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ACCT2511-无代写
时间：2023-05-02
Topic 4
Liabilities
UNSW Business School
School of Accounting, Auditing & Taxation
ACCT2511
Financial Accounting
Fundamentals
Lecture learning objectives
1. Know and be able to apply the definition and recognition
criteria of liabilities
2. Be able to account for current liabilities
3. Be able to account for non-current liabilities: borrowings
and bonds
4. Understand the difference between provisions and
contingent liabilities.
What part of a Company Annual Report are we looking at today?
•
•
Liabilities: Definition
• “A liability is a present obligation of the entity arising from
past events, the settlement of which is expected to result
in an outflow from the entity of resources embodying
economic benefits” (AASB Framework, paragraph 49)
• Essential characteristics:
– The existence of a present obligation arising from a
past event
– results in an outflow of economic benefits
4
LO 1
More on Definition criteria (1): Present obligation
• An obligation is a duty or responsibility to act or perform in
a certain way.
• Legally enforceable obligations: consequence of a
binding contract or statutory requirement.
– e.g. amounts payable for goods and services received
• Constructive obligations: arising from normal business
practice, custom and/or a desire to maintain good
business relations or act in an equitable manner.
– e.g. a policy to rectify product defects even after the
warranty period has expired.
5
Past Events
Liabilities result from past transactions or other past events.
• Somewhat redundant because in order to have a present
obligation there would need to be a past obligating
event. For example:
• Acquisition of goods => Accounts payable
• Sales => warranty
• Receipt of a bank loan => borrowings
•You can think of present obligation and past event as one
characteristic: Present obligation (because that must arise
from a past obligating event)
Outflow of economic benefits
Settlement of a present obligation usually involves the
entity giving up resources embodying economic benefits.
For example:
– transfer of other assets
– payment of cash
– provision of services
– replacement of that obligation with another obligation
– conversion of the obligation to equity.
Recall from last week:
Reporting Assets & Liabilities
• Not all assets & liabilities are on the balance sheet
• Assets and liabilities have to:
(1) Meet essential definition criteria (from previous two slides)
And THEN
(2) Meet recognition criteria (defined on the next slide)
To be recognised (reported) on the Balance Sheet.
If they meet (1) but not (2), they are disclosed in the notes
Recognition of Liabilities
Recognition is the process of incorporating assets and
liabilities that meet the definitions into the Balance Sheet.
An item that meets the definition of a liability
should be recognised if:
a) It is probable that any future economic benefit
associated with the item will flow from the entity;
and
b) The item has a cost or value that can be measured with
reliability.
AASB Framework, Paragraph 83
a)Probability of outflow of Future Economic Benefit
• Probable if the event is more likely than not to occur
• Where there are a number of similar obligations, need to
consider the class of obligations as a whole.
• E.g., Smoove Ltd sold 50,000 blenders in 2022
– Each blender comes with a 1 year warranty
– In previous years 2% of customers made warranty claims
– If considering each single blender by itself: no provision
for the warranty could be recognised (2% chance of
outflow of FEB is not probable)
– However, if considering all of the blenders together (as a
class of obligations): a provision can be recognised as it
is now probable that at least some of blenders will result in
a warranty claim
b) Reliable measurement
• The cost or value of the liability needs to be measured
with reliability
• The use of estimates does not undermine reliability.
• A range of possible outcomes is enough to make an
estimate that is sufficiently reliable to use.
Decision path for liability recognition
Does the item have all two essential
characteristics of a liability?
Does the liability meet
both the recognition
criteria?
Does not appear in
the balance sheet but
may appear in a note
Liability recognised in
the entity’s balance
sheet
Separately disclosed
in the notes
No
NoYes
Yes
Current vs. Non-Current Liabilities
A liability shall be classified as current when it satisfies any
of the following criteria (AASB101, para 60):
– It is expected to be settled in the entity’s normal
operating cycle.
– It is due to be settled within twelve months after the
reporting date.
All other liabilities shall be classified as non-current.
13
LO 2
An aside: Working Capital
• WC ($) = Current Assets - Current Liabilities
Low or negative working capital can be an indication of
short-term financial difficulties.
• Current ratio = Current Assets/Current Liabilities
This gives an indication of the magnitude of working
capital (rather than a $ value).
Current Liabilities
• Usually recorded at full maturity value
• Due to the short time frame involved
• Difference between maturity value and present value
is usually small and immaterial.
E.g.,
• Accruals for goods/services received but not paid for/earned such as
accounts payable, notes payable, accrued expenses, unearned
revenue
• Interest bearing liabilities that are due within 12 months
• Formal debt instrument to pay specified amount at specified time
• Tax liabilities
• Dividends Payable
• Provisions….
15
An aside about terminology
• Classify the following accounts as Asset, Liability,
Revenue or Expense:
– Rent Payable
– Rent Receivable
– Rent Revenue
– Rent Expense
– Accrued Rent Revenue
– Unearned Rent Revenue
– Accrued Rent Expense
– Prepaid Rent Expense
Notes Payable
• May be interest bearing or non-interest bearing.
• For interest bearing notes, the accounting treatment is
straight forward.
• Non-interest bearing notes will be covered in advanced courses
• E.g., on 30 June 2022, Apple Pie Ltd. signed a three-month
10 per cent annum note payable to purchase a new truck
costing $40,000. Interest and principal are paid at maturity.
What is the journal entry on June 30 2022?
17
Dr Motor Vehicle 40,000
Cr Note Payable 40,000
Current Maturities of Long Term Debt
• The portion of long term debt maturing within the next 12
months is reported as a current liability.
• E.g., At financial year end Banana Bread Ltd is holding a
mortgage of $850 000 that requires payments of $10 000
each month. Next year the interest component of the
payments will equal $70 000.
• What is the current liability that would be reported?
• (10 000 x 12) – 70 000 = $50 000
• What is the non-current liability that would be reported?
• 850 000 – 50 000 = $800 000
• What is the interest expense for next year?
• $70 000
18
Non-Current Liabilities
• Obligations that are not expected to be paid within the next
12 months / operating cycle
• Arising from specific financing situations
• E.g., borrowings, bonds
• Arising from ordinary business operations
• E.g., superannuation and other obligations to
employees, deferred income tax obligations, provisions
19
LO 3
Long Term Debt: Accounting for Borrowings
Recognising borrowing:
Dr Cash XXX
Cr Borrowings XXX
Recognition and payment of Interest:
Dr Interest Expense XXX
Cr Interest Payable XXX
Dr Interest Payable XXX
Cr Cash XXX
Repayment of principal:
Dr Borrowings XXX
Cr Cash XXX
20
Recall Banana Bread Ltd
Banana Bread Ltd is holding a mortgage of $850 000 that
requires payments of $10 000 each month. Next year the
interest component of the payments will equal $70 000.
