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WACC — SUMMARY NOTES
Business Insights and Analysis (BIA)
BUSINESS INSIGHTS AND ANALYSIS (BIA)
S U M M A R Y
N O T E S
WEIGHTED AVERAGE
COST OF CAPITAL
Key concepts · Examiner traps · Worked examples · Formula card
I N S I D E
01
What is WACC?
02
Cost of equity — dividend valuation model
03
CAPM
04
Cost of debt and preference shares
05
Cum-dividend, ex-dividend and the yield curve
06
Examiner trap — post-project equity value
07
Full WACC computation
08
Master formula card
By Hamza Ali · ARM Business School
WACC
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START HERE
WACC IN FIVE STEPS
THE BIG IDEA
Every WACC question — however long — is these five steps. Each step points to the section that
teaches it.
1
2
3
4
5
IDENTIFY
VALUE
COST
WEIGHT
WACC
long-term sources
that carry a cost
market values —
ex-div / ex-int
Ke · Kp · Kd(1 − t)
each source
MV × cost
for each source
Σ (MV × cost)
÷ Σ MV
§01
§01, §05
§02 – §04
§07
§07
How to read these notes
You will see…
What it means
What to do with it
THE BIG IDEA
The whole section in one sentence
Read it first; say it back after the section
FORMULA
A gold-framed box — a formula you must
know
Learn it exactly, including the notation
KEY RULE
Conditions and rules behind a method
These are where method marks are won
EXAMINER TRAP
A mistake ICAP deliberately tests
Check your answer against it every time
STEP /
A worked example, step by step
Cover the working and redo it yourself
Three checks at the end of every section
Tick only what you can say without looking
✔ ANSWER
QUICK RECALL
WACC
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SECTION 01
WHAT IS WACC?
THE BIG IDEA
WACC is the blended price of all long-term finance — each source’s cost, weighted by what the
market says that source is worth today.
The core concept
WACC is the average return, weighted by market values, that a company must pay to all its long-term providers of
finance — ordinary shareholders, preference shareholders and lenders. It is the minimum return the company
must earn on its existing assets to keep every provider satisfied, and it is the discount rate for new projects that
share the company’s current business risk and capital structure.
CORE WACC FORMULA
WACC = [ E × Ke + P × Kp + D × Kd(1 − t) ] ÷ ( E + P + D )
E, P, D = market values of equity, preference shares and debt. Kd(1 − t) = post-tax cost of debt. If there are no
preference shares, the P terms simply drop out.
Why market values, not book values?
Market values show what the finance is worth today — the amount investors would have to be paid to hold it
now. Book values are historical and ignore how the market currently prices each source. Book values are used
only for bank loans and other untraded debt (where book value = market value), or when the question gives no
market data at all.
Historic exam frequency — marks per sitting
Mar 22
Sep 22
Mar 23
Sep 23
Mar 24
Sep 24
Mar 25
Sep 25
Average
12
15
12
11
12
12
14
13
≈ 12.6
High-frequency topic: WACC has carried 11–15 marks in every sitting from March 2022 to September 2025.
Which sources enter WACC?
Only long-term sources of finance that carry a cost are included — together they make up capital employed.
Source
Cost
In WACC?
Ordinary equity (share capital +
reserves)
Ke
YES
Market value (shares × ex-div price)
Preference shares
Kp
YES
Market value
Long-term debt — bonds / debentures
Kd (post-tax)
YES
Market value (ex-interest)
Bank loans
Kd (post-tax)
YES
Book value (= market value)
Trade payables
No explicit cost
NO
—
Interest
Usually NO
Overdraft
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SUMMARY NOTES
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Value used
Include only if it is a permanent, “hardcore” source
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CAPITAL EMPLOYED — TWO ROUTES TO THE SAME FIGURE
Financing side: Capital employed = Equity + Preference shares + Long-term debt
Asset side: Capital employed = Non-current assets + (Current assets − Current liabilities)
Both give the same figure because the balance sheet balances — use whichever the question’s data makes
quicker.
