Question 1

  1. Yolanda bought a 180-day $100000 bank bill 74 days ago for $98300.00.She sold it to George today and received $99000.00.
    1. Draw a cash flow diagram that captures the details of Yolanda’s transactions.
    2. Calculate the purchase yield (simple interest rate) and sale yield (simple interest rate) of this bill (as a percentage, rounded to 2 decimal places).
    3. Without any further calculations, explain how the selling price will change if George accepts a lower yield.
    4. Calculate capital gain or capital loss component of Yolanda’s investment (in dollars and cents, to the nearest cent).
    5. Assuming Yolanda borrowed to purchase the bond, what is the break-even rate of interest of borrowing (simple interest, as a percentage, rounded to 2 decimal places)? If the borrowing cost rate is 10 basis points higher than the break-even rate, explain whether Yolanda will end up with a cash surplus or cash deficit.
  2. Max wants to raise funds by issuing eighty 180-day bank bills, each with a face value of $10000. The current yield on such bank bills is 5.4% p.a. Max must pay $25000 of fees and charges associated with this financing activity.
    1. Calculate the real cost of borrowing if fees and charges are paid on the date of issue. Express the cost as a rate of simple interest, as a percentage, rounded to 2 decimal places. Include a neatly drawn cash flow diagram that summarises Max’s transaction. Not included in solution.
    2. Calculate the real cost of borrowing if fees and charges are paid on the maturity date. Express the cost a rate simple interest, as a percentage, rounded to 2 decimal places.

Question 2

Clarrie has just bought a 14-year Treasury bond paying coupon semi-annually at j2 = 5% p.a. The bond matures at par.

  1. Find Clarrie’s purchase price (per $100 face value, rounded to 3 decimal places) of this Treasury bond, allowing for a 30% tax on interest only, to give a yield of j2 = 3.2% p.a. (net). Draw a cash flow diagram that models this scenario to accompany your answer. Not included in solution.
  2. Find Clarrie’s purchase price (per $100 face value, rounded to 3 decimal places) of this Treasury bond, allowing for a 30% tax on interest only. The tax on interest is paid one year later (e.g., for the coupon payment at t = 0.5 year, the tax payment will be paid at t = 1.5 years.), to give a yield of j2 = 3.2% p.a. (net). Draw a cash flow diagram that models this scenario to accompany your answer. Not included in solution.
  3. Justify the difference in your answers to parts and b. above.
  4. If Clarrie paid $95.268 per $100 face value for the bond, and was exempt from tax, what yield was associated with his purchase? Use linear interpolation to find this yield and express your yield as a j2 rate, to one decimal place.

Question 3

Mordecai bought a 3-year 15% Treasury bond on 8 May 2020 at a yield of j2 = 18.6% p.a. Coupons can be reinvested at j2 = 14.0% p.a. The bond will be redeemed at par on the maturity date (face value $100).

  1. Calculate the total accumulated value at maturity generated by this bond if Mordecai holds it to maturity and reinvests all coupon payments received at the available rate.
  2. Calculate the total realised compound yield (TRCY) of this bond.
  3. Decompose the total accumulated value generated by this bond into: original purchase price, coupons, interest on coupons, and capital gain/loss.
  4. If Mordecai holds the bond for 2 years and sells it for a yield of j2 = 18.8% p.a., calculate the holding period yield (HPY). Not included in solution.
  5. Calculate duration of this bond if it is held to maturity.
  6. Use the concept of modified duration to estimate the price of the bond if the yield to maturity increases to j2 = 18.7% p.a. immediately after Mordecai buys the bond.
  7. What fixed liability could Mordecai be reasonably confident of paying off in 21/2 years’ time? Why?

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