(1) Write a summary transaction to record the interest
payments for the year (assume interest is paid as incurred)
Dr interest expense 70 000
Cr Cash 70 000
(2) Write a summary transaction to record the principal
repayments for the year
Dr Borrowings/mortgage 50 000
Cr Cash 50 000
21
Accounting for Bonds
• Bonds are issued by companies, and are a promise to
pay interest and return the investor's capital on a
specified date (“maturity” date).
• i.e., A bond is a promise to pay something in the
future in exchange for receiving something today.
• The seller/issuer of a bond is a borrower
• The buyer of a bond is a lender
• Why issue bonds instead of borrowing from a bank?
• Borrowing directly from a bank can be more restrictive
and expensive
• Access to more lenders
Some more terminology relating to Bonds
• The amount to be repaid to the bond buyer (lender) at
maturity is known as the face value
• The explicit interest rate being offered by the bond seller
(borrower) is known as the coupon rate
• E.g., Bircher Ltd issues 100 bonds with a face value of
$1 000, with the principal to be paid at maturity in 2 years.
The coupon rate is 5% per annum and paid annually.
• Bircher Ltd is the borrower. The people buying the bonds from
Bircher are the lenders.
• Bircher will pay out $5 000 ($1 000 x 0.05 x 100) in coupon
payments each year, for two years
• At the end of two years, Bircher will also pay $100 000
($1 000 x 100) to the lenders to clear its debt.
Bircher
Seller/Borrower
Muesli
Buyer/Lender
2-year Bond with
FV = $1000, coupon 5%
Cash
At issue date
Year 1
Bircher
Seller/Borrower
Muesli
Buyer/Lender
$50 cash
coupon payment
Year 2 (at maturity)
Bircher
Seller/Borrower
Muesli
Buyer/Lender
$1050 cash
($50 coupon payment
+ $1000 FV)
Coupon rate vs Market rate
• Recall: the explicit interest rate being offered by the
bond seller (borrower) is known as the coupon rate
• Today we will call the rate that the market requires to
lend to this borrower the market rate
• Differences in the coupon rate and the market rate will
impact how the bond is valued/priced at the time of issue
• (1) Coupon rate = market rate – issued at face value
• (2) Coupon rate < market rate – issued at discount
• (3) Coupon rate > market rate – issued at premium
(1) Coupon rate = Market rate (bonds at face value)
• If the coupon rate and the market rate are equal, bonds
are said to be issued at their face value
• i.e., the amount received by the borrower at the time of
issue is the same as the face value that will be paid to
the lender at maturity
• Recall: Bircher issues 100 bonds with $1 000 face value,
with the principal to be paid at maturity in 2 years. The
coupon rate is 5% per annum and paid annually.
• Imagine the market rate is also 5%
The journal entry to recognise the issue:
• Dr Cash 100 000
Cr Bonds Payable 100 000
Recall: Bircher issues 100 bonds with $1 000 face value,
maturity in 2 years, coupon rate is 5% p.a. and paid annually,
market rate is also 5%
• End of year 1: Recognise the coupon payment
Dr Interest Expense 5 000
Cr Cash 5 000
• Note: coupon payment equals recorded interest expense
• End of year 2: Repay the principal and recognise the
2nd coupon payment:
Dr Interest Expense 5,000
Dr Bonds payable 100,000
Cr Cash 105,000
Journal entry is almost the same as when you have a loan!
(2) Coupon rate < Market rate (bonds at discount)
• If the coupon rate is lower than the market rate, the
bonds are issued at a discount
• This is because the present value of the bond is less
than the face value of the bond
• Bonds discount = the difference between the face value
and market value. It is a contra-liability account. Journal
entry when bonds are issued:
Dr Cash
Dr Bonds Discount
Cr Bonds Payable
(2) Coupon rate < Market rate (bonds at discount)
• Recall: Bircher issues 100 bonds with $1 000 face value, with
the principal to be paid at maturity in 2 years. The coupon rate
is 5% per annum and paid annually.
• Imagine the market rate is 7%
• What does this mean for bond valuation by the market?
For each bond: Present value = $963.84
=
(+.)
+
(+.)
+
+.
This means that Bircher will only receive $96 383.96 for 100
bonds, even though it will have to pay back the face value of
$100 000 at maturity
You will find a simple explanation regarding present value at
the very end of these lecture slides
(2) Coupon rate < Market rate (bonds at discount)
The journal entry to recognise the issue is:
Dr Cash 96 383.96 (2) next!
Dr Bonds Discount 3 616.03 (3) last step
Cr Bonds Payable 100 000 (1) start here!
The discount represents implicit additional interest of
$36.16 per bond. The journal entry above is recording all
of this interest at the time of issue, even though the debt
will not be paid for two years.
We will need to amortise this discount amount.
Bonds Discount
3616.03
T account representation
Bonds Payable
100 000
Balance sheet presentation at issuance:
Long-term liabilities
Bonds Payable 100 000
Less Bonds Discount 3 616
Carrying value 96 384
We need to amortise this
over the life of the bonds
Amortising the
discount will
eventually bring CV
to $100 000
Face Value
Bonds Discount
Issuance date
t= 0
Maturity date
t = 2
Carrying Value
$96 384
100,000
t=1
Bonds Discount of $3 616 is implicit additional interest to be
amortised over 2 years to bring carrying amount in line with face
value at maturity
Diagramatically
Bonds discount is amortised using effective interest method:
interest exp = market rate x carrying value
100,000
$3 616
Carrying Value at t =0
Bonds at discount – what happens after 1 year?
• At the end of year 1, three things have to happen:
• 1. Bircher has to pay the coupon for the first year
• ($1 000 x 0.05) x 100 bonds = $5 000
• This is the same every year!
• 2. Bircher has to amortise this bond discount using the
“effective interest method”
• The amortisation amount in each period will be added to
the interest expense recorded for that period
• 3. Bircher has to record the actual interest expense
• Interest exp = market rate x bonds’ carrying value
Journal entry at t = 1
• Dr Interest Expense
• Cr Bonds Discount
• Cr Cash
• Step 1: Calculate the coupon payment. It doesn’t change!