Why is Ke always higher than Kd?
1. Risk — lenders have a contractual right to interest and rank ahead of shareholders on liquidation;
shareholders are residual claimants, paid last and paid only if profits allow. More risk means a higher
required return.
2. Tax — interest is tax-deductible, so the company’s effective cost of debt is Kd × (1 − t). Dividends get no tax
relief.
Result: Kd(post-tax) < Kp < Ke under normal conditions.
QUICK RECALL
· tick when you can say it without looking
☐ Market values, not book values — except bank loans (book value = MV).
☐ Trade payables are excluded; an overdraft only if it is a permanent source.
☐ Kd(1 − t) < Kp < Ke — because of risk and tax relief on interest.
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SECTION 02
COST OF EQUITY — DIVIDEND VALUATION MODEL
THE BIG IDEA
A share is worth the present value of its future dividends. Turn that formula round and it gives you
Ke.
The principle
The market value of a share is the present value of all the dividends it is expected to pay, discounted at the
shareholders’ required return, Ke. Because a company is assumed to continue indefinitely, those dividends form a
perpetuity. Rearranging the valuation formula gives Ke.
NOTATION — GET THESE RIGHT EVERY TIME
D0 = dividend just paid (the current year’s dividend)
D1 = next year’s dividend = D0 × (1 + g)
P0 = current share price, always EX-dividend
g = constant annual growth rate of dividends (Ke must be greater than g)
The three dividend models
Model
When to use
Value formula
Ke from market value
① Constant dividend
Dividend expected to stay the
same forever (typically 100%
payout, no growth)
P0 = D ÷ Ke
Ke = D ÷ P0
② Constant growth
(Gordon)
Dividend grows at a steady g
forever (company retains part of
profit)
P0 = D1 ÷ (Ke − g)
= D0(1 + g) ÷ (Ke − g)
Ke = D1 ÷ P0 + g
= D0(1 + g) ÷ P0 + g
③ Multi-stage growth
Different growth rates in different
periods
PV of explicit dividends
+ PV of terminal value
Trial and error — IRR
interpolation
MULTI-STAGE MODEL — TERMINAL VALUE
Terminal value at the end of year n = Dn+1 ÷ (Ke − glong-term)
This is a value at year n, so it must be discounted back n years — the most common slip is discounting it n + 1
years or not at all.
Finding the growth rate, g — five methods
Method
Formula / logic
Class example
① Dividend history
Oldest dividend × (1 + g)n = latest dividend
n = years of growth (years of data − 1)
120 (1 + g)4 = 163 → g = 8%
② Gordon’s growth model
g=b×r
b = retention ratio, r = return on equity
g = 40% × 20% = 8%
③ Net asset growth
Opening net assets × (1 + g)n = closing net assets
1,000 (1 + g)5 = 1,469 → g = 8%
④ Profit history
Oldest profit × (1 + g)n = latest profit
200 (1 + g)4 = 272 → g = 8%
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Method
Formula / logic
Class example
⑤ Retained profit ÷
opening equity
g = (Profit − Dividend) ÷ Opening equity
(this is b × r in one step)
109 ÷ 1,360 = 8%
Counting n: five years of dividends (e.g. 20X1 to 20X5) contain only four years of growth, so n = 4. Getting n
wrong is the most common error in method ①.
GORDON’S MODEL — CONDITIONS AND INPUTS
▪ b = retained profit ÷ profit after tax = 1 − payout ratio.
▪ r = profit after tax ÷ OPENING equity (per share: EPS ÷ opening book value per share).
▪ Use the CURRENT year’s b and r — they represent the policy expected to continue.
▪ The model is valid only if b and r stay constant, all growth is financed by retained earnings, and Ke > g.
