WACC, NPV, IRR, Cost of Equity & Capital Structure Formulas
1. Cost of Equity (Dividend Growth Model)
Use when given the last dividend, growth rate, and price
Steps
Find next year’s dividend
Next dividend = Last dividend × (1 + growth rate)
Cost of equity = (Next dividend ÷ Stock price) + Growth rate
Excel
=(D0*(1+g)/Price) + g
2. Cost of Debt (Yield to Maturity)
Your system almost always uses annual coupons, even if the bond states semiannual.
Steps
Coupon payment = Coupon rate × Par value.
Discount each payment using a trial interest rate until the present value equals the price.
After-tax cost of debt = Yield × (1 − Tax rate).
Excel (fast)
=RATE(NumberOfYears, CouponPayment, -Price, ParValue)
3. Capital Structure Weights
These weights show how much of the company is financed by debt versus equity.
A. Market values (Salmon questions)
Use market value when stock price and bond price are given.
Market value of equity = Shares × Stock price
Market value of debt = Number of bonds × Bond price
Total value = Equity value + Debt value
Weight of equity = Equity value ÷ Total value
Weight of debt = Debt value ÷ Total value
4. WACC (Weighted Average Cost of Capital)
Formula in plain English
WACC = (Weight of equity × Cost of equity) + (Weight of debt × After-tax cost of debt)
Excel
=EquityWeight * EquityCost + DebtWeight * AfterTaxDebtCost
5. All-Debt WACC (Grey’s Pharmaceuticals)
Used when all financing is borrowed from lenders.
Steps
For each lender:
Weight = Loan amount ÷ Total loans
Contribution = Weight × Interest rateWACC = Sum of all contributions.
6. NPV (Net Present Value)
Formula in plain English
NPV = −Initial cost + Present value of all inflows
Present value = Cash flow ÷ (1 + discount rate)^(year)
Decision rule
NPV positive → Accept
NPV negative → Reject
Excel
=NPV(rate, CF1:CFn) + InitialCost
7. IRR (Internal Rate of Return)
IRR is the interest rate that makes NPV equal zero.
Excel
=IRR(range_of_all_cash_flows)
8. IRR Quick Rules
These solve many multiple-choice questions instantly:
If NPV at a discount rate is:
Positive → IRR is higher than that rate
Negative → IRR is lower than that rate
Zero → IRR equals that rate
9. IRR for a Single Inflow (like Dice, Inc.)
If the project has:
Only one inflow
Only one initial cost
Formula in plain English
Future value ÷ Initial cost
Raise that answer to the power of (1 ÷ number of years)
Subtract 1
Excel
=(FutureValue / InitialCost)^(1/Years) - 1
Universal Excel Template (No Abbreviations)
Cost of equity:=(D0*(1+g)/Price)+g
After-tax cost of debt:=YTM*(1-TaxRate)
Equity market value:=Shares*StockPrice
Debt market value:=Bonds*BondPrice
Weight of equity:=EquityMV/(EquityMV+DebtMV)
Weight of debt:=DebtMV/(EquityMV+DebtMV)
WACC:=EquityWeight*EquityCost + DebtWeight*AfterTaxDebtCost
NPV:=NPV(rate, CF1:CFn) + InitialCost
IRR:=IRR(range)
Single-flow IRR:=(FV/InitialCost)^(1/n)-1
NPV:
Formula: =NPV(rate, CF1:CFn) + CF0
Decision: NPV > 0 → ACCEPT, NPV < 0 → REJECT
Y-Intercept: NPV at 0 percent
IRR:
Formula: =IRR(CF_range)
Decision: IRR > cost of capital → ACCEPT, otherwise → REJECT
IF Function:=IF(value > 0, "ACCEPT", "REJECT")
Straight-Line Depreciation:
Annual Dep = (Cost + Install − Salvage) / Life
Accum Dep = AnnualDep * YearsUsed
Book Value = Cost + Install − AccDep
After-Tax Salvage CF = Sale − Tax * (Sale − BookValue)
WACC:=(Equity/(Equity+Debt))*Re + (Debt/(Equity+Debt))*Rd*(1 - Tax)
Weighted Borrowing Cost:
Before-Tax = (LoanA/Total)*RateA + (LoanB/Total)*RateB
After-Tax = BeforeTax*(1 – Tax)
CAPM (Cost of Equity):
If market return given: Re = Rf + Beta*(MarketReturn – Rf)
If MRP given: Re = Rf + Beta*MRP
Cost of Debt (Yield to Maturity):=RATE(Years, Par*Coupon, -Price, Par)
After-tax Rd = Rd*(1 – Tax)
EPS (Leverage Analysis):
Unlevered EPS = EBIT / UnleveredShares
Levered EPS = (EBIT − Interest) / LeveredShares
Break-even EBIT: where Unlevered EPS = Levered EPS
Leverage Rules:
EBIT > Break-even → MORE debt helps
EBIT < Break-even → LESS debt helps
Quick Rules:
Price < Par → YTM > Coupon
MRP = MarketReturn − Rf
Depreciation reduces book value evenly
IRR and NPV always agree for normal cash flows
Use after-tax Rd in WACC
Important Practice Values:
NPVs: 150, 81.15, 22.92, -26.75
IRR: 12.21%
EPS: BE=0.40, at 1.8M: 0.45/0.50, at 1.4M: 0.35/0.30
WACC example: 9.97%
CAPM examples: 5.88%, 11%
After-tax Rd: 5.13%
1. Capital Structure Basics
• Capital structure is the mix of debt and equity a firm uses.
• Optimal capital structure is the mix that gives the lowest WACC and highest firm value.
• Debt is cheaper than equity but increases financial risk when too high.
2. WACC
WACC = (Equity ÷ Value × Re) + (Debt ÷ Value × Rd)
• Adding low-cost debt reduces WACC.
• After the optimal point, extra debt raises WACC.
• A rising WACC reduces the value of future cash flows.
3. Leverage
Financial leverage
Using borrowed money to magnify equity returns.
Works only when: Return on assets > Cost of debt.
Operating leverage
Sensitivity of EBIT to sales due to fixed operating costs.
4. EPS and Debt
EPS = (EBIT − Interest) ÷ Shares
• If earnings return > interest → debt increases EPS.
• If earnings return < interest → debt decreases EPS.
• Compare EPS before and after debt to measure leverage benefit.
5. MM Theory (No Taxes)
• Firm value is irrelevant to capital structure.
• As debt rises, equity becomes riskier and Re increases.
• WACC stays the same in a no-tax world.
6. IRR Trial and Error
• IRR is the discount rate that makes NPV = 0.
• PV inflows < project cost → IRR is higher than tested rate.
• PV inflows > project cost → IRR is lower than tested rate.
7. Excel Essentials
PV = =PV(rate, nper, 0, FV)
IRR = =IRR(values)
NPV = =NPV(rate, cashflows) + InitialCost
EPS = =(EBIT - interest) / shares
8. Exam Logic
• Optimal structure = lowest WACC.
• More debt helps owners only when return > cost of debt.
• Rising WACC lowers firm value.
• Financial leverage always refers to borrowed money to increase equity earnings.
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