Bond Yields and the Australian Economy

This assignment delves into the analysis of bond yields and their relationship with economic factors in Australia. It examines the shape of the yield curve, investigates the impact of inflation expectations on interest rates, and applies the expectations theory to predict future bond yields. Furthermore, it explores the spread between government and treasury bonds, providing insights into risk premiums.

Question 1-Part a
CAPM
Expected Return = Risk free Rate + Beta * (Expected Market Return- Risk Free Rate)
 If expected return CAPM is greater Investors Return, then share is overpriced.
 If expected return CAPM is Investors Return, then share is underpriced.
 If expected return CAPM is equal to Investors Return, then share is overpriced
Share Beta Investors Return CAPM
A 1.5 14% 11% Underpriced
B 0.6 8% 6% Underpriced
C 1.2 9% 9% Correctly priced
D 1.8 10% 12% Overpriced
Part b
Need to construct a portfolio such that Wa *14% + (1-Wa) *8%≥ 10%
Wa = 33.33%. Therefore construct a portfolio with at least 33.3% shares A
Part c -e
3
4
5
6
7
8
9
10
11
12
B C D E
Year Project A Project B Project C
0 -20000 -40000 -70000
1 18000 5000 30000
2 18000 10000 30000
3 18000 30000 40000
4 80000 50000
5 100000 180000
NPV =C4+NPV($D$1,C5:C9) =D4+NPV($D$1,D5:D9) =E4+NPV($D$1,E5:E9)
IRR =IRR(C4:C8,10%) =IRR(D4:D9,30%) =IRR(E4:E9,50%)
Profitability Index =NPV($D$1,C5:C9)/-C4 =NPV($D$1,D5:D9)/-D4 =NPV($D$1,E5:E9)/-E4

3
4
5
6
7
8
9
10
11
12
B C D E
Year Project A Project B Project C
0 (20,000) (40,000) (70,000)
1 18,000 5,000 30,000
2 18,000 10,000 30,000
3 18,000 30,000 40,000
4 80,000 50,000
5 100,000 180,000
NPV 23,233 101,374 143,085
IRR 72.45% 55.51% 56.01%
Profitability Index 2.16 3.53 3.04
c. Net Present Value
Project C has the highest NPV-143,085, therefore it is the best. It is then followed by
project B with NPV -101,374 ,and lastly project A with NPV -23,233.
d. Payback Period
PBP A = 20,000/18,000 = 1.11
PBP B= 2 + (40,000-15,000)/30,000 = 2.83
PBP C= 2 + (70,000-60,000)/40,000 = 2.25
We observe Projects A and C have a payback period less than acceptance criteria 2.75,
therefore Sharpe should accept both Project A and project C..
e.IRR and Profitability index
IRR is the rate or return that NPV = 0
Profitability Index = PV of future cash flows/initial investment
A –IRR- 72.45% and PI- 2.16
B- IRR- 55.51% and PI- 3.53
C- IRR- 56.01% and PI- 3.04

Question 2
Part a
i.20 year Loan Term
The Loan Sam will borrow is 630,000 (90% *700,000)
PV= 630,000
i= 3.5% pa
n=20 years
Annual Payments, PMT=?
We need to compute PMT using annuity formula below
PV = PMT*( 1−(1+i ¿¿¿−n)
i )
630,000= PMT*( 1−(1+3.5 % ¿¿¿−20)
3.5 % )
Solve PMT
PMT = 44,327.478
ii.25 year Loan Term
The Loan Sam will borrow is 630,000 (0.9*700,000)
PV= 630,000
i= 3.5% pa
n=25 years
Annual Payments, PMT=?
We need to compute PMT using annuity formula below
PV = PMT*( 1−(1+i ¿¿¿−n)
i )
630,000= PMT*( 1−(1+3.5 % ¿¿¿−25)
3.5 % )
Solve PMT= 38,224.642

Part b
i.20 year Loan Term
Total Interest paid = Annual Repayments * number of years – Loan Amount
=(44,327.48* 20 )-630,000
=256,549.57
ii.25 year Loan Term
Total Interest paid = Annual Repayments * number of years – Loan Amount
=(38224.64*25)-630,000
=325,616.06
Part c
i. Loan term and annual repayments
As the loan term increases, the annual loan repayment will reduce because the loan
amount will be spread over a longer time period.
ii. Loan term and total interest paid
As the loan term increases, the total interest paid will increase because firstly, the loan
amount is being repaid over a longer period and secondly the risk of default is higher
and hence a lender would require a higher interest to compensate for the additional risk
being taken.

