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金融代写-FINS1612
时间：2021-07-22
FINS1612
Capital Markets & Institutions
Debt I: Short-term debt
Ian Kwan
i.kwan@unsw.edu.au
Week 02
Viney & Phillips (2019) Ch 08 & 09
Content of lecture
• Short‐term debt include instruments with maturity < 1 year
• Short‐term debt options for small‐ to medium‐sized firms:
– Trade financing
– Overdraft facilities
– Inventory finance, Accounts receivable financing, and Factoring
• Short term debt options for large good quality credit firms
– These instruments are issued and traded in the Money Market
– Commercial bills – issued by firms, accepted or discounted by banks, endorsed on sale
– Promissory notes (commercial paper) – issued by firm, no acceptor or endorsements
– Negotiable certificates of deposit (CD) – issued by banks
• Valuing short‐term debt
– Use Simple interest valuation – AUS issued discount securities, 365 days/year
– Use Simple discount valuation – USA and euromarket issued discount securities , 360 days/year
2
Learning Objectives
Viney & Phillips Chapter 8:
Mathematics of Finance
Simple interest and Simple discount
calculations relevant to short‐term
debt
LO 8.1: Understand simple
interest calculations
LO 8.1a Understand simple
discount calculations
3
Financial Valuation Methods
4
Simple
Compound
Interest Discount
Commercial bills
Promissory notes
Australian short-term
discount securities
US/EU short-term
discount securities
Commercial paper
Promissory notes
Bonds
Stocks
Most asset classes
Most of the world,
long-term securities
Focus now: Simple Interest valuation
Some on: Simple Discount valuation
Week 3 we will focus on
Compound Interest valuation
Simple interest
5
Interest Amount = Present Value x Rate x Time
ൌ ൈ ൈ
Future Value = Present Value + Interest Amount
ൌ ൌ . . ൌ 1 . ൌ 1 . 365
ൌ
365
Everything we do here is about playing with these equations!
It’s all about knowing what is what!!
Time is the number of periods,
usually in years or part of a year.
The USA or Bankers’ Rule
convention is 360 days in a year
Note: “Present value” often means “today”, “now”, but may
mean “earlier than future value”. See Examples.
Important:
Nominal interest rate is
always an annual rate!
Simple interest … IS SIMPLE!
6
You borrow $1000 at the rate of 12% per annum.
a) How much interest after 30, 60, 120 and180 days?
b) What is the future value after each of these periods?
1009.86
9.86 19.73 39.45 59.18
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
ൌ ሺ1000ሻሺ12%ሻ 30365 ൌ ሺ1000ሻሺ12%ሻ 60365 ൌ ሺ1000ሻሺ12%ሻ 120365 ൌ ሺ1000ሻሺ12%ሻ 180365
ൌ 1000 1 12% 30365 ൌ 1000 1 12% 60365
1019.73
ൌ 1000 1 12% 180365
1059.18
ൌ 1000 1 12% 120365
1039.45
Interest amount is proportional to principal, rate, and time
days 00
interest
Present Value
30 60 90 120 180
ൌ . .
ൌ 1 . 365
1000
0
Note: “Present value” often means “today”, “now”, but may mean “earlier than” or “to the left of future value”.
Similarly, “future value” means “later than or to the right of present value.
Future Value
Simple interest … IS SIMPLE!
7
Example 8.4: An investor owns an asset that will be worth $100 000 in
120 days. If the investor sells it today when the discount rate is 11.00%,
what will the investor sell it for now?
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Interest amount is proportional to principal, rate, and time
Identify then solve:
S
A
i
n
100 000
?
11%
120/365
ൌ 100 000 1 0.11 120365 ିଵ ൌ 96 509.78
ൌ 1 . ିଵ
Re-arrange
Simple interest … IS SIMPLE!
8
Example 8.7: What is the yield (rate of return) earned on a $50 000
deposit with a maturity value of $50 975 maturing in 93 days?
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Interest amount is proportional to principal, rate, and time
Identify then solve:
S
A
i
n
50 975
50 000
?
93/365
50 975 ൌ 50 000 1 93365
⇒ ൌ
ହଽହ
ହ
െ 1 ଷହ
ଽଷ
ൌ 0.07653 ൌ 7.65%
ൌ 1 . 365 െ ൌ . .50975 െ 50000 ൌ 50000. . 93365
⇒ ൌ
50975 െ 5000050000 36593 ൌ 0.07653 ൌ 7.65%
OR
Interest is difference
between the first
and last cash flows
This is the rate
over 93 days
This scales up the 93-day
rate into an annual rate
Simple interest … IS SIMPLE!
9
Example 8.9: A commercial bill with a face value of $100 000 and 180
days to maturity is purchased with a yield of 7.85%. The bill is held for 50
days then sold at a yield of 7.35%. (a) What is the rate of return of the
original bill? (b) What is the Holding Period Yield?
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
S
A
i
n
100 000
? (Buy Price)
7.85%
180/365
100 000 ൌ 1 0.0785 180365
⇒ ൌ 100 000 1 0.0785 180365 ିଵ
ൌ 96 273.05
ൌ 1 . 365
The HPY is the annualized return of the bill from when bought till sold ൌ ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
S
A
i
n
100 000
? (Sell Price)
7.35%
(180-50)/365
100 000 ൌ 1 0.0735 130365
⇒ ൌ 100 000 1 0.0735 130365 ିଵ
ൌ 97 448.97
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
ൌ
ଽସସ଼.ଽିଽଶଷ.ହ
ଽଶଷ.ହ ൈ ଷହହ ൌ 0.089166 ൌ 8.92%
Remaining period
At the beginning 50 days later
Return over d days Scaling factor to turn the return into a 1-year return
This is the rate
over 50 days This scales up the 50-day
rate into an annual rate
Simple interest … SIMPLIFIED
10
The textbook uses different formulas…or what LOOK LIKE different formulas,
but the underlying formula is the same!
DON’T GET CONFUSED! THEY’RE THE SAME UNDERLYING FORMULAS!
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
SIMPLY IDENTIFY EACH VARIABLE AND THEN SOLVE!
Practice problem – Your turn!
11
A commercial bill with a face value of $100 000 has 85 days to maturity is bought for $98 950 and sold 50 days later for
$99 450 (a) What is the yield when the bill was purchased? (b) What is the Holding Period Yield?