Price/earnings (P/E) method
When no share price is given but a P/E ratio is (often a proxy company’s ratio for an unlisted company), build the
price first, then find Ke.
P/E VALUATION
P0 = EPS × P/E ratio
Dividend = EPS × payout ratio → Ke = D0(1 + g) ÷ P0 + g
If there is no growth (g = 0, all earnings paid out), this collapses to Ke = D ÷ P0 = EPS ÷ P0 = 1 ÷ P/E ratio.
QUICK RECALL
· tick when you can say it without looking
☐ Ke = D0(1 + g) ÷ P0 + g, with P0 always ex-dividend.
☐ Growth from history: n = years of data − 1.
☐ Gordon: g = b × r, using the current year’s b and r on opening equity.
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SECTION 03
CAPM — CAPITAL ASSET PRICING MODEL
THE BIG IDEA
Shareholders are rewarded only for the risk they cannot diversify away. Beta measures it; CAPM
prices it.
Risk framework
Type of risk
Also known as
Removed by diversification?
Rewarded by the market?
Systematic
Market / undiversifiable risk
NO — always remains
YES — measured by β
Unsystematic
Company / industry-specific
YES
NO — not priced
Diversified investors have already removed unsystematic risk, so only systematic risk earns a premium. β
measures it against the market (market β = 1.0).
CAPM — COST OF EQUITY
Ke = Rf + (Rm − Rf) × β
Symbol
Meaning
Where it comes from in the exam
Rf
Risk-free rate
Government bond / T-bill yield
Rm
Expected return on the market portfolio
Return on the stock market index
Market risk premium (MRP)
“Market return 12%” → MRP = 12% − Rf. “Premium
12%” → use 12% as it stands
Systematic risk of the company’s equity vs the
market
Given, or derived from a proxy / project
(Rm − Rf)
β
Beta changes on a new project
A riskier project raises β and Ke; a safer one lowers them. Section 06 shows which revaluation route the examiner
expects.
Standard flow — “new project” CAPM questions
1. Existing Ke (DVM or CAPM) and existing MV of equity.
2. New β (given, or as instructed) → new Ke = Rf + (Rm − Rf) × new β.
3. New share price: P0 = D1 ÷ (new Ke − g), using the post-project dividend and growth.
4. New total MV = new P0 × (existing shares + any new shares issued).
5. Change in shareholder wealth = new total MV − old total MV − new money subscribed by shareholders.
QUICK RECALL
· tick when you can say it without looking
☐ Ke = Rf + (Rm − Rf) × β — a given “premium” is used as it stands.
☐ Systematic risk is priced; unsystematic risk is not.
☐ New project → new β → new Ke → revalue the equity.
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WACC — SUMMARY NOTES
Business Insights and Analysis (BIA)
SECTION 04
COST OF DEBT AND PREFERENCE SHARES
THE BIG IDEA
Investors price a bond with gross cash flows. The company’s cost is lower because the interest it pays
is tax-deductible.
The two viewpoints — investor vs company
A bond’s market value is set by INVESTORS, who receive gross interest and require a gross (pre-tax) yield. The
company’s cost of debt is lower because it gets tax relief on the interest it pays. Keep the two apart:
Investor (sets the market value)
Company (cost for WACC)
Cash flows
Gross interest (I) + redemption value
Interest net of tax, I(1 − t) + redemption value
Rate
Gross yield — Kd before tax
Kd after tax — the figure used in WACC
Instrument-by-instrument guide
Instrument
Market value
Cost used in WACC
Tax relief?
