The Weighted Average Cost of Capital (WACC) and Investment Appraisal

Learning Objectives

Acquire the ability to calculate the cost associated with preference shares, unquoted debt, and bank loans.
Understand and critically discuss the assumptions underlying the use of the Weighted Average Cost of Capital (WACC) as a discount rate for investment appraisal.
Demonstrate proficiency in answering numerical questions regarding WACC.
Utilize the Capital Asset Pricing Model (CAPM) to calculate WACC for companies with multiple divisions.
Explain, both verbally and diagrammatically, why WACC may lead to incorrect investment decisions in multi-divisional contexts.

Cost of Other Forms of Finance

Firms may fund investments through various financial assets beyond the standard ordinary shares and redeemable/irredeemable bonds.

Preference Shares
- These have characteristics of both debt and equity.
- Similar to Fixed Interest Debt: They have a par value and pay a fixed return.
- Unlike Debt: Interest cannot be offset against corporation tax.
- Similar to Equity: They imply ownership; the fixed return is viewed as a dividend rather than interest; they generally do not mature (assumed irredeemable).
- Valuation: Because they pay a guaranteed fixed dividend forever, they are treated as a perpetuity.
- Cost of Preference Share Capital ( $K_{ps}$ ): This is calculated as the dividend yield for the preference shares.
- Formula: $K_{ps} = \frac{d}{P_{ps}}$ where $d$ is the fixed dividend and $P_{ps}$ is the market price.
The Cost of Unquoted Debt Capital
- Unquoted debt has no market value, meaning the cost of debt cannot be found directly.
- Estimation Method: The cost can be estimated if the cost of quoted debt with similar risk is known.
- Example (Cranky Ltd. vs. Stanley Plc):
  - Cranky Ltd. has privately borrowed $£20\text{m}$ via unquoted irredeemable bonds with a $12\%$ coupon.
  - Stanley Plc is in the same industry, is of similar size, and has $10\%$ irredeemable bonds quoted at a price of $£110$ .
  - Corporation tax is $25\%$ .
  - To estimate Cranky's cost: Assume risk (and return) equals Stanley's.
  - Stanley's after-tax cost of debt ( $K_D$ ): $K_D = \frac{i(1 - T)}{P_D} = \frac{10(1 - 0.25)}{110} = 6.82\%$
  - Therefore, Cranky's cost of debt is also $6.82\%$ .
  - Implied Price for Cranky ( $P_D$ ): $P_D = \frac{i(1 - T)}{K_D} = \frac{12(0.75)}{0.0682} = £131.96$
The Cost of Bank Loans and Overdrafts
- These are variable (floating) coupon rate debt. The interest varies with current market rate movements.
- Base Rate: The minimum rate at which banks lend to customers.
- Assumptions: Bank loans are non-negotiable instruments.
- Market Value: Because they are non-negotiable, the Market Value ( $MV$ ) is equal to the nominal value (the original amount borrowed).
- Cost to Borrower: Equal to the current interest payable net of corporation tax.
- Formula: $K_{BL} = CIR(1 - T)$ where $CIR$ is the current interest rate.
- Example: A company borrows $£10\text{m}$ . The interest rate is $3\%$ above the base rate. Base rate is $13\%$ ; corporation tax is $35\%$ .
  - $CIR = 13 + 3 = 16\%$
  - $K_{BL} = 16(1 - 0.35) = 10.4\%$
  - $V_{BL} = £10\text{m}$

The WACC and Investment Appraisal

Capital Structure: Refers to the composition of a firm's financing. This can be:
- All-equity capital.
- Mixed capital: Varying proportions of debt and equity. This is the most common form.
Gearing (Leverage): This describes the capital structure and is represented by the ratio $V_D / V_E$ .
The Relevant Discount Rate: For a mixed capital structure, the correct discount rate for Net Present Value (NPV) calculations is the Weighted Average Cost of Capital (WACC), which weights the cost of each individual component.

Assumptions Behind WACC usage in Investment Appraisal

Constant Risk Profile: The project must not significantly change the company's overall systematic risk. WACC reflects the required return for the firm's existing risk level. If a project has a different risk level than the firm, WACC is inappropriate.
Small Project Scale: The project must be small relative to the firm. Significant financing needs for a large project might change the market price of shares and debentures, which in turn alters the WACC.
Optimal Capital Structure: It is assumed the firm has an optimal capital structure it wishes to maintain in the medium-to-long term. The project should be financed such that this structure does not change.
Perpetuity Assumption: For simplicity, all cash flows (dividends, interest, project returns) are assumed to be perpetuities.

Numerical Example: Delaware Plc

Balance Sheet Data (£000):
- Authorized Ordinary Shares (£1): $10,000$
- Issued Ordinary Shares: $8,000$ (Total £8,000)
- Share Premium: $2,000$ ; Reserves: $6,000$ ; Shareholders' Funds: $16,000$
- $12\%$ Irredeemable Debentures: $4,000$
Market Data:
- Current dividend ( $d_0$ ): $20\text{p}$ (just paid).
- Growth rate ( $g$ ): $10\%$
- Share price ( $P$ ): $£2.75$
- Debenture Price ( $P_{ID}$ ): $£80$
Calculations:
- (i) Cost ( $K_{OS}$ ) and Market Value ( $V_{OS}$ ) of Equity:
  - $V_{OS} = 8,000,000 \times 2.75 = £22,000,000$
  - $K_{OS} = \frac{d_0(1+g)}{P} + g = \frac{20(1 + 0.1)}{275} + 0.1 = 0.18$ (or $18\%$
- (ii) Cost ( $K_{ID}$ ) and Market Value ( $V_{ID}$ ) of Irredeemable Debt:
  - Number of debt units = $\frac{£4,000,000}{£100} = 40,000$
  - $V_{ID} = 40,000 \times £80 = £3,200,000$
  - $K_{ID} = \frac{i}{P_{ID}} = \frac{12}{80} = 0.15$ (or $15\%$
- (iii) WACC ( $K_0$ ):
  - $K_0 = K_{OS}\left(\frac{V_{OS}}{V_0}\right) + K_{ID}\left(\frac{V_{ID}}{V_0}\right)$
  - $K_0 = 18\left(\frac{22\text{m}}{22\text{m} + 3.2\text{m}}\right) + 15\left(\frac{3.2\text{m}}{22\text{m} + 3.2\text{m}}\right) = 17\%$