ൌ 1 . 365
soln
Simple Interest vs. Simple Discount
12
Interest Amount = Present value x Rate x Time
ൌ ൈ ൈ
Future Value = Present Value + Interest Amount
ൌ ൌ . . ൌ 1 . ൌ 1 . 365
ൌ
365 Time is the number of periods, usually in years or part of a year.
The USA or Bankers’ Rule
convention is 360 days in a year
Discount Amount = Future value x Rate x Time
ൌ ൈ ൈ
Present Value = Future Value – Discount Amount
ൌ െ ൌ െ . . ൌ 1 െ . ൌ 1 െ . 365
ൌ
365 Time is the number of periods, usually in years or part of a year.
The USA or Bankers’ Rule
convention is 360 days in a year
D = Discount Amount
A = Present value
S = Future or Face value
r = Discount rate
d = days of discounting
I = Interest Amount
A = Present value or Principal
S = Future value
i = Interest rate
d = days of interest
Simple Interest starts with Present Future
13
1009.86
9.86 19.73 39.45 59.18
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
ൌ ሺ1000ሻሺ12%ሻ 30365 ൌ ሺ1000ሻሺ12%ሻ 60365 ൌ ሺ1000ሻሺ12%ሻ 120365 ൌ ሺ1000ሻሺ12%ሻ 180365
ൌ 1000 1 12% 30365 ൌ 1000 1 12% 60365
1019.73
ൌ 1000 1 12% 180365
1059.18
ൌ 1000 1 12% 120365
1039.45
days 00
interest
Present value
30 60 90 120 180
ൌ . .
ൌ 1 . 365
1000
0
Future value
Simple interest adds interest to the present value
You borrow $1000 at the rate of 12%
per annum. What is the interest and
value along the way?
I = Interest Amount
A = Present value or Principal
S = Future value
i = Interest rate
d = days of interest
Simple Discount starts with Future Present
14
950.68
49.32 39.45 19.73 0
ൌ . . ൌ െ
ൌ 1 െ . ൌ 1 െ . 365
ൌ ሺ1000ሻሺ12%ሻ 150365 ൌ ሺ1000ሻሺ12%ሻ 120365 ൌ ሺ1000ሻሺ12%ሻ 60365 ൌ ሺ1000ሻሺ12%ሻ 0365
ൌ 1000 1 െ 12% 150365 ൌ 1000 1 െ 12% 120365
960.55
ൌ 1000 1 െ 12% 0365
1000
ൌ 1000 1 െ 12% 60365
980.27
days 00
Discount Amount
Present value
30 60 90 120 180
ൌ . .
ൌ 1 െ . 365
Simple discount discounts off the future value
D = Discount Amount
A = Present value
S = Face or future value
r = Discount rate
d = days of discounting
You have a face value $1000 discounted
at 12% per annum. What is the discount
and value along the way?
ൌ ሺ1000ሻሺ12%ሻ 180365
ൌ 1000 1 െ 12% 180365
59.18
940.82 Face / future value
Simple discount … USA and EU, but not AUS
15
ൌ . . ൌ െ
ൌ 1 െ . ൌ 1 െ . 360
D = Discount Amount
A = Present value
S = Face or future value
r = Discount rate
d = days of discounting
Example 9.8: What is the price of a 180-day discount security issued in the USA with a face value
of $100 000 and selling at a discount of 14.75%?
ൌ 100 000
ൌ 180
ൌ 14.75%
ൌ ?
ൌ 1 െ . ௗ
ଷ
ൌ 100 000 1 െ 14.75% ଵ଼
ଷ
ൌ 92 625.00
Note: market convention in the USA and euromarkets
is to use 360-day year (Bankers’ Rule)
Note: 360-day year (Bankers’ Rule)
Simple discount … USA and EU, but not AUS
16
ൌ . . ൌ െ
ൌ 1 െ . ൌ 1 െ . 360
D = Discount Amount
A = Present value
S = Face or future value
r = Discount rate
d = days of discounting
Example: A €100 000 euromarket-issued discount security with a 180-day maturity was issued
140 days ago for €98 899 is currently selling for €99 705? (1) At what discount rate was it issued
at, and (2) what is the current discount rate?
ൌ 100 000
ൌ 180 െ 0
ൌ?
ൌ 98 899
ൌ 1 െ . ௗ
ଷ98 899 ൌ 100 000 1 െ ଵ଼
ଷ
⇒ ൌ 1 െ 98899100000 ൈ 360180
ൌ 0.022020 = 2.20%
Note: 360-day year (Bankers’ Rule)
(1) At issue discount rate (2) Current discount rate
ൌ 100 000
ൌ ሺ180 െ 140ሻ
ൌ?
ൌ 99 705
ൌ 1 െ . ௗ
ଷ99 705 ൌ 100 000 1 െ ସ
ଷ
⇒ ൌ 1 െ 99 705100000 ൈ 36040
ൌ 0.026550 = 2.66%
Practice problem!
17
ൌ 1 െ . 365
A $100 000 US-issued discount security has 95 days to maturity and currently selling for $98 440
(1) What is the current discount rate? (2) If held until maturity, what is the Holding Period Yield?
ൌ 1 െ . 360
soln
Learning Objectives
Viney & Phillips Chapter 9:
Short‐term debt
LO 9.1‐9.4: Understand the
purpose and characteristics of
short‐term debt financing
LO 9.5: Learn to value discount
securities
LO 9.6‐9.8: Explain other forms of
short‐term debt instruments
18
LO 9.1
Purpose of short‐term debt
• Imagine you are the owner of an up‐market interior design
firm. Your business financial needs include:
– Rent: offices and showrooms
– Net working capital: demo designs, work in progress
materials, etc
– Salaries: Full‐time and part‐time staff
• Business is going great! But you have cash flow timing
problems: You need to pay rent, NWC, and salaries before
your customers pay you. Does that mean you have
managed your business poorly? NO! TIMING PROBLEM!
– Most businesses run into this problem
– Especially when a business is growing
• Short‐term debt financing helps businesses to bridge cash
flow timing problems
• Matching principle (from week 1) still applies: fund short‐
term needs with short‐term sources
– Characteristics: less than 1‐year, temporary need
– However, business growth, because it is more permanent,
should be funded with long‐term funding, e.g., equity
Short‐term financing instruments:
For small‐ to medium‐sized firms
• Trade credit
• Bank overdrafts
• Inventory finance, accounts
receivable financing, factoring
For large‐sized firms
• Commercial bills (of exchange)
• Promissory notes (commercial
paper)
• Negotiable certificates of deposit
19
LO 9.2
Trade credit
• Imagine you are an electrical fittings supplier. You
want tradie electricians to get their fittings from
you, so you offer them attractive payment terms:
– Well‐known repeat tradie customers: “No payment
for 30 days”
– Other repeat tradies: “No payment for 7 days”
– Unknowns: “CASH ON DELIVERY”
• When offering “no immediate payment” terms,
you are offering “Trade Credit”
– You are providing short‐term financing of your
customers’ purchases from you
– Trade credit is a deal sweetener
• In Australia, a significant volume of business is
financed by trade credit
– RBA estimates around $100 Billion
20
LO 9.2
Trade credit
• You offer trade credit, but you would like
customers to pay early, so you provide a discount
if they do so.
• Invoice contains trade terms: “2/10, n/30”
– “2/10” means 2% discount on the $5500 if paid
within 10 days
– “n/30” means that the net amount of $5500 must be
paid within 30 days
• As the customer, should you pay early or not?
How do you decide?