Redeemable bonds
PV of gross interest + redemption, at
the investor’s gross yield
IRR of: −MV (yr 0), +I(1 − t) (yrs 1–
n), +RV (yr n)
YES —
interest only
Irredeemable bonds
MV = I ÷ gross Kd
Kd = I(1 − t) ÷ MV
YES
Bank loan
Book value (= MV; not traded)
Interest rate × (1 − t)
YES
Convertible bonds
PV of gross interest + the higher of
cash redemption and conversion
value
IRR of: −MV, +I(1 − t), + higher of
cash / conversion value
Redeemable preference
shares
PV of dividends + redemption, at Kp
Kp = IRR of: −MV, +D, +RV
NO
Irredeemable
preference shares
MV = D ÷ Kp
Kp = D ÷ MV
NO
YES —
interest only
Market values are always ex-interest / ex-dividend. If a price is quoted cum-interest, deduct the interest
about to be paid before using it. If an irredeemable bond’s MV is not given, Kd = coupon rate × (1 − t) — this
assumes it trades at par.
Key debt formulas
IRREDEEMABLE BOND
Kd (post-tax) = I(1 − t) ÷ MVex-int
MV = I ÷ Kdgross
REDEEMABLE BOND
MV = PV of [ I + RV ] at the investor’s gross yield
Kd (post-tax) = IRR of [ −MV, I(1 − t), RV ]
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CONVERTIBLE BOND — REDEMPTION VALUE
RV = higher of: cash redemption OR shares received × expected share price
Expected share price at conversion = P0 × (1 + g)n
BANK LOAN
Kd = interest rate × (1 − t)
TAX RULES — CRITICAL
▪ Interest is tax-deductible for the company, so every interest flow in the company’s Kd calculation is I × (1
− t).
▪ The redemption value is a capital repayment — it is NOT multiplied by (1 − t).
▪ Rates in a question are pre-tax unless the examiner explicitly says they are post-tax.
▪ Preference dividends are paid out of post-tax profit — never apply (1 − t) to Kp.
IRR by interpolation
INTERPOLATION FORMULA
IRR = a + [ A ÷ (A − B) ] × (b − a)
a, b = the two trial rates; A = NPV at rate a (positive); B = NPV at rate b (negative). Because B is negative, (A − B)
is the total gap between the two NPVs.
Mini example — redeemable bond
10% bond, redeemable at par in 4 years, market value Rs 96 ex-interest, tax 30%. Post-tax interest = 10 × 0.7 = Rs
7.
Year
Cash flow
DF 8%
PV 8%
DF 9%
PV 9%
0
(96.00)
1.000
(96.00)
1.000
(96.00)
1–4
7.00
3.312
23.18
3.240
22.68
4
100.00
0.735
73.50
0.708
70.84
NPV
0.68
(2.48)
Kd = 8% + [ 0.68 ÷ (0.68 + 2.48) ] × (9% − 8%) = 8% + 0.22% = 8.22%
✔ Post-tax cost of debt, Kd = 8.22%
QUICK RECALL
· tick when you can say it without looking
☐ Redeemable: Kd = IRR of −MV, I(1 − t), RV.
☐ The redemption value is never multiplied by (1 − t).
☐ Preference dividends get no tax relief: Kp = D ÷ MV.
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WACC — SUMMARY NOTES
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SECTION 05
CUM-DIVIDEND, EX-DIVIDEND AND THE YIELD CURVE
THE BIG IDEA
A price must exclude anything about to be paid out; the yield curve lets each year’s cash flow carry
its own rate.
Cum-dividend vs ex-dividend
When a dividend has been declared but not yet paid, the share price includes the right to receive it — the cumdividend price. When the share goes ex-dividend, the buyer no longer gets that dividend and the price falls by
roughly the dividend amount.
Price
Meaning
What to do
Cum-dividend
Includes the dividend about to be paid
Convert first: P0 (ex-div) = Pcum − D0
Ex-dividend
Excludes that dividend
Use directly as P0 in every Ke formula
KE ALWAYS USES THE EX-DIVIDEND PRICE
Ke = D0(1 + g) ÷ P0 (ex-div) + g
Why ex-div? The DVM values only FUTURE dividends from D1 onwards. A cum-div price also contains D0, which
is about to be paid, so using it overstates the price and understates Ke. The same logic applies to bonds: quoted
cum-interest → deduct the interest due.