• Coupon payment = coupon rate x face value
• Steps 2 & 3: record actual interest expense & amortise discount
• Interest expense = market rate x bonds’ carrying value
• The bond discount amortisation is the difference between
the interest expense and the coupon payment
• = 6 746.88 – 5 000 = $1 746.88
5 000 (1)
6 746.88 (2)
1 746.88 (3)
Coupon payment = 0.05 x 100 000
Interest exp = 0.07 x 96 383.96
We will now have a new carrying value!
• Dr Interest Expense
• Cr Bonds Discount
• Cr Cash
Bonds Discount
3616.03
Bonds Payable
100 000
5 000
6 746.88
1 746.88
1 746.88
Balance sheet presentation
Long-term Liabilities t= 0 t=1
Bonds Payable 100 000 100 000
Less Bonds Discount 3 616 1 869
Carrying value 96 384 98 131
1 869.16
Face Value
Bonds Discount
Issuance date
t= 0
Maturity date
t = 2
Carrying Value at t =1$96 384
100,000
t=1
Diagramatically
100,000
$3616
$1869
$98 131
Carrying Value at t =0
Journal entry at t = 2 (maturity) – Part 1
• Dr Interest Expense
• Cr Bonds Discount
• Cr Cash
• Part 1: Record interest expense
• = market rate x bonds’ carrying value
• 0.07 x $98 130.84 = $6 869.16 (rounded)
• Discount amortisation = $1869.16
• As expected – brings account to 0
5 000 (1)
6 869.16 (2)
1 869.16 (3)
Bonds Discount
1 869.16 1 869.16
0
Journal entry at t = 2 (maturity) – Part 2
• Repay the principal! (Face value)
• = 100 bonds with face value of $ 1000 = $100 000
• Dr Bonds Payable
Cr Cash
100 000
Bonds Discount
1 869.16
0
1 869.16 (pt. 1)
100 000
Bonds Payable
100 000(pt. 2) 100 000
0
Our discount example - summary
• Bircher issued 100 bonds with $1 000 face value ($100 000),
with the principal to be paid at maturity in 2 years.
• Coupon rate was 5% per annum and paid annually ($5 000)
• BUT the market rate was 7%
• What did this mean for bond valuation by the market?
Each bond was valued at $963.84 (rounded)
• So Bircher issued the bonds at a discount - it only received
$96 383.96, even though it would have to pay back the face
value of $100 000 at maturity
• It paid explicit annual interest of $5 000 (coupon), plus implicit
interest in the form of the Bonds Discount of $3 616.04
• The Bonds Discount needed to be amortised to zero.
Bonds issued at Discount – Summary of entries
• When the bonds were issued (t=0):
Dr Cash 96 383.96
Dr Bonds Discount 3 616.04
Cr Bonds Payable 100,000.00
• Interest Expense (t=1):
Dr Interest Expense 6 746.88
Cr Bonds Discount 1 746.88
Cr Cash 5 000
• Interest Expense and Repayment of Principal (t=2):
Dr Interest Expense 6 869.16
Cr Bonds Discount 1 869.16
Cr Cash 5 000
Dr Bonds Payable 100,000
Cr Cash 100,000
Remember: Coupon rate vs Market rate
• Recall: the explicit interest rate being offered by the
bond seller (borrower) is known as the coupon rate
• Today we will call the rate that the market requires to
lend to this borrower the market rate
• Differences in the coupon rate and the market rate will
impact how the bond is valued/priced at the time of issue
• (1) Coupon rate = market rate – issued at face value
• (2) Coupon rate < market rate – issued at discount
• (3) Coupon rate > market rate – issued at premium
(3) Coupon rate > Market rate (bonds at premium)
• If the coupon rate is higher than the market rate, the
bonds are issued at a premium
• PV of the bond is higher than the Face V of the bond
• i.e., the issuing company receives a larger amount
than the face value (amount that will be paid to the
lender at maturity)
• Bond premium = the difference between the face value
and market value. It is an adjunct liability account.
Journal entry when bonds are issued:
Dr Cash
Cr Bonds Premium
Cr Bonds payable
(3) Coupon rate > Market rate (bonds at premium)
• Recall: Bircher issues 100 bonds with $1 000 face value, with
the principal to be paid at maturity in 2 years. The coupon rate
is 5% per annum and paid annually.
• Imagine the market rate is 3%
• What does this mean for bond valuation by the market?
For each bond: Present value = $1 038.27
=
(+.)
+
(+.)
+
+.
This means that Bircher will receive $103 826.90 for 100
bonds, even though it will only have to pay back the face
value of $100 000 at maturity
(3) Coupon rate > Market rate (bonds at premium)
The journal entry to recognise the issue is:
Dr Cash 103 826.90 (2) next!
Cr Bonds Premium 3 826.9 (3) last step
Cr Bonds Payable 100 000 (1) start here!
The premium represents implicit reduction in the interest
paid over the life of the bond. The journal entry above is
recording all of this benefit at t =0.
We will need to amortise this premium.
Bonds Premium
3 826.90
T account representation
Bonds Payable
100 000
Balance sheet presentation at issuance:
Long-term Liabilities
Bonds Payable 100 000.00
Add Bonds Premium 3 826.90
Carrying value 103 826.90
We need to amortise this
over the life of the bonds
Amortising the
discount will
eventually bring CV
to $100 000
Face Value
Bonds Premium
Issuance date t= 0 Maturity date t = 2
Carrying Value
$103 827
100,000
t=1
Bonds Premium of $3 827 is an implicit reduction in interest.
Amortised over 2 yrs to bring carrying amount in line with face
value at maturity
Diagramatically
Bonds premium is amortised using effective interest method:
interest exp = market rate x carrying value
100,000
$3 827
Carrying Value at t =0
Bonds at premium – what happens after 1 year?
• At the end of year 1, three things have to happen:
• 1. Bircher has to pay the coupon for the first year
• ($1 000 x 0.05) x 100 bonds = $5 000
• This is the same every year!
• 2. Bircher has to amortise this bond premium using the
“effective interest method”
• The amortisation amount in each period will be subtracted
from the interest expense recorded for that period
• 3. Bircher has to record the actual interest expense
• Interest expense = mkt rate x bonds’ carrying value
Journal entry at t = 1
• Dr Interest expense
• Dr Bonds Premium
• Cr Cash
• Step 1: calculate the coupon payment.