– It depends on your opportunity cost of capital or
alternative use of the funds
– If your capital funding cost is less than the savings you
get from paying early, then pay early
– But if your funding cost is more than the savings, then
delay payment for as long as you can
– How does this work? See example on the next slide.
21
Invoice
Purchase date: 7 June 2021
Electrical fittings: $5500
Terms: 2/10, n/30
LO 9.2
Trade credit
• Opportunity cost
ൌ
ଶ
ଵିଶ
ൈ
ଷହ
ଷିଵ
ൌ 0.372449
ൌ 37.24%
• If your after‐tax cost of capital is 20% (say) or your
alternative use of surplus cash only returns 23% (say), then
borrowing money to get a 37.34% discount is great deal, so
pay the bill early! Benefit = 37.34% ‐ 23% = 14.34%
• However, if your after‐tax cost of capital is 40% (say) or
your alternative use of surplus cash returns 42% (say), then
borrowing money to pay early means a lower return rate
and therefore losing money. In this case, wait for as long as
you can before paying the bill. Benefit = 37.34‐42= ‐ 4.66%
• Of course, you may not actually borrow the money to pay
the bill. “Borrowing money” expresses the idea that money
is not free – there is always an opportunity cost to get it.
22
Invoice
Purchase date: 7 June 2021
Electrical fittings: $5500
Terms: 2/10, n/30
ൌ
% 100% െ % ൈ 365
LO 9.3
Bank overdrafts
• Bank overdrafts are a major source of short‐term
finance
• An overdraft helps bridge short‐term cash flow
timing mismatches
– A firm needs to pay recurring month‐end expenses
such as salaries, rental, and networking capital needs
– But its customers won’t pay cash until after the start
of next month
• An overdraft facility allows a firm to overdraw its
operating account up to an agreed amount, for
which the bank charges interest
– The interest rate charge = prime rate + margin
– Prime rate is the firm’s reference rate and usually
compared with the bank bill swap rate (BBSR), a
floating short‐term rate
– Margin is the extra percentage above the prime rate,
indicating the credit risk of the borrower
23
LO 9.8
Inventory finance
• Inventory finance
– Different types:
– Floor plan finance
• Typical relationship between motor vehicle
dealers and finance companies
• The car dealer buys the vehicles direct from the
manufacturer and then promotes to customers
the finance company’s financing package
• In return, the finance company offers the
customer lower than market borrowing rates
making it attractive for the customer
– Bailment
• Takes floor plan finance a little further. The
finance company buys vehicles direct from the
manufacturer. The car dealer sells to customers
on behalf of the finance company.
• The car dealer promotes the financing package
offered at good rates. On sale, vehicle ownership
is passed from the finance company (bailor)
through the dealer (bailee) to the customer.
24
LO 9.8
Accounts receivable financing
and Factoring
• Accounts receivable financing
– A firm can borrow money from a finance company by
using its accounts receivable as collateral
– Not all the firm’s debtors are acceptable collateral,
e.g. unpaid debtors owing for more than 90 days are
excluded
• Factoring
– A firm can sell its accounts receivable to a factor
(finance) company, which takes on the liability of
collecting outstanding debts from debtors
– The sale of accounts receivable may be at a significant
discount to its book value, which means factor
financing is expensive for small firms
– However, for small firms where cash flow is often
difficult, the high cost of factor financing may be
worth it in the short‐run.
25
LO 9.4
Commercial bills
• So far, we have talked about small‐ to medium‐ sized firms.
We now look at large corporations.
• Large corporations raise short‐term debt through the
wholesale money market by issuing:
– Bills of exchange
– Promissory notes
– Negotiable certificates of deposit
• Bills of exchange are categorized as:
– Trade bills:
• used for financing international trade transactions
– Commercial bills:
• used for domestic borrowing and may not relate to any specific
transaction or trade purpose.
• Three types:
1. Bank‐accepted bill: A bank puts their name on the bill as the
acceptor endorsing it and increasing its credit‐worthiness
2. Bank‐endorsed bill: A bank, when selling it to another money
market party, signs the back of the bill providing endorsement for
the bill, making it more credit worthy. This forms a chain of
endorsement.
3. Non‐bank bills have no bank endorsement and trade on the
known creditworthiness of the corporate issuer itself.
26
LO 9.4
Commercial bills: features
• Important features of commercial bills include:
– A discount security with a fixed face value that is payable in
the future and hence issued at a discount.
– Pays no interest, hence sold at a discount to attract buyers
– The discount rate depends on the current market return
rate or yield for that type of bill
– The return to the bill holder depends on the difference
between purchase price and face value
– Issued by large‐ and medium‐sized firms which have the
scale economies to enter the wholesale money market
(small firms won’t qualify).
• Commercial bills involve several parties:
– Drawer: bill issuer
– Acceptor: the payer of the face value (i.e., bank)
– Payee: the issuer or a subsidiary firm of the issuer
– Discounter: bill purchaser (could be acceptor), who pays a
discount to receive the face value and becomes the owner
– Endorser: the previous bill owner who endorses (signs) the
back of the bill before selling it to the next owner
27
LO 9.4
Commercial bills: funds flow
• The flow of funds
Other features of commercial bills
• Maturity of 30 to 180 days
• Minimum face value is $100 000
• How do banks earn fees from the
drawer?
• Playing acceptor role
• Playing discounter role
• Playing acceptor and discounter
28Why are there different roles in commercial bills?
LO 9.4
Commercial bills: motivations
• Why issue a bill of exchange? Advantages for Borrowers
– The drawer (borrower) needs short‐term cash for a certain
period in days: 30, 45, 60, 90, 180 days
– The commercial bill market is very liquid and is easy for
drawer to raise short‐term funds
– Banks often provide a roll‐over facility that potentially
converts the short‐term into a medium‐ to long‐term loan
• Why purchase / sell a bill of exchange? Investor advantages
– An investor (e.g. a company) has excess short‐term funds
and wants to park it for a few days, weeks, or months
– The investor has a matching holding period and can hold a
newly issued bill until maturity (e.g., 30, 45, 60, 90, 180
days)
– A bill investor has a sudden cash flow shortage and sells it
in the highly liquid bill market. The ability to sell the
security at anytime is what attract many bill investors in the
first place
– An alternative security can be purchased at a better rate so
the bill investor sells to restructure their portfolio
29
Bill roll-over facility converts a $500 000 short-term
debt to medium- and long-term debt
(How does this work? To be explained)
LO 9.5 Valuing discounted securities
30
The commercial bill roll-over facility converts a $500 000 face value 180-day short-term bill to a 2-
year medium-term loan. At the beginning of the first 180 days, at t=0, the bill is discounted for the
first time and the drawer receives $479 317.14. At the end of the first 180 days, the Drawer should
pay back $500 000 face value, but instead the bill is discounted again for another 180 days and the
drawer only pays the difference between the face value and discounted price, $21 813.18,
effectively borrowing the original price for another 180 days. This is repeated two more times.