Numerical Example: Stanhope Plc

Project Context: Stanhope produces travel suitcases and needs $£10\text{m}$ for a new machine. It plans to issue new equity even though it views its current capital structure as optimal.
Market/Financial Data:
- $2.5\text{m}$ shares issued (£1 par); $£60\text{m}$ of $10\%$ irredeemable debentures.
- Share price: $£3.45$ (cum-div). A $25\text{p}$ dividend is about to be paid.
- Debenture price: $£82.50$ (ex-interest).
- Historical Dividends: 2019 ( $425$ ), 2020 ( $475$ ), 2021 ( $520$ ), 2022 ( $560$ ), 2023 ( $625$ ).
- Corporation Tax: Given as $0\%$
Calculations:
- Growth Rate ( $g$ ): using historical data from 2019 to 2023 ( $n=4$ years of growth).
  - $g = \left(\frac{D_t}{D_0}\right)^{\frac{1}{n}} - 1 = \left(\frac{625}{425}\right)^{\frac{1}{4}} - 1 = 10\%$
- Cost of Equity ( $K_e$ ): Using ex-div price ( $3.45 - 0.25 = 3.20$ ).
  - $K_e = \frac{25(1.1)}{320} + 0.1 = 18.6\%$
  - $V_e = 2.5\text{m} \times £3.20 = £8\text{m}$
- Cost of Irredeemable Debt ( $K_{ID}$ ):
  - $K_{ID} = \frac{10}{82.5} = 12.12\%$
  - $V_D = £82.50 \times \left(\frac{£60\text{m}}{£100}\right) = £49,500,000$
- WACC ( $K_0$ ):
  - $V_0 = 49.5 + 8 = £57.5\text{m}$
  - $K_0 = 18.6\left(\frac{8}{57.5}\right) + 12.12\left(\frac{49.5}{57.5}\right) = 13.02\%$
Appraisal Consistency:
- The project is an expansion of existing business, so risk likely remains same.
- However, the project ( $£10\text{m}$ ) is large relative to the company ( $V_{e} = £8\text{m}$ ), suggesting share prices and the WACC will change.
- The use of all-equity financing for the project will deviate from the optimal capital structure.
- Conclusion: It is not safe to use the current WACC for this appraisal.

The WACC and Project Risk (Multi-Divisional Firms)

Project Risk vs. Firm Risk: If a project move the firm into a new business area (diversification), systematic risk changes, making the current WACC inappropriate.
Multi-Product Companies: Most companies have multiple divisions. WACC represents the average systematic risk of the firm, not the risk of any specific division.
- Using the average WACC risks accepting high-risk projects that don't return enough to compensate for their specific risk.
- Conversely, it risks rejecting low-risk projects that are actually profitable given their lower required return.

Overcoming Problems with the CAPM

The Capital Asset Pricing Model (CAPM) can determine specific discount rates for each division based on the beta of their respective industry groups.
Rocha Plc Example:
- Two divisions: Supermarkets and Furniture manufacturing.
- Market Equity ( $V_E$ ): $£30.3\text{m}$ (ex-div).
- Debt ( $V_D$ ): $£12.625\text{m}$ book value at $8\%$ . Market price: $£80$ .
- Current Dividend ( $D_0$ ): $£4\text{m}$ ; Growth ( $g$ ): $6\%$
- Supermarket Beta: $0.8$ ; Furniture Beta: $1.92$
- Risk-free rate ( $R_f$ ): $8\%$ ; Market Return ( $R_m$ ): $15\%$
Step 1: Calculate Corporate WACC:
- $K_E = \frac{4(1.06)}{30.3} + 0.06 = 20\%$
- $V_D = \left(\frac{12.625\text{m}}{100}\right) \times 80 = £10.1\text{m}$
- $K_D = \frac{8}{80} = 10\%$
- $K_0 = 20\left(\frac{30.3}{40.4}\right) + 10\left(\frac{10.1}{40.4}\right) = 17.5\%$
Step 2: Calculate Divisional Rates using CAPM:
- Standard Formula: $E(R_i) = R_f + \beta_i[R_m - R_f]$
- Supermarkets: $E(R_{SUP}) = 8 + 0.8[15 - 8] = 13.6\%$
- Furniture: $E(R_{FURN}) = 8 + 1.92[15 - 8] = 21.4\%$
Analysis (SML Diagrammatic Implications):
- If Rocha used the average WACC ( $17.5\%$
  - It would incorrectly reject low-risk supermarket projects that return between $13.6\%$ and $17.5\%$
  - It would incorrectly accept high-risk furniture projects that return between $17.5\%$ and $21.4\%$ , which do not meet the risk-adjusted requirement.