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
• 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]
a) To calculate the price per bond and total price for each investment, we'll use the formula:
Price per bond = Face value / (1 + Yield/2)^ (2 * time to maturity)
Total price = Price per bond * Number of units
For Investment 1:
Face value = $100
Yield = 6.2% (j2 = 6.2% = 0.062)
Time to maturity = 7 years
Using the formula:
Price per bond = 100 / (1 + 0.062/2)^(2*7)
Total price for Investment 1 = Price per bond * 2,413 units
For Investment 2:
Face value = $100
Yield = 6.2% (j2 = 6.2% = 0.062)
Time to maturity = 6 years
Using the formula:
Price per bond = 100 / (1 + 0.062/2)^(2*6)
Total price for Investment 2 = Price per bond * 3,511 units
b) To calculate the accumulated value at years 4, 5, 6, and maturity, we'll use the formula:
Accumulated value = Coupon * (1 + Reinvestment rate)^(Number of periods)
For Investment 1:
Face value = $100
Coupon = Face value * Yield/2
Reinvestment rate = 50 basis points increase per annum = 0.5% increase per annum
Number of periods:
- At year 4: 7 - 4 = 3 periods
- At year 5: 7 - 5 = 2 periods
- At year 6: 7 - 6 = 1 period
- At maturity: 7 - 7 = 0 periods
Using the formula:
Accumulated value at year 4 = Coupon * (1 + 0.005)^3
Accumulated value at year 5 = Coupon * (1 + 0.005)^2
Accumulated value at year 6 = Coupon * (1 + 0.005)^1
Accumulated value at maturity = Coupon * (1 + 0.005)^0
For Investment 2, use the same formula with time to maturity = 5 instead of 7 for the calculations.
c) To calculate the holding period yield rate, we'll use the formula:
Holding period yield rate = ((Accumulated value at maturity / Total price)^(1/holding period) - 1) * 2
For Investment 1:
- Holding period = 4 years
- Holding period = 5 years
- Holding period = 6 years
For Investment 2:
- Holding period = 4 years
- Holding period = 5 years
- Holding period = 6 years
d) To calculate the duration of each bond using the weighted average cash flow method, we'll use the formula:
Duration = (Period 1 Cash Flow * Time to maturity 1 + Period 2 Cash Flow * Time to maturity 2 + ... + Period n Cash Flow * Time to maturity n) / Total price
Based on the observation in c) and d), the reason Matt has given Kim the advice to consider purchasing the 2 bonds can be determined once we have the specific values for the holding period yield rates and durations.
e) To plot the results for each bond in c), create a bar/column chart with the holding period on the x-axis and the holding period yield rate on the y-axis. Label the bars/columns for each bond accordingly. The explanation for why the holding period yield rate increases as the holding period increases is due to the reinvestment of the coupons at a higher rate of return over time.