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
I = Interest Amount
A = Present value or Principal
S = Future or face value
i = Interest rate or yield
d = days of interest
ൌ 1 . ିଵ
ൌ 1 . ௗ
ଷହ
ିଵ
ൌ 1 . 365
ൌ
1 . 365 ൌ 500 0001 8.75% 180365 500 0001 9.25% 180365
500 0001 9.30% 180365 500 0001 9.25% 180365
Current market yield
Commercial bill rollover facility explainedSimple interest valuation
Discount the
face value with
current yield Discount the
face value with
current yield
Discount the
face value with
current yield Discount the face value with
current yield
500 000 500 000 500 000 500 000
LO 9.5 Valuing discounted securities
31
Textbook uses different formulas
ൌ
ൈ
100 ൈ
ൌ 100 ൈ
ൈ
ൌ
െ
ൈ ൈ 100
I recommend ones you have seen already
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365 I = Interest AmountA = Present value or PrincipalS = Future or face valuei = Interest rate or yield
d = days of interest
Simple interest valuation
Annualized Holding Period Yield
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
Return over d days Scaling factor to turn the
return into a 1-year return
LO 9.5 Valuing discounted securities
32
Example 9.3
A company funds its short-term inventory needs issuing a 30-day bank accepted bill with
a face value of $500 000. It approaches two discounters that offer different yields, one
with 9.52% and another with 9.48%. Which one should it accept?
I = Interest Amount
A = Present value or Principal
S = Future or face value
i = Interest rate or yield
d = days of interest
THE QUESTION: Which variable are we trying to find in the formula?
ൌ 500 000
ଵ ൌ 9.52%
ଶ ൌ 9.48%
Have: Want:500 000 ൌ ଵ 1 9.52%. 30365 ⇒ ଵ ൌ 496 118.05500 000 ൌ ଶ 1 9.48%. 30365 ⇒ ଶ ൌ 496 134.23
Accept the one returning highest present value,
i.e., highest loan amount.
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Simple interest valuation
Annualized Holding Period Yield
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
Return over d days Scaling factor to turn the
return into a 1-year return
LO 9.5 Valuing discounted securities
33
Example 9.7 (following Example 9.3)
A discounter discounts a company’s 30-day bank accepted bill with a face value of $500
000 with a yield of 9.48% representing a price of $496 134.23. Seven days later, the
discounter sells the bill in the short-term money market for $497 057.36 and is held until
maturity. Calculate (1) yield of the discounter and (2) yield of holder at maturity
I = Interest Amount
A = Present value or Principal
S = Future or face value
i = Interest rate or yield
d = days of interest
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Simple interest valuation
Annualized Holding Period Yield
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
Return over d days Scaling factor to turn the
return into a 1-year return
ൌ 496 134.23
ൌ 497 057.36
ℎ ൌ ൌ 7
Original Discounter: Annualized Holding Period Yield
ൌ
ସଽ ହ.ଷ ିସଽ ଵଷସ.ଶଷ
ସଽ ଵଷସ.ଶଷ ൈ ଷହ ൌ 0.09702 ൌ 9.70%
ൌ 496 134.23
ൌ 500 000
ℎ ൌ ൌ 30 െ 7
Holder to maturity: Annualized Holding Period Yield
ൌ
ହ ିସଽ ହ.ଷ
ସଽ ହ.ଷ ൈ ଷହଶଷ ൌ 0.093949 ൌ 9.39%
LO 9.6
Promissory notes (P‐notes)
• Promissory notes
– P‐notes are an unconditional written promise to pay a sum
of money on demand at future date to a specified person or
bearer
– They are discount securities with a face value payable at
maturity
– They are an international security
– They are also called “Commercial Paper”
– They are unsecured notes
– They are typically only issued by large firms with an
excellent credit reputation that attracts investors, i.e.,
investment grade rating
• Differences with bills; pros/cons
– Unlike bills of exchange, there is no acceptor, therefore also
called “one‐name paper”.
– Unlike bills of exchange, there is no endorsement of the P‐
note when sold in the secondary market.
• Good for seller: no contingent liability
• Bad for buyer: must trust the credit worthiness of the issuer
What does “unsecured” mean?
Why would an investor accept this
condition?
34
LO 9.7
Negotiable certificates of
deposit (CD)
• Negotiable certificates of deposits (CD)
– A short‐term discount security with
typical maturity of 180 days
– Issued by banks to attract institutional
investors
– Large and active secondary market that
provides liquidity for investors
– Issued by a bank to manage their
liabilities and seasonal liquidity needs
• E.g., During the Christmas shopping period,
increased demand from credit card
spending is funded by issuing CD
• E.g., Financial year end spending means
business and consumer demand requires
funding from new CD issues
35
Summary
• Short‐term debt include instruments with maturity < 1 year
• Short‐term debt options for small‐ to medium‐sized firms:
– Trade financing
– Overdraft facilities
– Inventory finance, Accounts receivable financing, and Factoring
• Short term debt options for large good quality credit firms
– These instruments are issued and traded in the Money Market
– Commercial bills – issued by firms, accepted or discounted by banks, endorsed on sale
– Promissory notes (commercial paper) – issued by firm, no acceptor or endorsements
– Negotiable certificates of deposit (CD) – issued by banks
• Valuing short‐term debt
– Use Simple interest valuation – AUS issued discount securities, 365 days/year
– Use Simple discount valuation – USA and euromarket issued discount securities , 360 days/year
36
Solutions to Practice Problems
37
Practice problem – soln!
38
A commercial bill with a face value of $100 000 has 85 days to maturity is bought for $98 950 and sold 50 days later for
$99 450 (a) What is the yield when the bill was purchased? (b) What is the Holding Period Yield?
0 85
98 950 100 000
0 50
98 950 ?
ൌ 1 . 365
100 000 ൌ 98 950 1 . 85365
= 99 450
ൌ
99 450 െ 98 95098 950 ൈ 36550
ൌ 0.03689 ൌ 3.69%100 00098950 െ 1 ൌ . 85365100 00098950 െ 1 ൈ 36585 ൌ
ൌ 0.04556 ൌ 4.56%
back
Practice problem! soln!
39
ൌ 1 െ . 365
A $100 000 US-issued discount security has 95 days to maturity and currently selling for $98 440
(1) What is the current discount rate? (2) If held until maturity, what is the Holding Period Yield?
