Question

Today is 1 January 2019. Kim is looking for an investment that will give her $500,000 in 5 years’ time
so that she will have a sufficient deposit to purchase a $2.5m house in Sydney. Currently she has
saved about $380,000 to contribute to the deposit. She has started looking at Treasury bonds as she
thinks they are a relatively low risk investment. However, she did not study finance at University so
does not have a good understanding of Treasury Bonds. A friend of hers, Matt, works at the RBA
and has given her the following information:
• The expected change in market yield and reinvestment rates for the next 7 years is a 50
basis points increase per annum from the current market yield. This change is expected to
occur immediately after 1 January 2019.
• For a $500,000 investment in 5 years’ time, Kim can consider buying:
o Investment 1 – 2413 units of a 7 year 15.6% p.a. Treasury bond (bond 1) with a face
value of $100 at a yield of j2 = 6.2%. The bond is redeemable at par. The maturity
date is 1 January 2026.
o Investment 2 – 3511 units of a 6 year 7.2% p.a. Treasury bond (bond 2) with a face
value of $100 at a yield of j2 = 6.2%. The bond is redeemable at par. The maturity
date is 1 January 2025.
• On receipt of each coupon, Kim should deposit the coupon into a bank account earning the
reinvestment rate.
As you are a friend studying financial modelling, Kim has approached you to help her with some
analysis before she decides whether to invest in the Treasury bonds suggested by Matt. Her
questions are [25 marks]:
a) What is the price per bond and total price Kim will pay for 1 January 2019 for investment 1
and 2? [4 marks]
b) For each bond, calculate the accumulated value at years 4, 5 and 6 and maturity [7 marks]
c) For each bond, calculate the holding period yield rate (expressed as a j2 rate to 1 decimal
place) for each of the holding periods in b) [7 marks]
d) Calculate the duration of each bond using the weighted average cash flow method (to 2
decimal places). Based on your observation in c) and d), what is the reason Matt has given
Kim the advice to consider purchasing the 2 bonds? [4 marks]
e) Use a separate bar/column chart to plot your results for each bond in c). Provide an
explanation of why the holding period yield rate increases as the holding period increases. [3
marks]
Answer each of parts a–e on separate tabs in your spreadsheet. Label each of the tabs `Part a',
`Part b', ..., and `Part e'

Answer 1

1 Part (a) Calculation of price per bond and total payable value Investment 1 Investment 2 Inflows Present Value Inflows Present Value Year PV Factor Year PV Factor 0.9372 0.8702 0.8005 0.7296 0.6589 0.5897 0.5897 14.62 13.57 12.49 11.38 10.28 9.20 8.16 52.31 132.01 2413 0.9372 0.8702 0.8005 0.7296 0.6589 0.5897 0.5231 0.5231 Value of Bond 7.2 7.2 7.2 7.2 7.2 7.2 100 15.6 15.6 15.6 15.6 15.6 15.6 15.6 100 6.75 6.27 5.76 5.25 4.74 4.25 58.97 6 9 10 Value of Bond Number of Units 91.99 13 14 Number of Units Total payable value318541.15 3511 Total pavable value322994.36 Calculations are shown as below: 16

17 18 19 20 21 Calculation of price per bond and total pavable value Investment 1 Investment 2 Year Inflows PV Factor Present Value Year Inflows PV Factor Present Value -G21*H21 -G22*H22 -G23*H23 -G24*H24 -G25*H25 =G26*H26 -G27 H27 1100*15.6%1/1.0671 2 100*15.6%1/1.072A2 3 100*15.6%1/1.077A3 4 100*15.6%1/1.082A4 5 100*15.6%1/1.087A5 6|-100*15.6%| -1/1.09216 -100*15.6%| -1/1.09717 -1/1.097A7 | |-100*7.2% | 1 2 1/1.067a! -c21*D21 |-100*7.2961-1/1.07212 -C22 D22 -C23 D23 3 100*7.2%1/1.077A3 -C24 D24 -C25 D25 -C26 D26 -C27*D27 6 -C28 D28 23 4 |-100*7.2% 5-100*7.2961-1/1.08705 6 |-100* 1/1.082A4 -1/1.09206 -1/1.0926 26 27 28 29 7.2%) 100 100 Value of Bond SUM(E21:E28 Number of Units Value of Bond-SUM(I121:127 Number of Units Total payable value 2413 3511 =130*129 Total payable value-E29 E30 31

33 Part (b) 34 Accumulated value of bond will be calculated as follow: Note: premium paid on bonds will be write off over the life of bond. And Coupon interest will not be considered for calculating the axccumulated value of bond since it is invested in the bank account Investment 1 Investment 2 37 At end of Year 4 At end of Year 4 Inflows Present Value Inflows Present Value Year PV Factor Year PV Factor 0.9200 0.8386 0.8386 7.2 7.2 100 39 15.6 15.6 15.6 100 0.9200 0.8386 0.7575 0.7575 Value of Bond 14.35 13.08 11.82 75.75 115.00 2413 6.62 6.04 83.86 40 2 42 43 Value of Bond Number of Units 96.52 Number of Units 3511 Total Accumulated value 277495.18 Total Accumulated value338887.43 45 At end of Year 5 At end of Year 5 47 Year Inflows Present Value Year Inflows Present Value 6.59 91.58 PV Factor PV Factor 0.9158 0.9158 49 15.6 15.6 100 0.9158 0.8310 0.8310 Value of Bond 14.29 12.96 83.10 110.35 2413 266265.27 7.2 100 2 2 52 53 54 Value of Bond Number of Units 98.17 3511 Number of Units Total Accumulated value Total Accumulated value 344669.60