The yield curve
The yield curve plots the yield on government (risk-free) bonds against their time to maturity. Each year’s cash
flow can be discounted at its own spot rate rather than one average rate.
FLAT
Yield →
Yield →
INVERTED (DOWNWARD)
Yield →
NORMAL (UPWARD)
Time to maturity →
Time to maturity →
Time to maturity →
Long rates > short rates
Short rates > long rates
Same rate at all maturities
Shape
What it signals
Implication
Normal (upward)
Long rates > short rates — investors want extra return for
lending longer (liquidity preference) and/or expect rates to
rise
Longer-dated debt costs more
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Shape
What it signals
Implication
Inverted (downward)
Short rates > long rates — the market expects rates to fall
Short-term borrowing is currently
dearer
Flat
Similar rates at every maturity
One discount rate is reasonable
THREE RULES OF THE YIELD CURVE
▪ Yields on the curve are GROSS (pre-tax) yields.
▪ The curve is built from RISK-FREE government bonds, not corporate bonds.
▪ To value a corporate bond: discount each cash flow at the matching spot rate PLUS the bond’s credit
spread (if given); the IRR of the resulting price and cash flows is its yield to maturity.
Bootstrapping — building spot rates
1. 1-year bond: price 102, pays 106 at year 1 → 102 = 106 ÷ (1 + s1) → s1 = 3.922%.
2. 2-year bond: discount the year-1 coupon at s1; the only unknown left is s2: Price = C ÷ (1 + s1) + (C + 100) ÷ (1 +
s2)2.
3. Repeat for year 3 using s1 and s2, and so on — each step reuses the rates already found.
QUICK RECALL
· tick when you can say it without looking
☐ Pex = Pcum − D0 (bonds: deduct interest due).
☐ Yield-curve rates are gross and risk-free.
☐ Normal = long rates higher; inverted = market expects rates to fall.
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WACC — SUMMARY NOTES
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SECTION 06
EXAMINER TRAP — POST-PROJECT EQUITY VALUE
THE BIG IDEA
Ask one question first: has the examiner given a post-project dividend? That single answer picks the
route.
READ THIS BEFORE EVERY EXAM
In post-project equity questions ICAP uses two different routes. Sometimes the answer REVALUES the equity
from the post-project dividend (as in IPL and Lahore Quotient); sometimes it only recomputes Ke from the
new beta and adds the new financing to the existing market value. Students who apply the wrong route lose
the marks every time.
The deciding question
Does the question give a POST-PROJECT dividend
(D₀ or D₁) and/or growth rate for the equity?
YES
NO
ROUTE A — FULL REVALUATION
ROUTE B — OLD MV + FINANCING
▸ New Ke from new β (CAPM)
▸ New Ke from new β (CAPM)
▸ New P₀ = D₁ ÷ (Ke − g)
▸ MV(E) = old MV(E) + new equity raised
▸ MV = new P₀ × (old + new shares)
▸ MV(D) = old MV(D) + new debt raised
▸ Gain = new MV − old MV − new money in
▸ Re-weight the WACC table
New shares do not decide the route. A share issue happens in both: in Route A it increases the share count; in
Route B it increases the equity MV by the cash raised. What decides the route is whether you are given postproject dividend information to revalue with.