ൌ 1 െ . 360
0 95
98 440 100 000
98440 ൌ 100000 1 െ . 95360
ଽ଼ସସ
ଵ
ൌ 1 െ . ଽହ
ଷ
ൌ 1 െ ଽ଼ସସ
ଵ
ൈ
ଷ
ଽହ ൌ 0.05911 ൌ 5.91%
ൌ
100000 െ 9844098440 ൈ 36095
ൌ 0.06005 ൌ 6.01%US and EU use Banker’s rule,
360-day year
US and EU use
Banker’s rule,
360-day year
back
Capital Markets & Institutions
Debt I: Short-term debt
Ian Kwan
i.kwan@unsw.edu.au
Week 02
Viney & Phillips (2019) Ch 08 & 09
Content of lecture
• Short‐term debt include instruments with maturity < 1 year
• Short‐term debt options for small‐ to medium‐sized firms:
– Trade financing
– Overdraft facilities
– Inventory finance, Accounts receivable financing, and Factoring
• Short term debt options for large good quality credit firms
– These instruments are issued and traded in the Money Market
– Commercial bills – issued by firms, accepted or discounted by banks, endorsed on sale
– Promissory notes (commercial paper) – issued by firm, no acceptor or endorsements
– Negotiable certificates of deposit (CD) – issued by banks
• Valuing short‐term debt
– Use Simple interest valuation – AUS issued discount securities, 365 days/year
– Use Simple discount valuation – USA and euromarket issued discount securities , 360 days/year
2
Learning Objectives
Viney & Phillips Chapter 8:
Mathematics of Finance
Simple interest and Simple discount
calculations relevant to short‐term
debt
LO 8.1: Understand simple
interest calculations
LO 8.1a Understand simple
discount calculations
3
Financial Valuation Methods
4
Simple
Compound
Interest Discount
Commercial bills
Promissory notes
Australian short-term
discount securities
US/EU short-term
discount securities
Commercial paper
Promissory notes
Bonds
Stocks
Most asset classes
Most of the world,
long-term securities
Focus now: Simple Interest valuation
Some on: Simple Discount valuation
Week 3 we will focus on
Compound Interest valuation
Simple interest
5
Interest Amount = Present Value x Rate x Time
ൌ ൈ ൈ
Future Value = Present Value + Interest Amount
ൌ ൌ . . ൌ 1 . ൌ 1 . 365
ൌ
365
Everything we do here is about playing with these equations!
It’s all about knowing what is what!!
Time is the number of periods,
usually in years or part of a year.
The USA or Bankers’ Rule
convention is 360 days in a year
Note: “Present value” often means “today”, “now”, but may
mean “earlier than future value”. See Examples.
Important:
Nominal interest rate is
always an annual rate!
Simple interest … IS SIMPLE!
6
You borrow $1000 at the rate of 12% per annum.
a) How much interest after 30, 60, 120 and180 days?
b) What is the future value after each of these periods?
1009.86
9.86 19.73 39.45 59.18
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
ൌ ሺ1000ሻሺ12%ሻ 30365 ൌ ሺ1000ሻሺ12%ሻ 60365 ൌ ሺ1000ሻሺ12%ሻ 120365 ൌ ሺ1000ሻሺ12%ሻ 180365
ൌ 1000 1 12% 30365 ൌ 1000 1 12% 60365
1019.73
ൌ 1000 1 12% 180365
1059.18
ൌ 1000 1 12% 120365
1039.45
Interest amount is proportional to principal, rate, and time
days 00
interest
Present Value
30 60 90 120 180
ൌ . .
ൌ 1 . 365
1000
0
Note: “Present value” often means “today”, “now”, but may mean “earlier than” or “to the left of future value”.
Similarly, “future value” means “later than or to the right of present value.
Future Value
Simple interest … IS SIMPLE!
7
Example 8.4: An investor owns an asset that will be worth $100 000 in
120 days. If the investor sells it today when the discount rate is 11.00%,
what will the investor sell it for now?
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Interest amount is proportional to principal, rate, and time
Identify then solve:
S
A
i
n
100 000
?
11%
120/365
ൌ 100 000 1 0.11 120365 ିଵ ൌ 96 509.78
ൌ 1 . ିଵ
Re-arrange
Simple interest … IS SIMPLE!
8
Example 8.7: What is the yield (rate of return) earned on a $50 000
deposit with a maturity value of $50 975 maturing in 93 days?
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Interest amount is proportional to principal, rate, and time
Identify then solve:
S
A
i
n
50 975
50 000
?
93/365
50 975 ൌ 50 000 1 93365
⇒ ൌ
ହଽହ
ହ
െ 1 ଷହ
ଽଷ
ൌ 0.07653 ൌ 7.65%
ൌ 1 . 365 െ ൌ . .50975 െ 50000 ൌ 50000. . 93365
⇒ ൌ
50975 െ 5000050000 36593 ൌ 0.07653 ൌ 7.65%
OR
Interest is difference
between the first
and last cash flows
This is the rate
over 93 days
This scales up the 93-day
rate into an annual rate
Simple interest … IS SIMPLE!
9
Example 8.9: A commercial bill with a face value of $100 000 and 180
days to maturity is purchased with a yield of 7.85%. The bill is held for 50
days then sold at a yield of 7.35%. (a) What is the rate of return of the
original bill? (b) What is the Holding Period Yield?
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
S
A
i
n
100 000
? (Buy Price)
7.85%
180/365
100 000 ൌ 1 0.0785 180365
⇒ ൌ 100 000 1 0.0785 180365 ିଵ
ൌ 96 273.05
ൌ 1 . 365
The HPY is the annualized return of the bill from when bought till sold ൌ ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
S
A
i
n
100 000
? (Sell Price)
7.35%
(180-50)/365
100 000 ൌ 1 0.0735 130365
⇒ ൌ 100 000 1 0.0735 130365 ିଵ
ൌ 97 448.97
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
ൌ
ଽସସ଼.ଽିଽଶଷ.ହ
ଽଶଷ.ହ ൈ ଷହହ ൌ 0.089166 ൌ 8.92%
Remaining period
At the beginning 50 days later
Return over d days Scaling factor to turn the return into a 1-year return
This is the rate
over 50 days This scales up the 50-day
rate into an annual rate
Simple interest … SIMPLIFIED
10
The textbook uses different formulas…or what LOOK LIKE different formulas,
but the underlying formula is the same!
DON’T GET CONFUSED! THEY’RE THE SAME UNDERLYING FORMULAS!
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
SIMPLY IDENTIFY EACH VARIABLE AND THEN SOLVE!
Practice problem – Your turn!
11
A commercial bill with a face value of $100 000 has 85 days to maturity is bought for $98 950 and sold 50 days later for
$99 450 (a) What is the yield when the bill was purchased? (b) What is the Holding Period Yield?
