MAF303 – Treasury Management 2011 Topic 2 Tutorial Solutions 2011 Page 1 Topic 2 Tutorial Solutions Question 1 – Chapter 5 Q17. For help with class attendance, Email jaredericks [email protected]

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