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anon_ch posted a question Feb 03, 2015 at 7:22am Question 1
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A bond with face value of $500 is redeemable at par in 8 years. The coupon (interest) rate is 9.8% p.a. payable half-yearly. What price should be paid for the bond by an investor (who pays tax at 30.0% on interest) to produce a net yield to maturity of 6.6% p.a. convertible half-yearly?
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The correct answer is: 507.98
Question 2
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A debenture with face value of $100 pays interest at j4 = 14% and will mature 7 years from today at par. What net yield to maturity, j4 (as a %, 2 decimal places), would an investor taxed at 30% on interest obtain if the debenture was purchased for $84.60? Use the APPROXIMATE yield formula.
(The j4 value is required and not the quarterly rate.
When a question says to use the approximate formula, linear interpolation is not required.)
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The correct answer is: 13.00
Question 3
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A debenture with face value of $100 pays interest at j4 = 14% and will mature 7 years from today at par. What net yield to maturity, j4 (as a %, 2 decimal places) would an investor taxed at 30% on interest obtain if the debenture was purchased for $860? Use LINEAR INTERPOLATION between 3% and 3.5% for the quarterly yield.
(The j4 value is required and not the quarterly rate.)
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The correct answer is: 12.89
Question 4
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A bond with face value of $100 pays interest at j2 = 7.1% and is redeemable at par on 1 June 2019. What price should be paid for the bond on 29 August 2012 by an investor liable to tax on interest at 25% who wants to earn a net yield of 5.1% p.a. effective? Use compound interest for the fractional interest period.
(As the interest payments are half-yearly, the yield will need to be converted to a half-yearly rate to match the frequency of the payments. Use the unrounded yield (store it in the memory of your calculator) or your answer will probably be marked as incorrect.)
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The correct answer is: 102.92
Question 5
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A bond with face value of $100 pays interest at j2 = 7.4% and is redeemable at par in 5.5 years' time. Calculate the price which should be paid for the bond if a net yield to maturity of 6.5% p.a. convertible half-yearly is required and tax on both interest and capital gains is at the rate of 25%.
(The capital gain and hence the net redemption payment is based on the unknown purchase price P. A term involving P will appear on both sides of the equation of value.)
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The correct answer is: 94.74
Question 6
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A bond with face value of $100 pays interest at j2 = 7% and is redeemable at par in 10 years' time. The bond is purchased for $93.8. Calculate the net redemption payment allowing for capital gains tax at the rate of 25% if the bond is held to maturity.
(Net redemption payment = Gross redemption payment - Capital gains tax.)
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The correct answer is: 98.45
Question 7
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A bond was bought for $81 and sold for $97.2. The capital gains tax which will be payable is $3.7. Calculate the rate of capital gains tax (as a %, 2 decimal places).
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The correct answer is: 22.84
Question 8
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A bond with face value of $100 pays interest at j2 = 7.0% and is redeemable at par 7.5 years from now.
Three years ago, Joanna purchased the bond for $94.2. Joanna pays tax on interest at the rate of 30% and tax on capital gains at the rate of 20%.
If she holds the bond to maturity, use the APPROXIMATE formula (suitably adjusted to take account of taxation) to calculate the net yield, j2, earned by Joanna over the 10.5 years of her investment (as a %, 2 decimal places).
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The correct answer is: 5.53
Question 9
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Continuation of previous question.
If Joanna sells the bond today for $91.6, use the APPROXIMATE formula (suitably adjusted to take account of taxation) to calculate the net yield, j2, earned by Joanna over the 3 years of her investment (as a %, 2 decimal places). Ignore taxation on the capital loss.
(The C value will be the sale payment.)
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The correct answer is: 4.34
Question 10
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A bond with face value of $100 has interest payments of $3.5 on 1 December 2012 and $4 each half-year thereafter. The bond matures at par on 1 December 2018. The bond is bought on 2 October 2012 at a price to give a gross yield to maturity of j2 = 6.1%.
Calculate the price paid. Use the Reserve Bank method.
(First calculate the price on 1 December 2012, ignoring the interest payment on that date. Then add in the interest payment and move the resulting price back to 2 October 2012.)
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The correct answer is: 111.82
Question 11
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In a government bond tender the coupon rate was j2 = 6.5% and the weighted average yield was j2 = 6%. At this yield the bonds were issued
Select one:
a. at a premium to the face value.
b. at a discount to the face value. Incorrect
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The correct answer is: at a premium to the face value.
Question 12
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A Treasury Bond is
Select one:
a. Short-term equity
b. Short-term debt Incorrect
c. Long-term equity
d. Long-term debt
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The correct answer is: Long-term debt
Question 13
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Look up the financial pages of a newspaper.
Select one:
a. The yield on Australian government Treasury Bonds is less than the yield on NSW Treasury Bonds.
b. The yield on Australian government Treasury Bonds is greater than the yield on NSW Treasury Bonds. Incorrect
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The correct answer is: The yield on Australian government Treasury Bonds is less than the yield on NSW Treasury Bonds.
Question 14
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A capital indexed bond with face value of $1,000 pays interest each quarter at 1% of the indexed capital value. The index increases by 0.45% compound at the end of each of the first 7 quarters and by 0.74% compound at the end of each of the next 3 quarters. Calculate the interest payment at the end of the 10th quarter.
(First calculate the indexed capital value at the time the coupon is to be paid.
This is a question from Week 3 of Techniques of accumulating a single payment using 2 rates of compound interest.
Then multiply by the quarterly interest rate.)
(Table 12.4 (5th ed) of Viney sets out the calculations. A bond with face value of $1,000 has coupons paid at 1.5% quarterly on the inflation-adjusted principal. Inflation is a constant 1% per quarter.
For example at the end of the 4th quarter in Table 12.4 (5th ed)
Indexed capital value = 1,000(1.01)4
= 1,040.60
Interest payment = 0.015 × 1,040.60
= 15.61
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The correct answer is: 10.55
Question 15
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The successful bidders for Treasury bonds were:
Bidder A for $140 million face value at a yield of 6.61% p.a.
Bidder B for $50 million face value at a yield of 6.68% p.a.
Bidder C for $210 million face value at a yield of 6.76% p.a.
Calculate the weighted average yield (as a %, 2 decimal places) at which the Reserve Bank would be allocated bonds.
(This applies principles from first year statistics.
Weighted average yield = sum of (each yield times the face value of bonds issued at that yield)
total face value of bonds issued
ie Weighted average yield = Σxifi / Σfi
The answer will be similar to but not the same as adding up the three yields and dividing by 3.
You might try to verify the weighted average yield of 6.42% in Table 12.1 (5th ed and 6th ed).
The Grade Point Average (GPA) calculation is another example of finding a weighted average.)
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The correct answer is: 6.70