ൌ 1 . 365
soln
Simple Interest vs. Simple Discount
12
Interest Amount = Present value x Rate x Time
ൌ ൈ ൈ
Future Value = Present Value + Interest Amount
ൌ ൌ . . ൌ 1 . ൌ 1 . 365
ൌ
365 Time is the number of periods, usually in years or part of a year.
The USA or Bankers’ Rule
convention is 360 days in a year
Discount Amount = Future value x Rate x Time
ൌ ൈ ൈ
Present Value = Future Value – Discount Amount
ൌ െ ൌ െ . . ൌ 1 െ . ൌ 1 െ . 365
ൌ
365 Time is the number of periods, usually in years or part of a year.
The USA or Bankers’ Rule
convention is 360 days in a year
D = Discount Amount
A = Present value
S = Future or Face value
r = Discount rate
d = days of discounting
I = Interest Amount
A = Present value or Principal
S = Future value
i = Interest rate
d = days of interest
Simple Interest starts with Present Future
13
1009.86
9.86 19.73 39.45 59.18
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
ൌ ሺ1000ሻሺ12%ሻ 30365 ൌ ሺ1000ሻሺ12%ሻ 60365 ൌ ሺ1000ሻሺ12%ሻ 120365 ൌ ሺ1000ሻሺ12%ሻ 180365
ൌ 1000 1 12% 30365 ൌ 1000 1 12% 60365
1019.73
ൌ 1000 1 12% 180365
1059.18
ൌ 1000 1 12% 120365
1039.45
days 00
interest
Present value
30 60 90 120 180
ൌ . .
ൌ 1 . 365
1000
0
Future value
Simple interest adds interest to the present value
You borrow $1000 at the rate of 12%
per annum. What is the interest and
value along the way?
I = Interest Amount
A = Present value or Principal
S = Future value
i = Interest rate
d = days of interest
Simple Discount starts with Future Present
14
950.68
49.32 39.45 19.73 0
ൌ . . ൌ െ
ൌ 1 െ . ൌ 1 െ . 365
ൌ ሺ1000ሻሺ12%ሻ 150365 ൌ ሺ1000ሻሺ12%ሻ 120365 ൌ ሺ1000ሻሺ12%ሻ 60365 ൌ ሺ1000ሻሺ12%ሻ 0365
ൌ 1000 1 െ 12% 150365 ൌ 1000 1 െ 12% 120365
960.55
ൌ 1000 1 െ 12% 0365
1000
ൌ 1000 1 െ 12% 60365
980.27
days 00
Discount Amount
Present value
30 60 90 120 180
ൌ . .
ൌ 1 െ . 365
Simple discount discounts off the future value
D = Discount Amount
A = Present value
S = Face or future value
r = Discount rate
d = days of discounting
You have a face value $1000 discounted
at 12% per annum. What is the discount
and value along the way?
ൌ ሺ1000ሻሺ12%ሻ 180365
ൌ 1000 1 െ 12% 180365
59.18
940.82 Face / future value
Simple discount … USA and EU, but not AUS
15
ൌ . . ൌ െ
ൌ 1 െ . ൌ 1 െ . 360
D = Discount Amount
A = Present value
S = Face or future value
r = Discount rate
d = days of discounting
Example 9.8: What is the price of a 180-day discount security issued in the USA with a face value
of $100 000 and selling at a discount of 14.75%?
ൌ 100 000
ൌ 180
ൌ 14.75%
ൌ ?
ൌ 1 െ . ௗ
ଷ
ൌ 100 000 1 െ 14.75% ଵ଼
ଷ
ൌ 92 625.00
Note: market convention in the USA and euromarkets
is to use 360-day year (Bankers’ Rule)
Note: 360-day year (Bankers’ Rule)
Simple discount … USA and EU, but not AUS
16
ൌ . . ൌ െ
ൌ 1 െ . ൌ 1 െ . 360
D = Discount Amount
A = Present value
S = Face or future value
r = Discount rate
d = days of discounting
Example: A €100 000 euromarket-issued discount security with a 180-day maturity was issued
140 days ago for €98 899 is currently selling for €99 705? (1) At what discount rate was it issued
at, and (2) what is the current discount rate?
ൌ 100 000
ൌ 180 െ 0
ൌ?
ൌ 98 899
ൌ 1 െ . ௗ
ଷ98 899 ൌ 100 000 1 െ ଵ଼
ଷ
⇒ ൌ 1 െ 98899100000 ൈ 360180
ൌ 0.022020 = 2.20%
Note: 360-day year (Bankers’ Rule)
(1) At issue discount rate (2) Current discount rate
ൌ 100 000
ൌ ሺ180 െ 140ሻ
ൌ?
ൌ 99 705
ൌ 1 െ . ௗ
ଷ99 705 ൌ 100 000 1 െ ସ
ଷ
⇒ ൌ 1 െ 99 705100000 ൈ 36040
ൌ 0.026550 = 2.66%
Practice problem!
17
ൌ 1 െ . 365
A $100 000 US-issued discount security has 95 days to maturity and currently selling for $98 440
(1) What is the current discount rate? (2) If held until maturity, what is the Holding Period Yield?
ൌ 1 െ . 360
soln
Learning Objectives
Viney & Phillips Chapter 9:
Short‐term debt
LO 9.1‐9.4: Understand the
purpose and characteristics of
short‐term debt financing
LO 9.5: Learn to value discount
securities
LO 9.6‐9.8: Explain other forms of
short‐term debt instruments
18
LO 9.1
Purpose of short‐term debt
• Imagine you are the owner of an up‐market interior design
firm. Your business financial needs include:
– Rent: offices and showrooms
– Net working capital: demo designs, work in progress
materials, etc
– Salaries: Full‐time and part‐time staff
• Business is going great! But you have cash flow timing
problems: You need to pay rent, NWC, and salaries before
your customers pay you. Does that mean you have
managed your business poorly? NO! TIMING PROBLEM!
– Most businesses run into this problem
– Especially when a business is growing
• Short‐term debt financing helps businesses to bridge cash
flow timing problems
• Matching principle (from week 1) still applies: fund short‐
term needs with short‐term sources
– Characteristics: less than 1‐year, temporary need
– However, business growth, because it is more permanent,
should be funded with long‐term funding, e.g., equity
Short‐term financing instruments:
For small‐ to medium‐sized firms
• Trade credit
• Bank overdrafts
• Inventory finance, accounts
receivable financing, factoring
For large‐sized firms
• Commercial bills (of exchange)
• Promissory notes (commercial
paper)
• Negotiable certificates of deposit
19
LO 9.2
Trade credit
• Imagine you are an electrical fittings supplier. You
want tradie electricians to get their fittings from
you, so you offer them attractive payment terms:
– Well‐known repeat tradie customers: “No payment
for 30 days”
– Other repeat tradies: “No payment for 7 days”
– Unknowns: “CASH ON DELIVERY”
• When offering “no immediate payment” terms,
you are offering “Trade Credit”
– You are providing short‐term financing of your
customers’ purchases from you
– Trade credit is a deal sweetener
• In Australia, a significant volume of business is
financed by trade credit
– RBA estimates around $100 Billion
20
LO 9.2
Trade credit
• You offer trade credit, but you would like
customers to pay early, so you provide a discount
if they do so.
• Invoice contains trade terms: “2/10, n/30”
– “2/10” means 2% discount on the $5500 if paid
within 10 days
– “n/30” means that the net amount of $5500 must be
paid within 30 days
• As the customer, should you pay early or not?
How do you decide?
– It depends on your opportunity cost of capital or
alternative use of the funds
– If your capital funding cost is less than the savings you
get from paying early, then pay early
– But if your funding cost is more than the savings, then
delay payment for as long as you can
– How does this work? See example on the next slide.