At end of Year 6 At Maturi Inflows Present Value Inflows Present Value Year PV Factor Year PV Factor 57 0.9116 0.9116 Value of Bond 100 15.6 14.22 91.16 105.38 2413 0 1.0000 100.00 100 59 Value of Bond Number of Units 100.00 61 62 63 Number of Units 3511 Total Accumulated value 254277.85 Total Accumulated value 351100.00 At Maturi Inflows Present Value Year PV Factor 65 100 0 1.0000 100.00 67 Value of Bond Number of Units 100.00 69 70 71 2413 Total Accumulated value 241300.00

72 Part (c) 73 Calculation of Holding Period Yield Rate Investment 1 Holding Period Yield Rate 8.3% 8.2% 8.2% 8.1% Total Interest & Gain Combined holding rate 33.2% 41.2% 48.9% 56.4% Period Total Interest Gain Current Value 75 76 At Year 4 At Year 5 At Year 6 At Maturit 146710.4 183388 220065.6 256743.2 -41045.97 52275.87 64263.30 77241.15 105664.43 131112.13 155802.30 179502.05 318541.15 318541.15 318541.15 318541.15 78 79 80 81 Calculations are shown as below: Holding Period Yield Rate 83/4 184/5 185/6 186/7 Total Interest & Gain Combined holding rate -F83/H83 -F84/H84 -F85/H85 -F86/H86 Period Total Interest Gain Current Value 82 83 84 85 86 ESES14 ESES14 -$E$14 =SE$14 | | | | -2413*100*15.2%*4|-(SES45-SES14)| -2413*100*15.2%*5-(SES54-SES14)| -2413*100*15.2%*6 |-(SE$62-SES14)| -2413*100*15.2%*7-(SES70-SES14)| -E83+D83 -E84+D84 -E85+D85 -E86+D86 At Year 4 At Year 5 At Year 6 At Maturity

87 Investment 2 Holding Period Yield Rate 9.1% 9.2% 9.3% Total Interest & Gain Combined holding rate 36.2% 45.8% 55.7% Period Total Interest Gain Current Value 89 90 91 92 93 94 At Year 4 At Year 5 At Maturit 101116.8 126396 151675.2 15893.07 21675.24 28105.64 117009.87 148071.24 179780.84 322994.36 322994.36 322994.36 Calculations are shown as below: Holding Period Yield Rate 196/4 497 /5 =198/6 Total Interest & Gain Combined holding rate -F96/H96 -F97/H97 -F98/H98 Period Total Interest Gain Current Value 95 96 97 98 :3511*100*7.2%*4 :3511*100*7.2%"5 :3511*100*7.2%*6 |:($545-$1$14)| |s($1$54-$!$14)| |-(SIS62-SIS14) | -E96+D96 -E97+D97 -E98+D98 At Year 4 At Year 5 At Maturit

100 Part (d) 101 Calculation of Duration of Bond Investment 1 Investment 2 Inflows Present Value Inflows Present Value Weighted PV Factor Weighted PV Factor 0.9372 1.7404 2.4015 2.9184 3.2947 3.5385 3.5385 Year Year 102 103 104 105 106 107 108 109 110 14.62 27.15 37.46 45.53 51.40 55.20 57.12 366.14 654.62 2413 1579600.18 0.9372 1.7404 2.4015 2.9184 3.2947 3.5385 3.6614 3.6614 Value of Bond 15.6 15.6 15.6 15.6 15.6 15.6 15.6 100 7.2 7.2 7.2 7.2 7.2 7.2 100 6.75 12.53 17.29 21.01 23.72 25.48 353.85 2 4 4 Value of Bond 460.63 3511 112 113 114 115 116 Number of Units Number of Units Total payable value Total payable value (A) 1617264.38 Current Value(B)318541.15 Current Value(B)322994.36 Duration of Bond (A/B)4.96 Duration of Bond (A/B 5.01 On the basis of Part (c) and Part (d), Mr. Matt has given the advice to buy 2 bonds, being their duration is almost equal and they are generating the high holding period returns. 118

119 20 Part (e) 121 Data of Part (c) Investment 1 Investment 2 Holding Period 4 Holding riod return Holding period return 8.3% 8.2% 8.2% 8.1% Holding Period 4 123 124 125 126 9.1% 9.2% 9.3% 128 Investment 1 Chart Investment 2 Chart 130 131 132 133 9.4% 9.2% 9.0% 8.8% 10 8.3% 8.2% 8.1% 135 Investment 2 Holding Period Investment 2 Holding period return 137 139 140 141 Explanation:-Holding period return increases as the holding period increases, It is due to componding of value over the period of time