Unit 5: Money Markets
Lecture 2: Money Markets – Worked Examples
Yield Instruments
Money Markets
Yield Instruments
Yield (or Interest Add-On) Instruments:
•
Fixed Deposits
•
Negotiable Certificates of Deposit (NCD)
•
Repurchase agreements
3
Money Markets
Yield Instruments
Example 1: Fixed Deposit
Calculate the interest earned on a fixed deposit from 29/01/10 to 12/04/10 at a rate
of 11.25% and an amount of R10 million
d
 i
Interest earned = PV × 
× 
 100 B 
 11.25 73 
= 10,000,000 × 
×

 100 365 
= R 225,000
4
Money Markets
Yield Instruments
Example 1: NCD (Primary Market)
What amount of money is repaid to an investor who purchased an NCD with a face
value of R10 million at a coupon rate of 12.18% for a period of 181 days?
  c d im  
×
MV = N × 1 + 
 
  100 B  
  12.18 181  
= 10,000,000 × 1 + 
×
 
  100 365  
= R10,603,994.52
5
Money Markets
Yield Instruments
Example 2: NCD (Secondary Market)
You invest in a secondary market NCD with a face value of R5,000,000. The NCD
was issued at a coupon of 12.25% for 270 days and is currently trading at a yield of
11.85%, with 92 days left to maturity. What amount of money did you invest?
  c d im  
MV = N × 1 + 
×
 