21
Invoice
Purchase date: 7 June 2021
Electrical fittings: $5500
Terms: 2/10, n/30
LO 9.2
Trade credit
• Opportunity cost
ൌ
ଶ
ଵିଶ
ൈ
ଷହ
ଷିଵ
ൌ 0.372449
ൌ 37.24%
• If your after‐tax cost of capital is 20% (say) or your
alternative use of surplus cash only returns 23% (say), then
borrowing money to get a 37.34% discount is great deal, so
pay the bill early! Benefit = 37.34% ‐ 23% = 14.34%
• However, if your after‐tax cost of capital is 40% (say) or
your alternative use of surplus cash returns 42% (say), then
borrowing money to pay early means a lower return rate
and therefore losing money. In this case, wait for as long as
you can before paying the bill. Benefit = 37.34‐42= ‐ 4.66%
• Of course, you may not actually borrow the money to pay
the bill. “Borrowing money” expresses the idea that money
is not free – there is always an opportunity cost to get it.
22
Invoice
Purchase date: 7 June 2021
Electrical fittings: $5500
Terms: 2/10, n/30
ൌ
% 100% െ % ൈ 365
LO 9.3
Bank overdrafts
• Bank overdrafts are a major source of short‐term
finance
• An overdraft helps bridge short‐term cash flow
timing mismatches
– A firm needs to pay recurring month‐end expenses
such as salaries, rental, and networking capital needs
– But its customers won’t pay cash until after the start
of next month
• An overdraft facility allows a firm to overdraw its
operating account up to an agreed amount, for
which the bank charges interest
– The interest rate charge = prime rate + margin
– Prime rate is the firm’s reference rate and usually
compared with the bank bill swap rate (BBSR), a
floating short‐term rate
– Margin is the extra percentage above the prime rate,
indicating the credit risk of the borrower
23
LO 9.8
Inventory finance
• Inventory finance
– Different types:
– Floor plan finance
• Typical relationship between motor vehicle
dealers and finance companies
• The car dealer buys the vehicles direct from the
manufacturer and then promotes to customers
the finance company’s financing package
• In return, the finance company offers the
customer lower than market borrowing rates
making it attractive for the customer
– Bailment
• Takes floor plan finance a little further. The
finance company buys vehicles direct from the
manufacturer. The car dealer sells to customers
on behalf of the finance company.
• The car dealer promotes the financing package
offered at good rates. On sale, vehicle ownership
is passed from the finance company (bailor)
through the dealer (bailee) to the customer.
24
LO 9.8
Accounts receivable financing
and Factoring
• Accounts receivable financing
– A firm can borrow money from a finance company by
using its accounts receivable as collateral
– Not all the firm’s debtors are acceptable collateral,
e.g. unpaid debtors owing for more than 90 days are
excluded
• Factoring
– A firm can sell its accounts receivable to a factor
(finance) company, which takes on the liability of
collecting outstanding debts from debtors
– The sale of accounts receivable may be at a significant
discount to its book value, which means factor
financing is expensive for small firms
– However, for small firms where cash flow is often
difficult, the high cost of factor financing may be
worth it in the short‐run.
25
LO 9.4
Commercial bills
• So far, we have talked about small‐ to medium‐ sized firms.
We now look at large corporations.
• Large corporations raise short‐term debt through the
wholesale money market by issuing:
– Bills of exchange
– Promissory notes
– Negotiable certificates of deposit
• Bills of exchange are categorized as:
– Trade bills:
• used for financing international trade transactions
– Commercial bills:
• used for domestic borrowing and may not relate to any specific
transaction or trade purpose.
• Three types:
1. Bank‐accepted bill: A bank puts their name on the bill as the
acceptor endorsing it and increasing its credit‐worthiness
2. Bank‐endorsed bill: A bank, when selling it to another money
market party, signs the back of the bill providing endorsement for
the bill, making it more credit worthy. This forms a chain of
endorsement.
3. Non‐bank bills have no bank endorsement and trade on the
known creditworthiness of the corporate issuer itself.
26
LO 9.4
Commercial bills: features
• Important features of commercial bills include:
– A discount security with a fixed face value that is payable in
the future and hence issued at a discount.
– Pays no interest, hence sold at a discount to attract buyers
– The discount rate depends on the current market return
rate or yield for that type of bill
– The return to the bill holder depends on the difference
between purchase price and face value
– Issued by large‐ and medium‐sized firms which have the
scale economies to enter the wholesale money market
(small firms won’t qualify).
• Commercial bills involve several parties:
– Drawer: bill issuer
– Acceptor: the payer of the face value (i.e., bank)
– Payee: the issuer or a subsidiary firm of the issuer
– Discounter: bill purchaser (could be acceptor), who pays a
discount to receive the face value and becomes the owner
– Endorser: the previous bill owner who endorses (signs) the
back of the bill before selling it to the next owner
27
LO 9.4
Commercial bills: funds flow
• The flow of funds
Other features of commercial bills
• Maturity of 30 to 180 days
• Minimum face value is $100 000
• How do banks earn fees from the
drawer?
• Playing acceptor role
• Playing discounter role
• Playing acceptor and discounter
28Why are there different roles in commercial bills?
LO 9.4
Commercial bills: motivations
• Why issue a bill of exchange? Advantages for Borrowers
– The drawer (borrower) needs short‐term cash for a certain
period in days: 30, 45, 60, 90, 180 days
– The commercial bill market is very liquid and is easy for
drawer to raise short‐term funds
– Banks often provide a roll‐over facility that potentially
converts the short‐term into a medium‐ to long‐term loan
• Why purchase / sell a bill of exchange? Investor advantages
– An investor (e.g. a company) has excess short‐term funds
and wants to park it for a few days, weeks, or months
– The investor has a matching holding period and can hold a
newly issued bill until maturity (e.g., 30, 45, 60, 90, 180
days)
– A bill investor has a sudden cash flow shortage and sells it
in the highly liquid bill market. The ability to sell the
security at anytime is what attract many bill investors in the
first place
– An alternative security can be purchased at a better rate so
the bill investor sells to restructure their portfolio
29
Bill roll-over facility converts a $500 000 short-term
debt to medium- and long-term debt
(How does this work? To be explained)
LO 9.5 Valuing discounted securities
30
The commercial bill roll-over facility converts a $500 000 face value 180-day short-term bill to a 2-
year medium-term loan. At the beginning of the first 180 days, at t=0, the bill is discounted for the
first time and the drawer receives $479 317.14. At the end of the first 180 days, the Drawer should
pay back $500 000 face value, but instead the bill is discounted again for another 180 days and the
drawer only pays the difference between the face value and discounted price, $21 813.18,
effectively borrowing the original price for another 180 days. This is repeated two more times.
