MAF303 – Treasury Management 2011
Topic 2 Tutorial Solutions 2011 Page 1
Topic 2 Tutorial Solutions
Question 1 – Chapter 5 Q17
An insurance company issues a $100 000 one-year bond paying 7 per cent
annually in ord
...
MAF303 – Treasury Management 2011
Topic 2 Tutorial Solutions 2011 Page 1
Topic 2 Tutorial Solutions
Question 1 – Chapter 5 Q17
An insurance company issues a $100 000 one-year bond paying 7 per cent
annually in order to finance the acquisition of a $100 000 one-year
corporate loan paying 9 per cent semi-annually. (The loan contract
requires the corporate borrower to pay half of the principal at the end of six
months and the rest at the end of the year.)
(a) What is the insurance company’s maturity gap? What does the
maturity model state about interest rate risk exposure given the
insurance company’s maturity gap?
The maturity of assets is equal to the maturity of liabilities = 1 year. Thus,
the maturity gap is zero. The maturity model concludes that the
insurance company is not exposed to interest rate risk.
(b) Immediately after the insurance company makes these investments,
all interest rates increase by 3 per cent. What is the impact on the
asset (corporate loan) cash flows? What is the impact on the liability
(one-year note) cash flows? What is the impact on the insurance
company’s net interest income?
Asset - Corporate bond cash flows
Cash flow at 1
2
year:
1. Principal $50 000
2. Interest $4 500
Cash flow at 1 year:
1. Principal $50 000
2. Interest $2 250
3. Reinvestment income $57 770
Total cash flows $110 020
(Note: Reinvestment income is: $54 500(1.12)(0.5) = $57,770 since the
cash flows received at the end of six months are reinvested at the higher
market rate of 12% = 9% + 3%.)
Without the interest rate increase, the cash flow at 1 year of the
corporate bond would have been 50,000 + 2250 + 54500*1.09 =
$109,202.5
MAF303 – Treasury Management 2011
Topic 2 Tutorial Solutions 2011 Page 2
Hence the increase in interest rate has led to an increase in the cash
flows of the company’s asset by 110,020 – 109,202.5 = 817.5
Liability - 1 year note cash flows:
Cash flow at 1 year:
1. Principal $100 000
2. Interest $7 000
Total cash flows $107 000
The cash flow of the liability is not affected by the change in interest rate
Net cash flows at 1 year for the insurance company
$110 020 cash inflow - $107 000 cash outflow = $3,020 cash inflow
which includes a $817.5 increase in interest income as a result of the
interest rate change.
(c) Assume instead that all interest rates decline by 3 per cent
immediately after the insurance company makes the above
investments. What is the impact on the asset (corporate loan) cash
flows? What is the impact on the liability (one-year bond) cash
flows? What is the impact on the insurance company’s net interest
income?
Asset - Corporate bond cash flows
Cash flow at 1
2
year:
1. Principal $50 000
2. Interest $4 500
Cash Flow at 1 year:
1. Principal $50 000
2. Interest $2 250
3. Reinvestment income $56 135
Total cash flows $108 385
(Note: Reinvestment income is: $54 500(1.06)(0.5) = $56,135 since the
cash flows received at the end of six months are reinvested at the lower
market rate of 6% = 9% - 3%.)
MAF303 – Treasury Management 2011
Topic 2 Tutorial Solutions 2011 Page 3
Without the interest rate decrease, the cash flow at 1 year of the
corporate bond would have been 50,000 + 2250 + 54500*1.09 =
$109,202.5
Hence the increase in interest rate has led to a decrease in the cash
flows of the company’s asset by 109,202.5 – 108,385 = 817.5
Liability - 1 year note cash flows:
Cash flow at 1 year:
1. Principal $100 000
2. Interest $7 000
Total cash flows $107 000
The cash flow of the liability is not affected by the change in interest rate
Net cash flows at 1 year:
$108 385 cash inflow - $107 000 cash outflow = $1,385 net interest
income which includes a $817.5 decrease in interest income as a result
of the interest rate change.
(d) Are the maturity model’s conclusions about interest rate risk
exposure in part (a) correct? (Use your answer to part (b).) Why or
why not?
No, the conclusions of the maturity model are not correct. The insurance
company has some interest rate risk exposure as demonstrated by the
fluctuations in its net interest income as interest rates fluctuate. The
maturity model neglects the timing of cash flows and therefore yields
flawed results.
Question 2 – Chapter 6 Q6
Calculate the duration of a two-year Euro-note with $100,000 par value and
an annual coupon rate of 10 per cent if today’s yield to maturity is 11.5 per
cent. What would the duration be if today’s yield was 5.5 per cent? (Hint:
Interest is to be paid annually.)
years P
D 1.908 (1.115)
110,000 2
(1.115)
10,000 1
0
1 2
=
×
+
×
=
MAF303 – Treasury Management 2011
Topic 2 Tutorial Solutions 2011 Page 4
Where
$97,448.17
(1.115)
110,000
(1.115)
10,000
0 1 2 P = + =
If current yields are 5.5%
years P
D 1.912 (1.055)
110,000 2
(1.055)
10,000 1
0
1 2
=
×
+
×
=
$108,308.44
(1.055)
110,000
(1.055)
10,000
0 1 2 P = + =
Question 3 – Chapter 6 Q7
(a) Use duration to calculate the approximate price change if interest
rates increase by 10 basis points for the notes in Question 6.
(b) Use the mechanics of bond valuation to calculate the exact price
change if interest rates increase by 10 basis points for the notes in
Question 6.
(c) Why are your answers for parts (a) and (b) different?
Solution
(a) If current yields are 11.5%:
1.115
0.001 1.908
1 97 448.17
≈ − Δ
+
Δ
≈ − Δ P hence
R
R D
P
P
ΔP ≈ −$166.77
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