  100 B  
  12.25 270  
= 5,000,000 × 1 + 
×
 
  100 365  
= R5,453,082.19
MV
P =
  i y d sm  
1 + 
 
×

  100 B  
5,453,082.19
=
  11.85 92  
×
1 + 

  100 365  
= R5,294,930.59
6
Money Markets
Yield Instruments
Example 3: NCD (Primary and Secondary Market)
Bank A issues a NCD, with a face value of R10m, issued for a period of 91 days
at a rate of 11.5% p.a.
This is a PRIMARY MARKET calculation
Bank B now purchases the NCD at 10.95%. There are 30 days left to maturity
• What did Bank B invest? (secondary trade)
This part is the
SECONDARY
MARKET
calculation
7
Money Markets
Yield Instruments
Example 3: NCD (Primary and Secondary Market)
Bank A issues a NCD, with a face value of R10m, issued for a period of 91 days at
a rate of 11.5% p.a.
This is a PRIMARY MARKET calculation
How did we calculate the MV of this instrument (in primary market)?
91
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = 10000000 1 + 0.115 x
365
Using your financial calculator:
= 𝑅𝑅𝑅𝑅 286 712.33
N=1; PV = -10,000,000’; I% = 91/365 x 11.5; PMT = 0
 FV = 10 286 712.33 = MV (Maturity Value)
8
Money Markets
Yield Instruments
Example 3: NCD (Primary and Secondary Market)
How do we calculate what BANK B invested?
Calculation:
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 =
10000000 1 + 0.115x
1 + (0.1095x
91
365
30
)
365
RECOGNISE
THIS?
𝑅𝑅10 286 712.33
= 𝑅𝑅𝑅𝑅 194 957.71
Step 1: N=1; I%=91/365x11.5; PV = -10000000; PMT = 0  FV = 10 286 712.33
Step 2: I% = 30/365 x 10.95  PV = 10 194 957.71
9
Money Markets
Yield Instruments
Example 4: NCD (Primary Market)
All NCDs have interest payable at maturity and are traded on a yield basis
Amount invested / Face Value = R 1 000 000
Issue date = 1 April 2008
Maturity date = 31 July 2008
d = 121 days
𝒄𝒄𝒚𝒚 = 12%
10
Money Markets
Yield Instruments
Example 4: NCD (Primary Market)
121
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = 1000000 1 + 0.12 x
365
= 𝑅𝑅𝑅 039 780.82
Using your financial calculator:
N=1; PV = -1000000’; I% = 121/365 x 12; PMT = 0
 FV = 1 039 780.82 = MV (Maturity Value)
11
Money Markets
Money Market Instruments
Example 4 (cont.): NCD (Secondary Market)
MV = R 1 039 780.22
Contract date = 29 June 2008
Maturity date = 31 July 2008
d = 32 days
𝒊𝒊𝒚𝒚 = 12%
12
Money Markets
Yield Instruments
Example 4 (cont.): NCD (Secondary Market)
1039780.82
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 =
32
1 + 0.12 x
365
= 𝑅𝑅𝑅 028 955.64
Using your financial calculator:
N=1; I% = 32/365 x 12; PMT = 0; FV=1039780.82
 PV = 1 028 955.64 = Price / Sale Proceeds
13
Money Markets
Yield Instruments
Example 5: NCD (Secondary Market – Dirty Price)
‘Dirty’ price of a £1,000,000 NCD with an original maturity of 182 days, a coupon
of 7%, and remaining maturity of 60 days at a yield of 6.5% (Act/365)
£1,000,000 x [1 + (7% x 182/365)]
= £1,023,963.13
[1 + (6.5% x 60/365)]
‘Dirty price’ = ‘Clean price’ + accrued interest
Acc int = £1,000,000 × (𝑐𝑐×𝑑𝑑𝑖𝑖𝑖𝑖 ) = £1,000,000 × (0.07×(182−60)) = £23,397.26
𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦
365
‘Clean’ = £1,023,963.13 - £23,397.26 = £1,000,565.87
14
Money Markets
Yield Instruments
Example 6: NCD Table
ABSA
NCD rate
Bid
Offer
5.15
4.90
3m (30 day)
4.95
4.70
6m (180 day)
4.85
4.60
12m (360 day)
Given the quotes above, at what rate would you be able to buy a 6m
NCD from the bank? You always buy at the offer rate
15
Money Markets
Yield Instruments
Example 6: NCD Table
Three months later you need money urgently for bridging finance,
and obtain the following rates from Standard Bank:
SBSA
NCD rate
Bid
Offer
5.25
5.10
3m (30 day)
5.15
5.00
6m (180 day)
At what rate can you sell the NCD to Standard? You always sell at bid rate
16
Discount Instruments
Money Markets
Discount Instruments
Discount Instruments:
•
Treasury Bills
•
Bankers’ Acceptances
•
Promissory Notes
•
Commercial Paper
18
Money Markets
Discount Instruments
Example 7: Treasury Bill (Primary Market)
Calculate the amount to be invested in a 92-day Treasury bill at a rate of
10.25% and a face value of R10m.
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 =
10000000 x 1 − 0.1025
92
365
= R9 741 643.84
19
Money Markets
Discount Instruments
Example 8: Treasury Bill (Primary Market)
A tenderer (buyer) decides the discount rate that he/she would like to earn
is 15.80%.
1. The discount price/tender price will be:
Price = 100 – 100x(15.80% x 91/365)
= R96.061
He/she will submit a price of R96.06
2. The discount rate will then be:
Discount rate = (100 – 96.06) x 365/91
= 15.80%
20
Money Markets
Discount Instruments
Example 9: Treasury Bill (Primary and Secondary Market)
Bank A buys a 92-day Treasury bill that is issued at a rate of 10.25% with a
face value of R5 million (Remember this is the primary market transaction)
After 33 days the bank sells this T-Bill at 9.90% (This is the secondary
market transaction)
• What did the bank pay for the Treasury bill in the primary market?
• What did the bank receive when they sold the bill? (secondary market)
21
Money Markets
Discount Instruments
Example 9 (cont.): Treasury Bill (Primary Market)
What did Bank A pay for the TB?
92
= 5,000,000 − (5,000,000 × 0.1025 ×
)
365
= 4,870,821.92
22
Money Markets
Discount Instruments
Example 9 (cont.): Treasury Bill (Secondary Market)
What did Bank A receive when they sold the TB after 33 days at a rate of
9.90%?
59
= 5,000,000 − (5,000,000 × 0.0990 ×
)
365
= 4,919,986.30
23
Money Markets
Discount Instruments
Example 10: Banker’s Acceptance (Primary Market)
Issue mathematics: Proceeds payable to the drawer (the company) issued at discount)
Nominal Value
R 1 000 000
All in discount rate
10.70%
days
90
Proceeds
=R1 000 000 – (1 000 000 x (0.1070 x 90/365))
=R973 616.44
24
Money Markets
Discount Instruments
Example 11: Banker’s Acceptance (Primary Market)
A bankers acceptance with a nominal value of R50 000 000 is issued at a
discount of 9.95% for a period of 91 days. An acceptance commission of
1.5% of the nominal value is payable.
Calculate the proceeds if you include the acceptance commission
  9.95 + 1.5 91 
P = 50m × 1 − 
×

365 
  100
= R 48 572 671.23
25
Money Markets
Discount Instruments
Example 11 (cont.): Banker’s Acceptance (Primary Market)
A bankers acceptance with a nominal value of R50 000 000 is issued at a
discount of 9.95% for a period of 91 days. An acceptance commission of
1.5% of the nominal value is payable:
Calculate the proceeds if you exclude the acceptance commission
  9.95 91 
P = 50m × 1 − 
×