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
I = Interest Amount
A = Present value or Principal
S = Future or face value
i = Interest rate or yield
d = days of interest
ൌ 1 . ିଵ
ൌ 1 . ௗ
ଷହ
ିଵ
ൌ 1 . 365
ൌ
1 . 365 ൌ 500 0001 8.75% 180365 500 0001 9.25% 180365
500 0001 9.30% 180365 500 0001 9.25% 180365
Current market yield
Commercial bill rollover facility explainedSimple interest valuation
Discount the
face value with
current yield Discount the
face value with
current yield
Discount the
face value with
current yield Discount the face value with
current yield
500 000 500 000 500 000 500 000
LO 9.5 Valuing discounted securities
31
Textbook uses different formulas
ൌ
ൈ
100 ൈ
ൌ 100 ൈ
ൈ
ൌ
െ
ൈ ൈ 100
I recommend ones you have seen already
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365 I = Interest AmountA = Present value or PrincipalS = Future or face valuei = Interest rate or yield
d = days of interest
Simple interest valuation
Annualized Holding Period Yield
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
Return over d days Scaling factor to turn the
return into a 1-year return
LO 9.5 Valuing discounted securities
32
Example 9.3
A company funds its short-term inventory needs issuing a 30-day bank accepted bill with
a face value of $500 000. It approaches two discounters that offer different yields, one
with 9.52% and another with 9.48%. Which one should it accept?
I = Interest Amount
A = Present value or Principal
S = Future or face value
i = Interest rate or yield
d = days of interest
THE QUESTION: Which variable are we trying to find in the formula?
ൌ 500 000
ଵ ൌ 9.52%
ଶ ൌ 9.48%
Have: Want:500 000 ൌ ଵ 1 9.52%. 30365 ⇒ ଵ ൌ 496 118.05500 000 ൌ ଶ 1 9.48%. 30365 ⇒ ଶ ൌ 496 134.23
Accept the one returning highest present value,
i.e., highest loan amount.
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Simple interest valuation
Annualized Holding Period Yield
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
Return over d days Scaling factor to turn the
return into a 1-year return
LO 9.5 Valuing discounted securities
33
Example 9.7 (following Example 9.3)
A discounter discounts a company’s 30-day bank accepted bill with a face value of $500
000 with a yield of 9.48% representing a price of $496 134.23. Seven days later, the
discounter sells the bill in the short-term money market for $497 057.36 and is held until
maturity. Calculate (1) yield of the discounter and (2) yield of holder at maturity
I = Interest Amount
A = Present value or Principal
S = Future or face value
i = Interest rate or yield
d = days of interest
ൌ . . ൌ െ
ൌ 1 . ൌ 1 . 365
Simple interest valuation
Annualized Holding Period Yield
ൌ
ௌ ି௨௬
௨௬
ൈ
ଷହ
ௗ
Return over d days Scaling factor to turn the
return into a 1-year return
ൌ 496 134.23
ൌ 497 057.36
ℎ ൌ ൌ 7
Original Discounter: Annualized Holding Period Yield
ൌ
ସଽ ହ.ଷ ିସଽ ଵଷସ.ଶଷ
ସଽ ଵଷସ.ଶଷ ൈ ଷହ ൌ 0.09702 ൌ 9.70%
ൌ 496 134.23
ൌ 500 000
ℎ ൌ ൌ 30 െ 7
Holder to maturity: Annualized Holding Period Yield
ൌ
ହ ିସଽ ହ.ଷ
ସଽ ହ.ଷ ൈ ଷହଶଷ ൌ 0.093949 ൌ 9.39%
LO 9.6
Promissory notes (P‐notes)
• Promissory notes
– P‐notes are an unconditional written promise to pay a sum
of money on demand at future date to a specified person or
bearer
– They are discount securities with a face value payable at
maturity
– They are an international security
– They are also called “Commercial Paper”
– They are unsecured notes
– They are typically only issued by large firms with an
excellent credit reputation that attracts investors, i.e.,
investment grade rating
• Differences with bills; pros/cons
– Unlike bills of exchange, there is no acceptor, therefore also
called “one‐name paper”.
– Unlike bills of exchange, there is no endorsement of the P‐
note when sold in the secondary market.
• Good for seller: no contingent liability
• Bad for buyer: must trust the credit worthiness of the issuer
What does “unsecured” mean?
Why would an investor accept this
condition?
34
LO 9.7
Negotiable certificates of
deposit (CD)
• Negotiable certificates of deposits (CD)
– A short‐term discount security with
typical maturity of 180 days
– Issued by banks to attract institutional
investors
– Large and active secondary market that
provides liquidity for investors
– Issued by a bank to manage their
liabilities and seasonal liquidity needs
• E.g., During the Christmas shopping period,
increased demand from credit card
spending is funded by issuing CD
• E.g., Financial year end spending means
business and consumer demand requires
funding from new CD issues
35
Summary
• Short‐term debt include instruments with maturity < 1 year
• Short‐term debt options for small‐ to medium‐sized firms:
– Trade financing
– Overdraft facilities
– Inventory finance, Accounts receivable financing, and Factoring
• Short term debt options for large good quality credit firms
– These instruments are issued and traded in the Money Market
– Commercial bills – issued by firms, accepted or discounted by banks, endorsed on sale
– Promissory notes (commercial paper) – issued by firm, no acceptor or endorsements
– Negotiable certificates of deposit (CD) – issued by banks
• Valuing short‐term debt
– Use Simple interest valuation – AUS issued discount securities, 365 days/year
– Use Simple discount valuation – USA and euromarket issued discount securities , 360 days/year
36
Solutions to Practice Problems
37
Practice problem – soln!
38
A commercial bill with a face value of $100 000 has 85 days to maturity is bought for $98 950 and sold 50 days later for
$99 450 (a) What is the yield when the bill was purchased? (b) What is the Holding Period Yield?
0 85
98 950 100 000
0 50
98 950 ?
ൌ 1 . 365
100 000 ൌ 98 950 1 . 85365
= 99 450
ൌ
99 450 െ 98 95098 950 ൈ 36550
ൌ 0.03689 ൌ 3.69%100 00098950 െ 1 ൌ . 85365100 00098950 െ 1 ൈ 36585 ൌ
ൌ 0.04556 ൌ 4.56%
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Practice problem! soln!
39
ൌ 1 െ . 365
A $100 000 US-issued discount security has 95 days to maturity and currently selling for $98 440
(1) What is the current discount rate? (2) If held until maturity, what is the Holding Period Yield?
ൌ 1 െ . 360
0 95
98 440 100 000
98440 ൌ 100000 1 െ . 95360
ଽ଼ସସ
ଵ
ൌ 1 െ . ଽହ
ଷ
ൌ 1 െ ଽ଼ସସ
ଵ
ൈ
ଷ
ଽହ ൌ 0.05911 ൌ 5.91%
ൌ
100000 െ 9844098440 ൈ 36095
ൌ 0.06005 ൌ 6.01%US and EU use Banker’s rule,
360-day year
US and EU use
Banker’s rule,
360-day year
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