Decision framework
Route A — full revaluation
Route B — old MV + financing
Use when
The question gives a post-project dividend (D0 or
D1) and/or growth, and asks for a share price,
total value or change in wealth
No post-project dividend is given; the question
needs the revised WACC weights
Ke
New β → new Ke (CAPM)
New β → new Ke (CAPM); new Kd if new debt
Equity MV
New P0 = D1 ÷ (new Ke − g)
MV = new P0 × (old + new shares)
MV(E) = old MV(E) + new equity raised
(+ project NPV only if told the market reflects it)
Output
Change in wealth = new MV − old MV − new
money subscribed
Revised WACC table
Class examples
IPL · Lahore Quotient · Sadagopan · Plasto Plastic
Maqbool · Zaryaab
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WACC — SUMMARY NOTES
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Side-by-side — two Route A class examples
Lahore Quotient (LQ) — D0 given
Plasto Plastic (PPL) — D1 given
Setup
β 1.3 → 1.2; Rf 8%, Rm 12%
D0 = Rs 14, g = 11.868%
1,000,000 shares; old MV Rs 1,168m
Rs 50m raised by new shares at Rs 1,168
β 0.8 → 1.05; Rf 12%, MRP 9%
D1 = Rs 26, g = 5%
15m shares; old MV Rs 2,205m
Rs 600m raised by 5m new shares
Existing Ke
8% + (12% − 8%) × 1.3 = 13.2%
12% + 9% × 0.8 = 19.2%
New Ke
8% + (12% − 8%) × 1.2 = 12.8%
12% + 9% × 1.05 = 21.45%
New P0
14 × 1.11868 ÷ (12.8% − 11.868%)
= Rs 1,680 per share
26 ÷ (21.45% − 5%)
= Rs 158 per share
New total MV
(1,000,000 + 42,808) × 1,680
= Rs 1,752m
(15m + 5m) × 158
= Rs 3,160m
Change in
wealth
1,752 − 1,168 − 50 = Rs 534m
3,160 − 2,205 − 600 = Rs 355m
D₀ OR D₁? — THE SECOND TRAP
▪ LQ gives the dividend just paid (D₀), so it is grown by (1 + g) before dividing. PPL gives next year’s
dividend (D₁), so it is used as it stands.
▪ Read the wording: “has just paid / current dividend” = D₀; “next year’s / expected dividend” = D₁.
QUICK RECALL
· tick when you can say it without looking
☐ Dividend given → Route A: revalue. Not given → Route B: old MV + financing.
☐ Change in wealth = new MV − old MV − new money subscribed.
☐ D0 is grown by (1 + g); a given D1 is not.
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SECTION 07
FULL WACC COMPUTATION
THE BIG IDEA
Four columns — source, MV, cost, MV × cost — and one division. Lay the table out cleanly and the
marks follow.
The WACC table — layout that scores
Source
Market value
Cost
MV × cost
Equity
Shares × ex-div price
Ke (DVM or CAPM)
E × Ke
Preference shares
Number × ex-div price
Kp
P × Kp
Bonds
Nominal × ex-int price ÷ 100
Kd post-tax (IRR)
D × Kd
Bank loan
Book value
Rate × (1 − t)
L × Kd
Total
Σ MV
Σ (MV × cost)
WACC
Σ (MV × cost) ÷ Σ MV
Worked example
DATA
Equity: 10m shares at Rs 50 ex-div; dividend just paid Rs 4; growth 5% a year.
Bonds: Rs 200m nominal, 10% coupon, redeemable at par in 4 years, price Rs 96 ex-interest (Kd = 8.22% —
Section 04).
Bank loan: Rs 100m at 12%. Preference shares: Rs 50m nominal, 10% irredeemable, price Rs 80 per Rs 100.
Tax 30%.
