CFA Level I · CFA Level I Exam

Topics in Long-Term Liabilities and Equity: formula sheet

Full chapter guide

Key formulas

Issue price: Price = Σ [Coupon ÷ (1 + r)^t] + Face value ÷ (1 + r)^n; r is the market rate per period at issuance. Coupon = face value × coupon rate per period.
Interest expense (effective interest method): Interest expense = Opening carrying amount × market rate per period; The market rate is the one set at issuance. It does not change over the life of a fixed-rate bond.
Cash coupon: Coupon paid = Face value × coupon rate per period; Fixed by the contract. It does not depend on the issue price.
Amortization: Discount: amortization = interest expense − coupon. Premium: amortization = coupon − interest expense; Discount amortization increases the carrying amount. Premium amortization decreases it.
Ending carrying amount: Discount: ending = opening + amortization. Premium: ending = opening − amortization; Equivalent: ending = opening + interest expense − coupon paid.
Total interest expense over the life: Total interest expense = total coupons + discount (or − premium); Equivalently: total cash repaid (coupons + face value) − cash received at issuance.
Gain or loss on early extinguishment: Gain (loss) = Carrying amount − Repurchase price; A positive result is a gain. Repurchase price above carrying amount is a loss.
Par, discount, premium rule: Market rate = coupon rate: par. Market rate > coupon rate: discount. Market rate < coupon rate: premium; Compare the rates on the same periodic basis.
Interest expense (effective interest): Interest expense = Opening carrying value × market yield per period; Use the market rate at issuance, not the coupon rate. Halve the annual rate for semiannual bonds.
Coupon paid: Coupon = Face value × coupon rate per period; This is the cash paid. It stays constant.
Discount amortization: Amortization = Interest expense − Coupon paid; Carrying value rises by this amount each period.
Premium amortization: Amortization = Coupon paid − Interest expense; Carrying value falls by this amount each period.
Ending carrying value: Ending = Opening + Interest expense − Coupon paid; Works for both discounts and premiums. It reaches face value at maturity.
Issue price: Price = PV of coupons + PV of face value, discounted at the market yield; Equals the opening carrying value.
Straight-line amortization: Per period = (Face − Issue price) ÷ number of periods, for a discount; (Issue price − Face) ÷ number of periods, for a premium; Interest expense = coupon ± this fixed amount. Expense is constant.
Carrying amount of a bond: Carrying amount = Face value + Unamortized premium (or − Unamortized discount) − Unamortized issuance costs (IFRS); Under the effective interest method, it equals the present value of the remaining cash flows discounted at the effective rate set at issue. Under IFRS, unamortized issuance costs reduce the carrying amount.
Gain or loss on extinguishment: Gain (loss) = Carrying amount − Cash paid to retire (including any call premium); Positive means gain. Negative means loss. The carrying amount is net of unamortized issuance costs under IFRS, so those costs are included in the gain or loss.
Partial retirement: Carrying amount retired = Total carrying amount × (Face value retired ÷ Total face value); Use when only part of an issue is bought back.
Cash flow treatment: CFF outflow = cash paid; CFO adjustment = − gain (or + loss); Indirect method only. The gain or loss is non-cash in the CFO reconciliation.
Fair value option (IFRS): Change in fair value from own credit risk → OCI; remainder → profit or loss; Designation is irrevocable and made at initial recognition. If OCI treatment would create or enlarge an accounting mismatch in profit or loss, the whole change goes to profit or loss.
Lease liability at inception: Lease liability = PV of remaining lease payments, discounted at the rate implicit in the lease or the lessee's incremental borrowing rate; Use annuity due if payments are at the start of each period.
Right-of-use asset at inception: ROU asset = Lease liability + initial direct costs + prepaid lease payments − lease incentives; With no extra costs, ROU asset = lease liability.
Interest expense each period: Interest = Opening lease liability × discount rate; Applies to IFRS lessees and US GAAP finance leases.
Closing lease liability: Closing liability = Opening liability + Interest − Payment; Payment minus interest is the principal repaid.
Depreciation of ROU asset: Depreciation = (ROU asset − residual value) ÷ shorter of lease term and useful life; If ownership transfers or a purchase option is reasonably certain, use useful life.
US GAAP operating lease expense: Single lease cost = total lease payments ÷ lease term (straight-line); Presented as one operating expense; all cash in CFO.
Lessor classification (IFRS): Finance lease if substantially all risks and rewards transfer; otherwise operating; Lessor accounting is largely unchanged from before.
Funded status: Funded status = Fair value of plan assets − PBO; Negative means a net pension liability. Positive means a net asset, subject to the asset ceiling under IFRS.
Ending PBO: Ending PBO = Beginning PBO + Current service cost + Interest cost + Past service cost + Actuarial losses (− gains) − Benefits paid; Interest cost = discount rate × beginning PBO.
Ending plan assets: Ending assets = Beginning assets + Actual return + Employer contributions − Benefits paid; Employee contributions, if any, are also added.
IFRS pension cost in profit or loss: Service cost (current + past) + Net interest expense; Net interest = discount rate × beginning net pension liability (or minus the same for a net asset).
IFRS remeasurements (OCI): Actuarial gains/losses + (Actual return on assets − Discount rate × beginning plan assets); Stays in OCI and is not recycled to profit or loss.
US GAAP periodic pension cost: Service cost + Interest cost − Expected return on plan assets + Amortization of prior service cost + Amortization of actuarial losses (− gains); Expected return = expected rate × beginning plan assets. Actual-minus-expected return goes to OCI first.
DC plan expense: Expense = Employer contribution for the period; No PBO or plan assets on the employer's books.
Total compensation cost (equity-settled): Total cost = Grant-date fair value per award × Number of awards expected to vest; Fair value is fixed at grant date. Only the expected number of awards is updated.
Annual expense, straight-line: Annual expense = Total cost ÷ Vesting period in years; Used for cliff vesting when no other pattern is given.
Restricted stock fair value: Fair value per share = Market price of the share at grant date; No pricing model is needed.
Cumulative catch-up: Expense this year = Cumulative cost to date (revised estimate) − Expense already recognised; Use when the expected number vesting changes.
Journal entry each period: Dr Compensation expense; Cr Paid-in capital (equity); Net income falls, paid-in capital rises, total equity unchanged. Cash flow: add back as a non-cash item.
Option exercise (cash received): Dr Cash (exercise price × options); Dr Paid-in capital (previously recorded); Cr Share capital and share premium; Equity increases by the cash received. The previously recorded paid-in capital is transferred within equity to share capital and share premium.