• Steps 2 & 3: record actual interest expense & amortise discount
• Interest expense = market rate x bonds’ carrying value
• The bond premium amortisation is the difference between
the coupon payment and the interest expense
• = 5 000 - 3 114.81 = $1 885.19
5 000 (1)
3114.81 (2)
1 885.19 (3)
Coupon payment = 0.05 x 100 000
Interest exp = 0.03 x 103 826.90
We will now have a new carrying value!
• Dr Interest expense
• Dr Bonds Premium
• Cr Cash
Bonds Premium
1 885.19
Bonds Payable
100 000 3 826.94
Balance sheet presentation
Long-term liabilities t= 0 t=1
Bonds Payable 100 000 100 000
Add Bonds Premium 3 827 1 942
Carrying value 103 827 101 942
1 941.75
5 000
3114.81
1 885.19
Face Value
Bonds Premium
Issuance date t= 0 Maturity date t = 2
Carrying Value
$103 827
100,000
t=1
Diagramatically
100,000
$3 827
Carrying Value at t =0
$101 942
Carrying Value at t =1
Journal entry at t = 2 (maturity) – Part 1
• Dr Interest expense
• Dr Bonds Premium
• Cr Cash
• Part 1: Record interest expense
• = market rate x bonds’ carrying value
• 0.03 x $101 941.70= $3 058.25 (rounded)
• Premium amortisation = $1 941.75
• As expected – brings account to 0
5 000 (1)
3 058.25 (2)
1 941.75 (3)
Bonds Premium
1 941.751 941.75
0
Journal entry at t = 2 (maturity) – Part 2
• Repay the principal! (Face value)
• = 100 bonds with face value of $ 1000 = $100 000
• Dr Bonds Payable
Cr Cash
100 000
100 000
Bonds payable
100 000(pt. 2) 100 000
0
Bonds Premium
1 941.75(pt. 1) 1 941.75
0
Uncertainty: Provisions and contingent liabilities
• Provisions are uncertain in timing or amount
• Provisions are recognised on balance sheet
In comparison …
• ‘Contingent’ liabilities:
1) A possible obligation arising from past events but whose
existence depends on uncertain future events not wholly
within the control of the entity or
2) A present obligation that does not meet recognition
criteria (not probable and/or can’t be reliably measured)
Contingent liabilities are not recognised on balance sheet,
but are disclosed in the notes
53
LO 4
Provisions: May be Current or Non-current
• Some liabilities can be measured only by using a
substantial degree of estimation due to uncertainty.
• Provisions are estimates due to uncertainty in:
– Timing and/or
– Amount
• May arise from either a legal or constructive obligation e.g.,
• Warranties
• Amount uncertain, timing is uncertain
• Employee benefits (e.g., annual leave, bonuses).
• Timing is uncertain as don’t know when leave will be
claimed. Amount and timing may be uncertain in the
case of bonuses.
54
Provisions are recognised on the balance sheet
• Provisions are reported separately from payables and
accruals on the balance sheet.
– Remember, if there is no present obligation, then no
provision!
– e.g., no provision for (future) maintenance.
• Journal entries when creating a provision (normally):
Dr …. Expense
Cr Provision for…
• Journal entries when actual claims are made (and
redeemed):
Dr Provision for…
Cr Cash
55
Example: Warranty Plan
Oat Cookie Ltd. has a warranty plan set up. Normally
warranty costs amount to 10% of COGS (Customers receive
refunds). This year, COGS was $10,000. Required:
(i) Prepare journal entries for the warranty plan this year.
(ii) The actual warranty claim amount paid out was $1100.
Journal entry?
(iii) What if customers received replacements to the value of
$1100, instead of refunds?
Dr Warranty Expense 1 000
Cr Provision for Warranty 1 000
Dr Provision for Warranty 1 000
Dr Warranty Expense 100
Cr Cash 1 100
56
Dr Provision for Warranty 1 000
Dr Warranty Expense 100
Cr Inventory 1 100
Contingent liabilities are NOT recognised
• A contingent liability is:
• A possible obligation that arises from past events &
whose existence will be confirmed only by the
occurrence or non-occurrence of one or more uncertain
future events not wholly within the control of the entity;
• or
• A present obligation that arises from past events but is
not recognised because:
• It is not probable that an outflow of resources
embodying economic benefits will be required to
settle the obligation; or
• The amount of the obligation cannot be measured
with sufficient reliability.
57
LO 4
Contingent liabilities are NOT recognised on
balance sheet
Examples:
• Loan guarantee for a highly profitable subsidiary.
– Reason:
• Liability arising out of litigation in progress.
– Reason:
Disclosure in the notes to the financial statements is
required if the amount is material, unless the possibility of
an outflow of economic resources is remote.
58
E.g., Boeing Annual Report 2021
Note 21 Legal Proceedings (Excerpt)
Multiple legal actions have been filed against us ….
Further, we are subject to, and cooperating with, ongoing governmental
and regulatory investigations and inquiries relating to the accidents and
the 737 MAX. Among these is an ongoing investigation by the
Securities and Exchange Commission, the outcome of which may be
material. Other than with respect to the agreement described below
with the U.S. Department of Justice entered in 2021, we cannot
reasonably estimate a range of loss, if any, not covered by available
insurance that may result given the current status of the pending
lawsuits, investigations and inquiries related to the 737 MAX.
Picture sourced from ABC News, accessed 19/6/2022
Pricing of bonds requires an understanding of
Discounted Cash Flow (DCF) analysis
Extra slides
• DCF analysis explicitly considers time value of money
• $100 today is worth more than $100 in a year
• E.g., invest $100 at 10% now
• What will it be worth next year?
• $100 x 1.1 = $110 next year (assuming no inflation!)
• What will it be worth in two years?
• $100 x 1.1 x 1.1 = $121 in two years
An aside: Discounted cash flow (DCF) analysis
• What if we want to work backwards?
• i.e., we don’t have $100 now; we are going to receive it
in the future
• Assume the rate, i, is still 10%
• $100 to be received in a year… what is it worth today?
i.e., what is its present value (PV)?
• PV x 1.1 = $100 next year
• PV = 100/1.1 = $90.91
• $100 received in 2 years… what is it worth today?
• PV x 1.1 x 1.1 = $100 in two years
• PV = 100 / (1.1)2 = $82.64 PV =
100
(1 + 0.10)2
= $82.64
PV =
100
(1 + 0.10)1
= $90.91
Net present value (NPV)
• The present value of any given cash flow using a discount
rate or required rate of return of i:
• Net present value
= present value of all project cash flows – initial investment
• The “internal rate of return” is the rate of return that will give
you a NPV of zero → this is the “market rate” referred to in
this lecture
ni) (1
CF
PV
+
=
Liabilities
UNSW Business School
School of Accounting, Auditing & Taxation
ACCT2511
Financial Accounting
Fundamentals
Lecture learning objectives
1. Know and be able to apply the definition and recognition
criteria of liabilities
2. Be able to account for current liabilities
3. Be able to account for non-current liabilities: borrowings
and bonds
4. Understand the difference between provisions and
contingent liabilities.