Step 1: Cost of each source
Ke = 4 × 1.05 ÷ 50 + 5% = 8.4% + 5% = 13.4%
Kd (bonds) = 8.22% post-tax (IRR)
Kd (bank) = 12% × (1 − 0.30) = 8.4%
Kp = 10 ÷ 80 = 12.5% (no tax adjustment)
Step 2: Weighted table (Rs m)
Source
MV
Cost
MV × cost
Equity (10m × 50)
500
13.40%
67.00
Bonds (200 × 96%)
192
8.22%
15.78
Bank loan
100
8.40%
8.40
Preference (50 × 80%)
40
12.50%
5.00
Total
832
96.18
WACC = 96.18 ÷ 832 = 11.56%
✔ WACC = 11.56%
WACC
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SUMMARY NOTES
CAF – 07 · Business Insights and Analysis (BIA)
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C O S T
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F I N A N C E
CAF – 07
P A G E
15
WACC — SUMMARY NOTES
Business Insights and Analysis (BIA)
PBIT shortcut — only when its conditions hold
ALTERNATIVE WACC
WACC = PBIT × (1 − t) ÷ (E + D)
This works only when earnings are constant in perpetuity (no growth), all post-tax earnings are paid out as
dividends, debt is irredeemable, and E and D are at MARKET values. Under those conditions E × Ke + D × Kd(1 −
t) = PBIT × (1 − t), so the formula gives the same answer as the full table. Use it when Ke and Kd are not
separately available; never mix it with book values.
Critical exam rules
#
Rule
Common mistake
1
WACC uses MARKET values
Using share capital + reserves (book value) as equity
2
Company’s Kd is post-tax; the investor’s yield is gross
Forgetting (1 − t) on interest — or applying it to the
redemption value
3
Preference dividends get no tax relief
Applying (1 − t) to Kp
4
Bond issued today at par: coupon = market rate, MV = face
value
Trying to discount when MV is simply face value
5
Once market rates move away from the coupon, MV ≠ face
value
Keeping face value as MV after rates change
6
Gordon: use the CURRENT year’s b and r (r on opening
equity)
Averaging historical ROE or payout ratios
7
MRP = (Rm − Rf); if “premium” is given, use it as is
Using Rm as the premium, or deducting Rf twice
8
P0 is always ex-div (bonds ex-interest)
Using a cum-div price in the DVM
9
Count growth years: n = number of dividends − 1
Using the number of years of data as n
10
D0 × (1 + g) = D1; never grow D1 again
Multiplying a given D1 by (1 + g)
11
The DVM requires Ke > g
Accepting a negative or absurd price without
checking
QUICK RECALL
· tick when you can say it without looking
☐ Equity MV = number of shares × ex-div price.
☐ PBIT shortcut only under its no-growth, full-payout conditions.
☐ Sense-check: WACC must sit between the cheapest and the dearest source.
WACC
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SUMMARY NOTES
CAF – 07 · Business Insights and Analysis (BIA)
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01
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WACC — SUMMARY NOTES
CAF – 07
P A G E
16
Business Insights and Analysis (BIA)
SECTION 08
MASTER FORMULA CARD
WACC
KE — CONSTANT DIVIDEND
WACC = Σ (MV × cost) ÷ Σ MV
Ke = D ÷ P0
KE — CONSTANT GROWTH
KE — CAPM
Ke = D0(1 + g) ÷ P0 + g
Ke = Rf + (Rm − Rf) × β
G — HISTORICAL
G — GORDON
Oldest × (1 + g) = Latest
g=b×r
PRICE FROM P/E
EX-DIV PRICE
P0 = EPS × P/E ratio
Pex = Pcum − D0
IRREDEEMABLE BOND
REDEEMABLE BOND
Kd = I(1 − t) ÷ MV
Kd = IRR of [−MV, I(1 − t), RV]
BANK LOAN
IRREDEEMABLE PREFERENCE
Kd = rate × (1 − t)
Kp = D ÷ MV
n
CONVERTIBLE — RV
IRR INTERPOLATION
Higher of cash or shares × P0(1 + g)
a + [A ÷ (A − B)] × (b − a)
TERMINAL VALUE (YR N)
PBIT SHORTCUT
TV = Dn+1 ÷ (Ke − g)
WACC = PBIT(1 − t) ÷ (E + D)
WEALTH CHANGE
FAIR VALUE OF ANY ASSET
New MV − Old MV − new money in
PV of its cash flows @ required return
n
WACC
—
SUMMARY NOTES
CAF – 07 · Business Insights and Analysis (BIA)
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