Quick revision

Bond issued at a discount means the market rate is above the coupon rate; at a premium means the market rate is below it.
Interest expense = opening carrying amount × effective interest rate set at issue. The effective rate equals the market rate at issue when there are no issuance costs and is higher than the market rate once costs are included. It is not the coupon rate.
Cash coupon = face value × coupon rate, and it does not change under the effective interest method.
A discount amortizes upward toward face value; a premium amortizes downward toward face value.
Debt issuance costs under IFRS reduce the initial carrying amount and raise the effective rate.
On early redemption, gain or loss = carrying amount minus the amount paid to redeem.
Covenants restrict actions or require ratios; a breach can make debt payable on demand.
Under IFRS a lessee records a right-of-use asset and a lease liability for most leases.
A lessor classifies a lease as finance or operating based on whether risks and rewards of ownership transfer.
Defined benefit plan: funded status = fair value of plan assets minus the benefit obligation.
Share-based pay is expensed over the vesting period at grant-date fair value.
Higher leases and pension deficits raise adjusted debt, so solvency ratios look weaker.

Common mistakes

Calculating interest expense as face value × market rate. Fix: Interest expense uses the opening carrying amount. Coupon uses face value. Keep the two bases separate.
Using the coupon rate to discount the cash flows. Fix: Always discount at the market rate at issuance. Discounting at the coupon rate always gives par.
Using the coupon rate to compute interest expense. Fix: Coupon rate gives only the cash paid. Interest expense always uses the market yield at issuance applied to the carrying value.
Multiplying the yield by face value instead of carrying value. Fix: Coupon = face × coupon rate. Expense = carrying value × market yield. Write both lines every time.
Using face value instead of carrying amount to compute the gain or loss Fix: Always adjust face value for unamortized premium or discount at the repurchase date.
Reversing the sign of the gain or loss Fix: Paying more than carrying amount is a loss. Paying less is a gain.
Saying US GAAP operating leases stay off the balance sheet. Fix: Under ASC 842 operating leases create an ROU asset and a lease liability. Only the income statement and cash flow pattern differ.
Using straight-line expense for an IFRS lessee. Fix: IFRS 16 always uses depreciation plus interest for lessees, so expense is front-loaded.
Using the expected or actual return on assets to compute IFRS pension expense. Fix: Under IFRS, assets earn the discount rate in net interest. The gap between actual return and that interest goes to OCI.
Putting IFRS remeasurements through profit or loss later. Fix: Under IFRS, remeasurements stay in OCI and are never reclassified to profit or loss. They may be transferred within equity.

Exam tips

Do the direction check first. Many questions can be answered by noting that a discount bond has interest expense above the coupon, and a premium bond below it.
Watch the base. Questions often put face value and carrying amount side by side to tempt you into the wrong base.
Read the periods carefully. A semiannual bond needs half the rate and double the periods, and each coupon is half the annual coupon.
Expect conceptual items too. Typical points: discount carrying amount rises, premium carrying amount falls, principal repayment is financing, and total interest expense equals total cash repaid minus cash received.
Remember that IFRS requires amortized cost with the effective interest method for most issued bonds. Items state US GAAP when it matters.
Most questions ask for one period's expense or carrying value. Do one multiplication and one subtraction, not the whole schedule.
Read the stem for the yield used at issuance. Distractors often come from using the coupon rate or the face value as the base.
Know the direction rules cold: discount means rising expense and carrying value, premium means falling. This answers many conceptual questions with no calculation.