  100 365 
= R 48 759 657.53
26
Money Markets
Discount Instruments
Example 12: Commercial Paper
You are interested in investing in a commercial paper issue with a face
value of $20 million and181 days to maturity at a yield of 5.05%
Calculate the amount that you would need to invest
20 ,000 ,000
P=
181 
 5.05
1 +
×

360 
 100
= $19,504,768.51
27
Discount to Yield Instrument
Money Markets
Discount to Yield Instrument
Example 13: Commercial Paper (Zero Coupon)
A small South African company issues zero-coupon commercial paper at
the going YTM (yield) rate of 7.5% p.a. for 182-days, and a face value (FV)
of R1m. Calculate the investment price?
NB! We are looking for the discounted price to FV
1,000,000
Price
Pr ice =
182 

1 +  0.075 ×

365 

P = R 963950,88
Note: At maturity recieve R 1 000 000.00
i.e. the Future value
29
Money Markets
Discount to Yield Instrument
Example 14: Commercial Paper (Zero Coupon)
A CP of face value of EUR 10 million with 91 days to maturity at a yield of
4.10%
10 ,000 ,000
91 
 4.1
×
1 +

360 
 100
= EUR 9,897,424.20
30
Returns and Yields
Money Markets
Returns and Yields
Example 15: Commercial Paper (Zero Coupon)
Example: NCD, issued for 91 days at 11.15% p.a. OR TB, issued for 91 days at
10.80% p.a.
Conversion from discount to yield
Formula:
Example:
Discountrate
 
days 
−
×
discountra
te
1



Base

 
Yield =
Yield =
10.80%
 
91 
1 − 10.80% × 365 

 
= 11.10%
32
Money Markets
Returns and Yields
Example 15 (cont.): Comparing Discount to Yield Issued Securities
Example continued: NCD, issued for 91 days at 11.15% p.a. OR TB, issued for 91
days at 10.80% p.a.
Conversion from yield to discount
Formula:
Discountrate =
Yield
 
days 
+
×
yield
1



Base

 
Example:
Discountrate =
11.15%
 
91 
+
×
1
11
.
15
%



365 
 
Discountrate = 10.85%
33
Money Markets
Returns and Yields
Example 16: Comparing Discount to Yield Issued Securities
Convert the following rates:
id = 6.7%, d = 30, B = 365 to iy
iy = 12.3%, d = 30, B = 365 to id
iy
id =
id =
100
 iy
d
× 
1 + 
 100 B 
0.123
30 

1 +  0.123 ×

365


= 12.1769%
iy
iy =
id
100
=
d
 i
1 − d × 
 100 B 
0.067
30 

1 −  0.067 ×

365


= 6.7371%
34
Money Markets
Returns and Yields
Example 17: Holding Period Return – Yield Instruments
Calculate the holding period return for the NCD, with a face value of R10m, issued
for a period of 91 days and a maturity value of R10,277,986.30.
  10,277,986.30   36500
= 11.15%
 − 1 ×
𝑖𝑖ℎ =  
91
  10,000,000  
Using the financial calculator
N =1
PV = -10,000,000
FV = 10,277,986.30, PMT = 0, I% = 2,7799 (x 365/91) to annualize
35
Money Markets
Returns and Yields
Example 17 (cont.): Holding Period Return – Yield Instruments
Calculate the holding period return for the NCD, if it was sold after 61 days for
issued for a R10 186 309.52,and has a maturity value of R10,277,986.30.
  10,277,986.30   36500
= 10.95%
 − 1 ×
𝑖𝑖ℎ =  
30
  10,186,309.52  
Note: 10.95% is the true
yield on this investment.
Using the financial calculator
N =1
PV = -10,186,309.52
FV = 10,277,986.30
PMT = 0
I% = 0.90 (x 365/30) = 10.95%
36
Money Markets
Returns and Yields
Example 18: Holding Period Return – Yield Instruments
You invested in a 270 day NCD with a face value of R10,000,000 and a coupon of
12.25%. You sold the NCD at a yield of 11.85% with 92 days left to maturity.
Calculate your HPY on this NCD?
ih
  12.25 270   
×
 
