**Question 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.
- Draw a cash flow diagram that captures the details of Yolanda’s transactions.
- Calculate the purchase yield (simple interest rate) and sale yield (simple interest rate) of this bill (as a percentage, rounded to 2 decimal places).
- Without any further calculations, explain how the selling price will change if George accepts a lower yield.
- Calculate capital gain or capital loss component of Yolanda’s investment (in dollars and cents, to the nearest cent).
- 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.

- 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.
- 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. - 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.

- 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.

**Question 2**

Clarrie has just bought a 14-year Treasury bond paying coupon semi-annually at *j*_{2 }= 5% p.a. The bond matures at par.

- 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
*j*_{2 }= 3*.*2% p.a. (net).~~Draw a cash flow diagram that models this scenario to accompany your answer.~~Not included in solution. - 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*j*_{2 }= 3*.*2% p.a. (net).~~Draw a cash flow diagram that models this scenario to accompany your answer.~~Not included in solution. - Justify the difference in your answers to parts and
**b.**above. - 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
*j*_{2 }rate, to one decimal place.

**Question 3**

Mordecai bought a 3-year 15% Treasury bond on 8 May 2020 at a yield of *j*_{2 }= 18*.*6% p.a. Coupons can be reinvested at *j*_{2 }= 14*.*0% p.a. The bond will be redeemed at par on the maturity date (face value $100).

- 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.
- Calculate the total realised compound yield (TRCY) of this bond.
- Decompose the total accumulated value generated by this bond into: original purchase price, coupons, interest on coupons, and capital gain/loss.
~~If Mordecai holds the bond for 2 years and sells it for a yield of~~Not included in solution.*j*_{2 }= 18*.*8% p.a., calculate the holding period yield (HPY).- Calculate duration of this bond if it is held to maturity.
- Use the concept of modified duration to estimate the price of the bond if the yield to maturity increases to
*j*_{2 }= 18*.*7% p.a. immediately after Mordecai buys the bond. - What fixed liability could Mordecai be reasonably confident of paying off in 2
^{1}/_{2 }years’ time? Why?

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