Part d
i.20 year Loan Term
Step 1
We need to compute outstanding loan balance at year 3 using old interest rate 3.5%
Formula
O/S Loan Balance at t-3 = 630,000(1+I)3 - PMT(1+3.5 % ¿ ¿¿ 3−1)
3.5 % )
= 560,801.14
Step 2
Next we need to compute the revised loan payment using new interest rate 6% for 17
years (20-3) and equate it to the o/s loan balance calculated in step 1.
O/S Loan balance = RevisedPMT *( 1−(1+ j ¿¿¿−n)
j )
560,801.14 = RevisedPMT *( 1−(1+6 %¿¿¿−17)
6 % )
Solve RevisedPMT
Revised Payment = $53,525.56
T=0
Loan=630,000
T=3
O/S Loan
Balance=?
T=2T=1

ii.25 year Loan Term
Step 1
We need to compute outstanding loan balance at year 3 using old interest rate 3.5%
Formula
O/S Loan Balance = 630,000(1+I)3 - PMT (1+3.5 % ¿ ¿¿ 3−1)
3.5 % )
= 579,757.92
Step 2
Next we need to compute the revised loan payment using new interest rate 6% for
22 years (25-3) and equate it to the o/s loan balance calculated in step 1.
O/S Loan balance = RevisedPMT*( 1−(1+ j ¿¿¿−n)
j )
579,757.92 = RevisedPMT*(1−(1+ 6 %¿¿¿−22)
6 % )
Solve RevisedPMT
Revised Payment= 48,146.33
We observe the new loan repayment for the 20 year term is bigger than the new
loan repayment for the 25 year term
T=0
Loan=630,000
T=3
O/S Loan
Balance=?
T=2T=1

Question 3
Part a
0 1 2 3 4 5 6 7 8 9 10
4.00
5.00
6.00
7.00
8.00
Yield Curve
Jun-2007 Dec-2007 Jun-2008
Part b
The shape of yield curve is upward sloping in normal circumstances. The reason is as
the term to maturity increases, the credit risk increases, and hence an investor will
require a higher yield. In addition, according to liquidity preference theory, as the term to
maturity increases, an investor will require a higher yield to compensate for increased
opportunity risk.
Part c
From year 0 to 1, all three curves were upward sloping. However, from year 1 to 2, the
yields dropped suddenly and from year 2 to 10 the yields continued to drop but
gradually. This information tells us that the expectations regarding future inflation and
short term interest rates in the Australian economy is low

Part d
2f07 = 6.18%
Expectations theory
(1+2f07)2 = (1+1f07) *(1+1f08)
(1+0.0618)2 = (1+0.0626) *(1+1f08)
1f08 =6.098%
Therefore an investor will expect an interest rate of 6.098% on a 1 year bond in 2008
Month 1f2008
Jan 6.098%
Feb 5.935%
Mar 5.782%
Apr 6.201%
May 6.029%
Jun 6.310%
Jul 6.194%
Aug 6.064%
Sep 6.099%
Oct 6.296%
Nov 6.501%
Dec 6.578%

Part e
We observe the expected interest rates differ significantly from the actual interest rates
hence do not validate the expectations theory. The reason may be due to inflation
changes, the economy and monetary policy.
Part f
The spread is the difference between the yield of the Australian government bond and
the NSW Treasury bond. Using the arithmetic mean, the average spread was 0.5 for 3
year bonds, 0.55 for 5 year bonds and 0.53 for 10 year bonds.
The spread tells us the additional yield required by an investor to invest in treasury
bonds which in this case are more risky assets than the government bonds
Part g
Jan-2007
Mar-2007
May-2007
Jul-2007
Sep-2007
Nov-2007
Jan-2008
Mar-2008
May-2008
Jul-2008
Sep-2008
Nov-2008
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Graph showing Spread between NSW T Bills and Australian
Government Bonds
3 years
5 Years
10 Years
Spread
The graph is sloping upwards because we expect that as the term to maturity increases,
an investor will require a high yield to compensate them for liquidity and credit risk.