What part of a Company Annual Report are we looking at today?
•
•
Liabilities: Definition
• “A liability is a present obligation of the entity arising from
past events, the settlement of which is expected to result
in an outflow from the entity of resources embodying
economic benefits” (AASB Framework, paragraph 49)
• Essential characteristics:
– The existence of a present obligation arising from a
past event
– results in an outflow of economic benefits
4
LO 1
More on Definition criteria (1): Present obligation
• An obligation is a duty or responsibility to act or perform in
a certain way.
• Legally enforceable obligations: consequence of a
binding contract or statutory requirement.
– e.g. amounts payable for goods and services received
• Constructive obligations: arising from normal business
practice, custom and/or a desire to maintain good
business relations or act in an equitable manner.
– e.g. a policy to rectify product defects even after the
warranty period has expired.
5
Past Events
Liabilities result from past transactions or other past events.
• Somewhat redundant because in order to have a present
obligation there would need to be a past obligating
event. For example:
• Acquisition of goods => Accounts payable
• Sales => warranty
• Receipt of a bank loan => borrowings
•You can think of present obligation and past event as one
characteristic: Present obligation (because that must arise
from a past obligating event)
Outflow of economic benefits
Settlement of a present obligation usually involves the
entity giving up resources embodying economic benefits.
For example:
– transfer of other assets
– payment of cash
– provision of services
– replacement of that obligation with another obligation
– conversion of the obligation to equity.
Recall from last week:
Reporting Assets & Liabilities
• Not all assets & liabilities are on the balance sheet
• Assets and liabilities have to:
(1) Meet essential definition criteria (from previous two slides)
And THEN
(2) Meet recognition criteria (defined on the next slide)
To be recognised (reported) on the Balance Sheet.
If they meet (1) but not (2), they are disclosed in the notes
Recognition of Liabilities
Recognition is the process of incorporating assets and
liabilities that meet the definitions into the Balance Sheet.
An item that meets the definition of a liability
should be recognised if:
a) It is probable that any future economic benefit
associated with the item will flow from the entity;
and
b) The item has a cost or value that can be measured with
reliability.
AASB Framework, Paragraph 83
a)Probability of outflow of Future Economic Benefit
• Probable if the event is more likely than not to occur
• Where there are a number of similar obligations, need to
consider the class of obligations as a whole.
• E.g., Smoove Ltd sold 50,000 blenders in 2022
– Each blender comes with a 1 year warranty
– In previous years 2% of customers made warranty claims
– If considering each single blender by itself: no provision
for the warranty could be recognised (2% chance of
outflow of FEB is not probable)
– However, if considering all of the blenders together (as a
class of obligations): a provision can be recognised as it
is now probable that at least some of blenders will result in
a warranty claim
b) Reliable measurement
• The cost or value of the liability needs to be measured
with reliability
• The use of estimates does not undermine reliability.
• A range of possible outcomes is enough to make an
estimate that is sufficiently reliable to use.
Decision path for liability recognition
Does the item have all two essential
characteristics of a liability?
Does the liability meet
both the recognition
criteria?
Does not appear in
the balance sheet but
may appear in a note
Liability recognised in
the entity’s balance
sheet
Separately disclosed
in the notes
No
NoYes
Yes
Current vs. Non-Current Liabilities
A liability shall be classified as current when it satisfies any
of the following criteria (AASB101, para 60):
– It is expected to be settled in the entity’s normal
operating cycle.
– It is due to be settled within twelve months after the
reporting date.
All other liabilities shall be classified as non-current.
13
LO 2
An aside: Working Capital
• WC ($) = Current Assets - Current Liabilities
Low or negative working capital can be an indication of
short-term financial difficulties.
• Current ratio = Current Assets/Current Liabilities
This gives an indication of the magnitude of working
capital (rather than a $ value).
Current Liabilities
• Usually recorded at full maturity value
• Due to the short time frame involved
• Difference between maturity value and present value
is usually small and immaterial.
E.g.,
• Accruals for goods/services received but not paid for/earned such as
accounts payable, notes payable, accrued expenses, unearned
revenue
• Interest bearing liabilities that are due within 12 months
• Formal debt instrument to pay specified amount at specified time
• Tax liabilities
• Dividends Payable
• Provisions….
15
An aside about terminology
• Classify the following accounts as Asset, Liability,
Revenue or Expense:
– Rent Payable
– Rent Receivable
– Rent Revenue
– Rent Expense
– Accrued Rent Revenue
– Unearned Rent Revenue
– Accrued Rent Expense
– Prepaid Rent Expense
Notes Payable
• May be interest bearing or non-interest bearing.
• For interest bearing notes, the accounting treatment is
straight forward.
• Non-interest bearing notes will be covered in advanced courses
• E.g., on 30 June 2022, Apple Pie Ltd. signed a three-month
10 per cent annum note payable to purchase a new truck
costing $40,000. Interest and principal are paid at maturity.
What is the journal entry on June 30 2022?
17
Dr Motor Vehicle 40,000
Cr Note Payable 40,000
Current Maturities of Long Term Debt
• The portion of long term debt maturing within the next 12
months is reported as a current liability.
• E.g., At financial year end Banana Bread Ltd is holding a
mortgage of $850 000 that requires payments of $10 000
each month. Next year the interest component of the
payments will equal $70 000.
• What is the current liability that would be reported?
• (10 000 x 12) – 70 000 = $50 000
• What is the non-current liability that would be reported?
• 850 000 – 50 000 = $800 000
• What is the interest expense for next year?
• $70 000
18
Non-Current Liabilities
• Obligations that are not expected to be paid within the next
12 months / operating cycle
• Arising from specific financing situations
• E.g., borrowings, bonds
• Arising from ordinary business operations
• E.g., superannuation and other obligations to
employees, deferred income tax obligations, provisions
19
LO 3
Long Term Debt: Accounting for Borrowings
Recognising borrowing:
Dr Cash XXX
Cr Borrowings XXX
Recognition and payment of Interest:
Dr Interest Expense XXX
Cr Interest Payable XXX
Dr Interest Payable XXX
Cr Cash XXX
Repayment of principal:
Dr Borrowings XXX
Cr Cash XXX
20
Recall Banana Bread Ltd
Banana Bread Ltd is holding a mortgage of $850 000 that
requires payments of $10 000 each month. Next year the
interest component of the payments will equal $70 000.
