Question

Today is 1 July 2018. Matt is 30 years old today. Matt has a portfolio which consists of three Treasury bonds (henceforth referred to as bond A, bond B and bond C). There are 200 units of bond A, 300 units of bond B and 500 units of bond C.

• Bond A is a Treasury bond which matures on 1 January 2027. One unit of bond A has a coupon rate of j2 = 2.95% p.a. and a face value of $100. Matt purchased this Treasury bond on 15 March 2018. The purchase yield rate was j2 = 3.5% p.a. • Bond B is a Treasury bond which matures on 1 July 2023. One unit of bond B has a coupon rate of j2 = 3.15% p.a. and a face value of $100. Matt purchased this Treasury bond on 28 June 2018. The purchase yield rate was j2 = 3.3% p.a. • Bond C is a Treasury bond which matures on 1 January 2021. One unit of bond C has a coupon rate of j2 = 3.35% p.a. and a face value of $100. Matt purchased this Treasury bond on 1 January 2018. The purchase yield rate was j2 = 3.4% p.a.

Calculate • The purchase price of one unit of bond A • The purchase price of one unit of bond B • The purchase price of one unit of bond C

Round your answer to three decimal places. The price of both bond A and bond B should be calculated by using the RBA method. b. [8 marks] Matt decides to sell each of the three bond types today. All the bonds are sold at a yield rate of j2 = 3.25% p.a. Calculate • The sale price of one unit of bond A • The sale price of one unit of bond B

The sale price of one unit of bond C Round your answer to three decimal places. Then calculate the total sale price of the portfolio (round your answer to the nearest dollar). Note that the sale of each bond occurs after a coupon payment. c. [4 marks] Matt plans to use part of the sale proceeds calculated in part b to purchase two bank bills (henceforth referred to as bank bill D and bank bill E) today. Matt will use the remaining part of the sale proceeds for living expense. • Bank bill D is a 180-day $40,000 bank bill. The purchase yield rate is 3.1% p.a. (simple interest rate). • Bank bill E is a 270-day $50,000 bank bill. The purchase yield rate is 3.2% p.a. (simple interest rate). Calculate the purchase price of bank bill D and bank bill E. Round your answer to three decimal places. d. [6 marks] Matt plans to sell both bank bill D and bank bill E on 1 October 2018 and use the sale proceeds to purchase a car. Calculate the sale price of bank bill D and bank bill E. Assume the sale yield rate is 3% p.a. (simple interest rate). Round your answer to three decimal places. e. [5 marks] From Matt’s perspective, draw a carefully labelled cash flow diagram to represent the above financial transactions of parts c and d.

Answer 1

Bond Price Formula:
Bond Value = C*{[1-(1+YTM)^-t/(YTM)] + [F / (1+ YTM)^t]

Where:

B₀ = ? (Bond Price)
C = Coupon payment
F = Face value
YTM = yield to maturity
t = number of periods

Purchase Price of Bond A:

B₀ = ? (Bond Price)
C = Coupon payment = $100 x 2.95% = $2.95
F = Face value = $100
YTM = yield to maturity = 3.5% or 0.035 (Yield rate at which bonds are sold)
t = number of periods = 8.5 Years

= $2.95*{[1-(1+0.035)^-8.5/(0.035)] + [$100 / (1+ 0.035)^8.5]
=> $2.95*[0.253539/0.035] + [100/1.33965501]
=> $21.36973 +$74.64608
= $96.01581 or $96.016

Purchase Price of Bond B:

B₀ = ? (Bond Price)
C = Coupon payment = $100 x 3.15% = $3.15
F = Face value = $100
YTM = yield to maturity = 3.3% or 0.033 (Yield rate at which bonds are sold)
t = number of periods = 5 Years + (3/365) Years = 5.008219 Years

= $3.15*{[1-(1+0.033)^-5.008219/(0.033)] + [$100 / (1+ 0.033)^5.008219]
=> $3.15*[0.150071/0.033] + [100/1.188022173]
=> $14.32499 +$84.17351
= $98.4985 or $98.499

Purchase Price of Bond C:

B₀ = ? (Bond Price)
C = Coupon payment = $100 x 3.35% = $3.35
F = Face value = $100
YTM = yield to maturity = 3.4% or 0.034 (Yield rate at which bonds are sold)
t = number of periods = 3 Years

= $3.35*{[1-(1+0.034)^-3/(0.034)] + [$100 / (1+ 0.034)³]
=> $3.35*[0.095438/0.034] + [100/1.105507304]
=> $9.403441 +$90.45621
= $99.85965 or $99.86

Please post remaining questions separately as only 1 question per post is allowed. However, I've already answered 3 here.