 1 + 
100 365    365



−1 ×
=
 11.85 92    178

 1 +  100 × 365   
 

= 12.0955%
37
Money Markets
Returns and Yields
Example 19: Price, Yield and EAY – Discount Instrument
Assume that you decide to tender for Treasury Bills at the weekly Friday SARB
tender (91 day TBs) at a rate of 10.75%. Calculate the tender price
  10.75 91 
P = 100 × 1 − 
×

  100 365 
= 97,32% (97.3199)
38
Money Markets
Returns and Yields
Example 19 (cont.): Price, Yield and EAY – Discount Instrument
Assume that you decide to tender for Treasury Bills at the weekly Friday SARB
tender (91 day TBs) at a rate of 10.75%. Calculate the yield (both methods)
100 − 97.32 365
iy =
×
97.32
91
= 11.05% (11.0455)
OR
iy =
0.1075
91 

1 −  0.1075 ×

365 

= 11.05% (11.0460 )
39
Money Markets
Returns and Yields
Example 19 (cont.): Price, Yield and EAY – Discount Instrument
Assume that you decide to tender for Treasury Bills at the weekly Friday SARB
tender (91 day TBs) at a rate of 10.75%. Calculate the effective rate?
 11.05

100 
ie = 1 +


365
91 

365
91
−1
= 11.52% (11.5168)
40
Money Markets
Returns and Yields
Example 20: Holding Period Yield and EAY – Discount Instrument
You purchased a Treasury Bill issued for 91 days at 12.35%. You sell the Bill after 33
days at 12%. Assuming a face value of R5,000,000. Calculate your holding period
yield?
  i
d 
P = N × 1- d × sm 
  100 B 
  12.35 91 
= 5,000,000 × 1-
×

100
365



= R 4,846,047.95
  i
d 
P = N × 1- d × sm 
  100 B 
  12.00 58 
= 5,000,000 × 1-
×

100
365

 
 FV   B
ih = 
 − 1 ×
 PV   d is
 4,904,657.53   365
= 
 − 1 ×
 4,846,047.95   33
= 13.38%
= R 4,904,657.53
41
Money Markets
Returns and Yields
Example 20 (cont.): Holding Period Yield and EAY – Discount Instrument
You purchased a Treasury Bill issued for 91 days at 12.35%. You sell the Bill after 33 days at
12%. Assuming a face value of R5,000,000. Calculate your holding period yield?
𝑖𝑖ℎ =
𝑖𝑖ℎ =
𝑖𝑖𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑑𝑑𝑠𝑠𝑠𝑠
x
100
𝐵𝐵
𝑖𝑖
𝑑𝑑
1 − 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 x 𝑖𝑖𝑖𝑖
100
𝐵𝐵
1−
12
58
x
100 365
12.35
91
1−
x
100
365
1−
𝑖𝑖ℎ = 13.38%
𝐵𝐵
−1 x
𝑑𝑑𝑖𝑖𝑖𝑖
365
−1 x
33
42
Money Markets
Returns and Yields
Example 20 (cont.): Holding Period Yield and EAY – Discount Instrument
You purchased a Treasury Bill issued for 91 days at 12.35%. You sell the Bill after 33
days at 12%. Assuming a face value of R5,000,000. Calculate the effective yield?
 iy



100
ie = 1 +

B


d


B
d
−1
 13.38

100 
= 1 +

365
33 

= 14.2247%
365
33
−1
43
Money Markets
Returns and Yields
Example 21: Price and Holding Period Yield – Discount Instrument
Assume that you decide to tender for Treasury Bills at a SARB special tender (135 day
TBs) at a rate of 11.55%. Calculate the tender price?
  11.55 135 
P = 100 × 1 − 
×

  100 365 
= 95,73% (95.7281)
44
Money Markets
Returns and Yields
Example 21 (cont.): Price and Holding Period Yield – Discount Instrument
Assume that you decide to tender for Treasury Bills at a SARB special tender (135 day
TBs) at a rate of 11.55%. Calculate the yield (both methods)?
100 − 95.73 365
iy =
×
95.73
135
= 12.06% (12.0598)
iy =
OR
0.1155
135 

1 −  0.1155 ×

365 

= 12.07% (12.0654 )
45
Money Markets
Returns and Yields
Example 21 (cont.): Price and Holding Period Yield – Discount Instrument
Assume that you decide to tender for Treasury Bills at a SARB special tender (135 day
TBs) at a rate of 11.55%. Calculate the effective rate?
 12.07

100 
ie = 1 +


365
135 

365
135
−1
= 12.53% (12.5338)
46
End of lecture 2: Money Markets – Worked Examples