(1) Write a summary transaction to record the interest
payments for the year (assume interest is paid as incurred)
Dr interest expense 70 000
Cr Cash 70 000
(2) Write a summary transaction to record the principal
repayments for the year
Dr Borrowings/mortgage 50 000
Cr Cash 50 000
21
Accounting for Bonds
• Bonds are issued by companies, and are a promise to
pay interest and return the investor's capital on a
specified date (“maturity” date).
• i.e., A bond is a promise to pay something in the
future in exchange for receiving something today.
• The seller/issuer of a bond is a borrower
• The buyer of a bond is a lender
• Why issue bonds instead of borrowing from a bank?
• Borrowing directly from a bank can be more restrictive
and expensive
• Access to more lenders
Some more terminology relating to Bonds
• The amount to be repaid to the bond buyer (lender) at
maturity is known as the face value
• The explicit interest rate being offered by the bond seller
(borrower) is known as the coupon rate
• E.g., Bircher Ltd issues 100 bonds with a face value of
$1 000, with the principal to be paid at maturity in 2 years.
The coupon rate is 5% per annum and paid annually.
• Bircher Ltd is the borrower. The people buying the bonds from
Bircher are the lenders.
• Bircher will pay out $5 000 ($1 000 x 0.05 x 100) in coupon
payments each year, for two years
• At the end of two years, Bircher will also pay $100 000
($1 000 x 100) to the lenders to clear its debt.
Bircher
Seller/Borrower
Muesli
Buyer/Lender
2-year Bond with
FV = $1000, coupon 5%
Cash
At issue date
Year 1
Bircher
Seller/Borrower
Muesli
Buyer/Lender
$50 cash
coupon payment
Year 2 (at maturity)
Bircher
Seller/Borrower
Muesli
Buyer/Lender
$1050 cash
($50 coupon payment
+ $1000 FV)
Coupon rate vs Market rate
• Recall: the explicit interest rate being offered by the
bond seller (borrower) is known as the coupon rate
• Today we will call the rate that the market requires to
lend to this borrower the market rate
• Differences in the coupon rate and the market rate will
impact how the bond is valued/priced at the time of issue
• (1) Coupon rate = market rate – issued at face value
• (2) Coupon rate < market rate – issued at discount
• (3) Coupon rate > market rate – issued at premium
(1) Coupon rate = Market rate (bonds at face value)
• If the coupon rate and the market rate are equal, bonds
are said to be issued at their face value
• i.e., the amount received by the borrower at the time of
issue is the same as the face value that will be paid to
the lender at maturity
• Recall: Bircher issues 100 bonds with $1 000 face value,
with the principal to be paid at maturity in 2 years. The
coupon rate is 5% per annum and paid annually.
• Imagine the market rate is also 5%
The journal entry to recognise the issue:
• Dr Cash 100 000
Cr Bonds Payable 100 000
Recall: Bircher issues 100 bonds with $1 000 face value,
maturity in 2 years, coupon rate is 5% p.a. and paid annually,
market rate is also 5%
• End of year 1: Recognise the coupon payment
Dr Interest Expense 5 000
Cr Cash 5 000
• Note: coupon payment equals recorded interest expense
• End of year 2: Repay the principal and recognise the
2nd coupon payment:
Dr Interest Expense 5,000
Dr Bonds payable 100,000
Cr Cash 105,000
Journal entry is almost the same as when you have a loan!
(2) Coupon rate < Market rate (bonds at discount)
• If the coupon rate is lower than the market rate, the
bonds are issued at a discount
• This is because the present value of the bond is less
than the face value of the bond
• Bonds discount = the difference between the face value
and market value. It is a contra-liability account. Journal
entry when bonds are issued:
Dr Cash
Dr Bonds Discount
Cr Bonds Payable
(2) Coupon rate < Market rate (bonds at discount)
• Recall: Bircher issues 100 bonds with $1 000 face value, with
the principal to be paid at maturity in 2 years. The coupon rate
is 5% per annum and paid annually.
• Imagine the market rate is 7%
• What does this mean for bond valuation by the market?
For each bond: Present value = $963.84
=
(+.)
+
(+.)
+
+.
This means that Bircher will only receive $96 383.96 for 100
bonds, even though it will have to pay back the face value of
$100 000 at maturity
You will find a simple explanation regarding present value at
the very end of these lecture slides
(2) Coupon rate < Market rate (bonds at discount)
The journal entry to recognise the issue is:
Dr Cash 96 383.96 (2) next!
Dr Bonds Discount 3 616.03 (3) last step
Cr Bonds Payable 100 000 (1) start here!
The discount represents implicit additional interest of
$36.16 per bond. The journal entry above is recording all
of this interest at the time of issue, even though the debt
will not be paid for two years.
We will need to amortise this discount amount.
Bonds Discount
3616.03
T account representation
Bonds Payable
100 000
Balance sheet presentation at issuance:
Long-term liabilities
Bonds Payable 100 000
Less Bonds Discount 3 616
Carrying value 96 384
We need to amortise this
over the life of the bonds
Amortising the
discount will
eventually bring CV
to $100 000
Face Value
Bonds Discount
Issuance date
t= 0
Maturity date
t = 2
Carrying Value
$96 384
100,000
t=1
Bonds Discount of $3 616 is implicit additional interest to be
amortised over 2 years to bring carrying amount in line with face
value at maturity
Diagramatically
Bonds discount is amortised using effective interest method:
interest exp = market rate x carrying value
100,000
$3 616
Carrying Value at t =0
Bonds at discount – what happens after 1 year?
• At the end of year 1, three things have to happen:
• 1. Bircher has to pay the coupon for the first year
• ($1 000 x 0.05) x 100 bonds = $5 000
• This is the same every year!
• 2. Bircher has to amortise this bond discount using the
“effective interest method”
• The amortisation amount in each period will be added to
the interest expense recorded for that period
• 3. Bircher has to record the actual interest expense
• Interest exp = market rate x bonds’ carrying value
Journal entry at t = 1
• Dr Interest Expense
• Cr Bonds Discount
• Cr Cash
• Step 1: Calculate the coupon payment. It doesn’t change!
