🗓 Day 4 Directive: Cost of Capital / WACC

📌 Today's Basic Information

Item Details Date June 3, 2026 (Wed) *Can be read as the actual implementation date Phase Phase 1 (Finance Restart) Day 4 / 25 Total Topics Topic Cost of Capital / Weighted Average Cost of Capital (WACC) + Calculation of Cost of Equity (CAPM/DDM) / After-tax Cost of Debt Priority A (Appeared 5 times out of 8. The discount rate r for investment decisions itself. WACC/CAPM/DDM are in the must-pass zone even in mock exams, so mark with O) Recommended Time 60 minutes (+ approx. 15 minutes for checking answers to the 2 remaining tasks from Day 3 at the beginning)

🔥 First things first: Remaining tasks from Day 3 (Checking answers for 2 past exam questions)

Past Exam Topic Check FY2020 Question 23 After-tax CF (Capital Investment) □ FY2025 Question 19 Comparison of Investment Evaluation Criteria (ARR/IRR/PI/Discounted Payback Period) □

*To Maimai: The formula you completed yesterday, "After-tax Operating CF = (Sales - Cash Expenses - Depreciation) × (1 - Tax Rate) + Depreciation", works directly for R2-23. R7-19 is a question about organizing evaluation criteria—remember the weaknesses of the payback period method (ignores time value, ignores post-recovery period). Once you solve them, explain why you chose that option in a few words each. When finished, update the notes in the progress chart.

🎯 Why this topic today (Motivation for Maimai)

In Days 2-3, you completed the flow of "Create future CF → discount → subtract → decide". But that "r when discounting" was always a number given in the problem statement.

Today, we finally have a session where you create the identity of that r = Cost of Capital (WACC) yourself. For a company to "raise" money, it must pay costs to both shareholders and banks. The average cost of the raising side becomes the **discount rate (hurdle rate)** for the side evaluating the investment. The investment story (the using side) and the financing story (the raising side) connect here as one.

Even in mock exams, Maimai was able to get the correct answer for WACC/CAPM/DDM (Question 14). So today is a session focused on recall and speed. It's a session to confirm, "Can you remember and reproduce the formula by hand?"

🏁 Today's Learning Objectives (Pass if you can do these)

1. Write the WACC formula by hand: WACC = E/(E+D) × rE + D/(E+D) × rD × (1 - Tax Rate) (E = Market value of equity, D = Market value of debt, rE = Cost of equity, rD = Cost of debt)

2. Explain the reason for multiplying the cost of debt by (1 - Tax Rate) (Because interest payments are tax-deductible = have a tax-saving effect, so the actual burden is lighter) ← a critical point Maimai tends to forget once

3. Calculate the cost of equity rE using CAPM: rE = rf + β × (rm - rf) (rf = risk-free rate, (rm - rf) = market risk premium)

4. Calculate the cost of equity rE using DDM (Dividend Discount Model): rE = D1 / P0 + g (Next period dividend yield + expected growth rate)

5. Weights (E/(E+D), etc.) should in principle be taken on a market value basis, it can be said.

6. rE > rD (Shareholders have higher risk = demand higher returns).

7. WACC is the discount rate for investment decisions = the true identity of r in Day 2-3, and it makes sense.

📖 Study Material Guide

Study Material Reference TBC Textbook Chapter 9 Cost of Capital (p.286-290): Overview of Cost of Capital (p.286) / Weighted Average Cost of Capital (p.287) / Calculation Method of Cost of Capital (p.288) (rE Tool ①) TBC Chapter 11 Return and Risk: Risk Premium / CAPM Concept (β) *Only the range necessary for calculating rE (rE Tool ②) TBC Chapter 10 Dividend Discount Model (p.310-313): Form to derive rE using DDM Past Exam Questions Open the relevant year from the project's past exam question URL (refer to the corresponding past questions below).

🧠 Important Points (Knowledge Claude will use for comprehension checks)

WACC (Today's Main Character)

Companies raise money from shareholders and creditors (banks/bonds) and pay different costs for each. The weighted average of these is the WACC.

• WACC = E/(E+D) × rE + D/(E+D) × rD × (1 - tax rate)

• The weights E/(E+D) and D/(E+D) should in principle be measured at **market value** (not book value, which is a trap).

• This is the discount rate (hurdle rate) when evaluating investment proposals. Investments that generate returns exceeding the WACC create value.

