (1.08 + 0.92 + 1.15) ÷ 3 = 3.15 ÷ 3 = 1.05 (105%)

Area 3: Bonus Pool

Formula: Pool = (Annual Profit − Threshold) × Pool Percentage

Practice Problem 5: Annual profit: ¥15,000,000. Threshold: ¥4,000,000. Pool percentage: 12%. Amoeba A achieved 110% of UTP target, Amoeba B achieved 85%. Target allocations: A = ¥600,000, B = ¥500,000 (cap at 120%). Calculate actual bonus for each.

Solution: Pool = (¥15,000,000 − ¥4,000,000) × 12% = ¥1,320,000. A: ¥600,000 × min(1.10, 1.20) = ¥660,000. B: ¥500,000 × 0.85 = ¥425,000.

Area 4: KPI Bonus and Vesting

KPI Formula: Bonus = Base Bonus × Achievement Ratio × Individual Multiplier

Practice Problem 6: Base salary ¥6,000,000. Base bonus 20% of salary. Achievement ratio 0.95. Individual multiplier 1.3 (capped at 1.5). Calculate the bonus.

Solution: Base bonus = ¥6,000,000 × 20% = ¥1,200,000. Bonus = ¥1,200,000 × 0.95 × 1.3 = ¥1,482,000

Vesting Practice Problem 7: Employee granted 8,000 options at exercise price ¥800. Standard 4-year vesting, 1-year cliff. At the end of year 3, share price is ¥1,500. How many shares are vested? What is the total intrinsic value of vested options?

Solution: After year 3: 75% vested = 6,000 shares. Intrinsic value = (¥1,500 − ¥800) × 6,000 = ¥4,200,000

Key Takeaways

• Four calculation areas: UTP, efficiency ratio, bonus pool, KPI bonus and vesting.
• Always show your formula and calculation steps — partial credit requires visible method.
• Unit time profit is always (Revenue − Expenses) ÷ Work Hours. Never divide by days or by employees.
• Cap awareness: achievement ratio caps, individual multiplier caps, and pool allocation caps appear frequently in exam questions.