• Coupon payment = coupon rate x face value
• Steps 2 & 3: record actual interest expense & amortise discount
• Interest expense = market rate x bonds’ carrying value
• The bond discount amortisation is the difference between
the interest expense and the coupon payment
• = 6 746.88 – 5 000 = $1 746.88
5 000 (1)
6 746.88 (2)
1 746.88 (3)
Coupon payment = 0.05 x 100 000
Interest exp = 0.07 x 96 383.96
We will now have a new carrying value!
• Dr Interest Expense
• Cr Bonds Discount
• Cr Cash
Bonds Discount
3616.03
Bonds Payable
100 000
5 000
6 746.88
1 746.88
1 746.88
Balance sheet presentation
Long-term Liabilities t= 0 t=1
Bonds Payable 100 000 100 000
Less Bonds Discount 3 616 1 869
Carrying value 96 384 98 131
1 869.16
Face Value
Bonds Discount
Issuance date
t= 0
Maturity date
t = 2
Carrying Value at t =1$96 384
100,000
t=1
Diagramatically
100,000
$3616
$1869
$98 131
Carrying Value at t =0
Journal entry at t = 2 (maturity) – Part 1
• Dr Interest Expense
• Cr Bonds Discount
• Cr Cash
• Part 1: Record interest expense
• = market rate x bonds’ carrying value
• 0.07 x $98 130.84 = $6 869.16 (rounded)
• Discount amortisation = $1869.16
• As expected – brings account to 0
5 000 (1)
6 869.16 (2)
1 869.16 (3)
Bonds Discount
1 869.16 1 869.16
0
Journal entry at t = 2 (maturity) – Part 2
• Repay the principal! (Face value)
• = 100 bonds with face value of $ 1000 = $100 000
• Dr Bonds Payable
Cr Cash
100 000
Bonds Discount
1 869.16
0
1 869.16 (pt. 1)
100 000
Bonds Payable
100 000(pt. 2) 100 000
0
Our discount example - summary
• Bircher issued 100 bonds with $1 000 face value ($100 000),
with the principal to be paid at maturity in 2 years.
• Coupon rate was 5% per annum and paid annually ($5 000)
• BUT the market rate was 7%
• What did this mean for bond valuation by the market?
Each bond was valued at $963.84 (rounded)
• So Bircher issued the bonds at a discount - it only received
$96 383.96, even though it would have to pay back the face
value of $100 000 at maturity
• It paid explicit annual interest of $5 000 (coupon), plus implicit
interest in the form of the Bonds Discount of $3 616.04
• The Bonds Discount needed to be amortised to zero.
Bonds issued at Discount – Summary of entries
• When the bonds were issued (t=0):
Dr Cash 96 383.96
Dr Bonds Discount 3 616.04
Cr Bonds Payable 100,000.00
• Interest Expense (t=1):
Dr Interest Expense 6 746.88
Cr Bonds Discount 1 746.88
Cr Cash 5 000
• Interest Expense and Repayment of Principal (t=2):
Dr Interest Expense 6 869.16
Cr Bonds Discount 1 869.16
Cr Cash 5 000
Dr Bonds Payable 100,000
Cr Cash 100,000
Remember: Coupon rate vs Market rate
• Recall: the explicit interest rate being offered by the
bond seller (borrower) is known as the coupon rate
• Today we will call the rate that the market requires to
lend to this borrower the market rate
• Differences in the coupon rate and the market rate will
impact how the bond is valued/priced at the time of issue
• (1) Coupon rate = market rate – issued at face value
• (2) Coupon rate < market rate – issued at discount
• (3) Coupon rate > market rate – issued at premium
(3) Coupon rate > Market rate (bonds at premium)
• If the coupon rate is higher than the market rate, the
bonds are issued at a premium
• PV of the bond is higher than the Face V of the bond
• i.e., the issuing company receives a larger amount
than the face value (amount that will be paid to the
lender at maturity)
• Bond premium = the difference between the face value
and market value. It is an adjunct liability account.
Journal entry when bonds are issued:
Dr Cash
Cr Bonds Premium
Cr Bonds payable
(3) Coupon rate > Market rate (bonds at premium)
• Recall: Bircher issues 100 bonds with $1 000 face value, with
the principal to be paid at maturity in 2 years. The coupon rate
is 5% per annum and paid annually.
• Imagine the market rate is 3%
• What does this mean for bond valuation by the market?
For each bond: Present value = $1 038.27
=
(+.)
+
(+.)
+
+.
This means that Bircher will receive $103 826.90 for 100
bonds, even though it will only have to pay back the face
value of $100 000 at maturity
(3) Coupon rate > Market rate (bonds at premium)
The journal entry to recognise the issue is:
Dr Cash 103 826.90 (2) next!
Cr Bonds Premium 3 826.9 (3) last step
Cr Bonds Payable 100 000 (1) start here!
The premium represents implicit reduction in the interest
paid over the life of the bond. The journal entry above is
recording all of this benefit at t =0.
We will need to amortise this premium.
Bonds Premium
3 826.90
T account representation
Bonds Payable
100 000
Balance sheet presentation at issuance:
Long-term Liabilities
Bonds Payable 100 000.00
Add Bonds Premium 3 826.90
Carrying value 103 826.90
We need to amortise this
over the life of the bonds
Amortising the
discount will
eventually bring CV
to $100 000
Face Value
Bonds Premium
Issuance date t= 0 Maturity date t = 2
Carrying Value
$103 827
100,000
t=1
Bonds Premium of $3 827 is an implicit reduction in interest.
Amortised over 2 yrs to bring carrying amount in line with face
value at maturity
Diagramatically
Bonds premium is amortised using effective interest method:
interest exp = market rate x carrying value
100,000
$3 827
Carrying Value at t =0
Bonds at premium – what happens after 1 year?
• At the end of year 1, three things have to happen:
• 1. Bircher has to pay the coupon for the first year
• ($1 000 x 0.05) x 100 bonds = $5 000
• This is the same every year!
• 2. Bircher has to amortise this bond premium using the
“effective interest method”
• The amortisation amount in each period will be subtracted
from the interest expense recorded for that period
• 3. Bircher has to record the actual interest expense
• Interest expense = mkt rate x bonds’ carrying value
Journal entry at t = 1
• Dr Interest expense
• Dr Bonds Premium
• Cr Cash
• Step 1: calculate the coupon payment.
• Steps 2 & 3: record actual interest expense & amortise discount
• Interest expense = market rate x bonds’ carrying value
• The bond premium amortisation is the difference between
the coupon payment and the interest expense
• = 5 000 - 3 114.81 = $1 885.19
5 000 (1)
3114.81 (2)
1 885.19 (3)
Coupon payment = 0.05 x 100 000
Interest exp = 0.03 x 103 826.90
We will now have a new carrying value!