After-tax Cost of Debt (Critical Point)

• Multiply the cost of debt rD by (1 - tax rate). Why? → Interest payments are expenses (tax-deductible), which reduce taxable income = reduces taxes. Because of that tax savings, the real cost of debt becomes lighter.

• Same concept as the tax shield in Day 3 (Expense → reduced taxable income → reduced tax burden). It connects if you think of it as the "debt version" of the tax-saving effect of depreciation.

Cost of Equity rE (Two ways to derive)

A company does not directly pay a "cost of equity" (dividends are not mandatory). However, shareholders "expect this much return" = that is the cost to the company. There are two ways to derive it:

1. CAPM: rE = rf + β × (rm - rf)

   • rf = risk-free rate (e.g., government bonds), (rm - rf) = market risk premium, β = market sensitivity of the stock.

2. DDM (Dividend Discount Model): rE = D1 / P0 + g

   • D1 = next dividend, P0 = current stock price, g = expected dividend growth rate. "Dividend yield + growth rate".

   • Question 16 of Reiwa 7 is a type where you calculate rE using this DDM and plug it into WACC.

Magnitude of rE and rD

• rE > rD is the standard. Shareholders demand a higher return because they are lower in the repayment priority (higher risk).

• Therefore, the idea that increasing debt (which increases the ratio of debt, which has a seemingly lower cost) lowers WACC leads to tomorrow's MM theory.

⚠️ Points targeted in exams (watch out for traps)

• Forgetting to multiply by (1 - tax rate): Options that use the cost of debt before tax are incorrect. This is the most frequent trap.

• Using book value for weights (be careful with options; the principle is market value).

• Cost of equity < cost of debt (options stating this are incorrect; usually rE > rD).

• WACC reverse calculation type (Question 14 of Reiwa 6): WACC is given, and you must reverse-calculate rE or β. The key is whether you can rearrange the formula.

• Definition of Risk Premium(2025 Question 15): (rm − rf) is the market risk premium. β × (rm − rf) is the risk premium for an individual stock. Be careful not to confuse them.

Today's Positioning (The Roadmap)

In Days 2-3, we covered 'creating CFs and discounting them,' and today we complete the set by 'creating the discount rate r (WACC).' The engine for investment evaluation is now complete. Tomorrow, Day 5, is MM Theory—'What happens to WACC and firm value when debt is increased?' The (1 − tax rate) we created today is the very core of MM (where debt increases firm value in the presence of corporate taxes). Today's WACC is the perfect setup for tomorrow.

✏️ Relevant Past Exam Questions (Solving Together)

Solve them on your own first, then check your answers.

Priority Past Question Topic ◎ 2021 Question 15 WACC Calculation (Standard) ◎ 2019 Question 21 WACC Calculation (Standard) ◎ 2025 Question 16 WACC (Calculating cost of equity using DDM) ◎ 2024 Question 14 Cost of Equity / Risk Premium (WACC reverse calculation) ○ 2025 Question 15 Nature of Risk Premium (Knowledge)

📤 Output at the end of the session (Created by the active Claude)

【Day 4 学習報告：資本コスト・WACC】
- Day3残タスク（過去問2問）：◯問中◯問正解（R2-23／R7-19）
- 理解度（1-5）：
- 過去問演習（本日分）：◯問中◯問正解
- 特に思い出せた / 深まった点：
- まだ不安な点：
- 疑問プール行き（未解決の疑問）：
- 明日のDay 5（MM理論・最適資本構成・財務レバレッジ）への申し送り：

🔄 Mini Review (Starting in earnest today)

Finance is a calculation-heavy subject. Don't finish a topic in just one go. Starting today, we will insert 'just one calculation problem from a slightly earlier topic.'

Review Slot Target Task 3 Days Ago Day 1: Present Value / Present Value Factor Solve just one past exam question involving compound present value / annuity present value (e.g., 2020 Question 17 = Relationship between compound present value factor and annuity present value factor). Quickly recall and confirm. 1 Week Ago (None yet) Starting next week. Skipping today is fine.

From the 'side being discounted' to the 'side creating the discount rate.' Today, the investment evaluation engine is complete, and it serves as a run-up to tomorrow's MM theory. Off you go, Maimai. 🔥

Credits
Lead Agent & Text Draft: Claude Opus 4.8
Cover Image: GPT-5.5 Thinking
Orchestration & Human Director: Maimai