• Dr Interest expense
• Dr Bonds Premium
• Cr Cash
Bonds Premium
1 885.19
Bonds Payable
100 000 3 826.94
Balance sheet presentation
Long-term liabilities t= 0 t=1
Bonds Payable 100 000 100 000
Add Bonds Premium 3 827 1 942
Carrying value 103 827 101 942
1 941.75
5 000
3114.81
1 885.19
Face Value
Bonds Premium
Issuance date t= 0 Maturity date t = 2
Carrying Value
$103 827
100,000
t=1
Diagramatically
100,000
$3 827
Carrying Value at t =0
$101 942
Carrying Value at t =1
Journal entry at t = 2 (maturity) – Part 1
• Dr Interest expense
• Dr Bonds Premium
• Cr Cash
• Part 1: Record interest expense
• = market rate x bonds’ carrying value
• 0.03 x $101 941.70= $3 058.25 (rounded)
• Premium amortisation = $1 941.75
• As expected – brings account to 0
5 000 (1)
3 058.25 (2)
1 941.75 (3)
Bonds Premium
1 941.751 941.75
0
Journal entry at t = 2 (maturity) – Part 2
• Repay the principal! (Face value)
• = 100 bonds with face value of $ 1000 = $100 000
• Dr Bonds Payable
Cr Cash
100 000
100 000
Bonds payable
100 000(pt. 2) 100 000
0
Bonds Premium
1 941.75(pt. 1) 1 941.75
0
Uncertainty: Provisions and contingent liabilities
• Provisions are uncertain in timing or amount
• Provisions are recognised on balance sheet
In comparison …
• ‘Contingent’ liabilities:
1) A possible obligation arising from past events but whose
existence depends on uncertain future events not wholly
within the control of the entity or
2) A present obligation that does not meet recognition
criteria (not probable and/or can’t be reliably measured)
Contingent liabilities are not recognised on balance sheet,
but are disclosed in the notes
53
LO 4
Provisions: May be Current or Non-current
• Some liabilities can be measured only by using a
substantial degree of estimation due to uncertainty.
• Provisions are estimates due to uncertainty in:
– Timing and/or
– Amount
• May arise from either a legal or constructive obligation e.g.,
• Warranties
• Amount uncertain, timing is uncertain
• Employee benefits (e.g., annual leave, bonuses).
• Timing is uncertain as don’t know when leave will be
claimed. Amount and timing may be uncertain in the
case of bonuses.
54
Provisions are recognised on the balance sheet
• Provisions are reported separately from payables and
accruals on the balance sheet.
– Remember, if there is no present obligation, then no
provision!
– e.g., no provision for (future) maintenance.
• Journal entries when creating a provision (normally):
Dr …. Expense
Cr Provision for…
• Journal entries when actual claims are made (and
redeemed):
Dr Provision for…
Cr Cash
55
Example: Warranty Plan
Oat Cookie Ltd. has a warranty plan set up. Normally
warranty costs amount to 10% of COGS (Customers receive
refunds). This year, COGS was $10,000. Required:
(i) Prepare journal entries for the warranty plan this year.
(ii) The actual warranty claim amount paid out was $1100.
Journal entry?
(iii) What if customers received replacements to the value of
$1100, instead of refunds?
Dr Warranty Expense 1 000
Cr Provision for Warranty 1 000
Dr Provision for Warranty 1 000
Dr Warranty Expense 100
Cr Cash 1 100
56
Dr Provision for Warranty 1 000
Dr Warranty Expense 100
Cr Inventory 1 100
Contingent liabilities are NOT recognised
• A contingent liability is:
• A possible obligation that arises from past events &
whose existence will be confirmed only by the
occurrence or non-occurrence of one or more uncertain
future events not wholly within the control of the entity;
• or
• A present obligation that arises from past events but is
not recognised because:
• It is not probable that an outflow of resources
embodying economic benefits will be required to
settle the obligation; or
• The amount of the obligation cannot be measured
with sufficient reliability.
57
LO 4
Contingent liabilities are NOT recognised on
balance sheet
Examples:
• Loan guarantee for a highly profitable subsidiary.
– Reason:
• Liability arising out of litigation in progress.
– Reason:
Disclosure in the notes to the financial statements is
required if the amount is material, unless the possibility of
an outflow of economic resources is remote.
58
E.g., Boeing Annual Report 2021
Note 21 Legal Proceedings (Excerpt)
Multiple legal actions have been filed against us ….
Further, we are subject to, and cooperating with, ongoing governmental
and regulatory investigations and inquiries relating to the accidents and
the 737 MAX. Among these is an ongoing investigation by the
Securities and Exchange Commission, the outcome of which may be
material. Other than with respect to the agreement described below
with the U.S. Department of Justice entered in 2021, we cannot
reasonably estimate a range of loss, if any, not covered by available
insurance that may result given the current status of the pending
lawsuits, investigations and inquiries related to the 737 MAX.
Picture sourced from ABC News, accessed 19/6/2022
Pricing of bonds requires an understanding of
Discounted Cash Flow (DCF) analysis
Extra slides
• DCF analysis explicitly considers time value of money
• $100 today is worth more than $100 in a year
• E.g., invest $100 at 10% now
• What will it be worth next year?
• $100 x 1.1 = $110 next year (assuming no inflation!)
• What will it be worth in two years?
• $100 x 1.1 x 1.1 = $121 in two years
An aside: Discounted cash flow (DCF) analysis
• What if we want to work backwards?
• i.e., we don’t have $100 now; we are going to receive it
in the future
• Assume the rate, i, is still 10%
• $100 to be received in a year… what is it worth today?
i.e., what is its present value (PV)?
• PV x 1.1 = $100 next year
• PV = 100/1.1 = $90.91
• $100 received in 2 years… what is it worth today?
• PV x 1.1 x 1.1 = $100 in two years
• PV = 100 / (1.1)2 = $82.64 PV =
100
(1 + 0.10)2
= $82.64
PV =
100
(1 + 0.10)1
= $90.91
Net present value (NPV)
• The present value of any given cash flow using a discount
rate or required rate of return of i:
• Net present value
= present value of all project cash flows – initial investment
• The “internal rate of return” is the rate of return that will give
you a NPV of zero → this is the “market rate” referred to in
this lecture
ni) (1
CF
PV
+
=
