Question

On 15 September 2020 you plan to buy a 6% p.a. Treasury bond maturing on 15 September 2026(Note that all the interest rates given in this question are j2 rate)

a. How much would you pay to earn 7% p.a. on your transaction? Ignore taxation considerations.

b How much would you pay to earn a net return of 7% p.a. on your transaction, allowing for tax on interest-only of 30%? In this instance, assume tax on interest is paid immediately.

c. How much would you pay to earn a net return of 7% p.a. on your transaction, allowing for tax on interest and capital gains of 30%? In answering this question, you should assume that the tax on interest and capital gains is deferred by twelve months.

d. Allowing for tax on interest and capital gains of 30%, what would your net annual yield be if you paid $97.447 for the bond? Again, assume that the tax on interest and capital gains is deferred by twelve months.

Answer 1

Answer for (a)

Since there is not tax cash flow the every year will be coupone received. For the final year there will be two cash flow coupone and principle payment.

Calculation of Bond price with the yeild of 7%.

Year	Cash flows	Discounting factor @ 7%		Present Value
1	$                 6.00	0.9346	1(1.07)^1	$                 5.61
2	$                 6.00	0.8734	1(1.07)^2	$                 5.24
3	$                 6.00	0.8163	1(1.07)^3	$                 4.90
4	$                 6.00	0.7629	1(1.07)^4	$                 4.58
5	$                 6.00	0.7130	1(1.07)^5	$                 4.28
6	$                 6.00	0.6663	1(1.07)^6	$                 4.00
6	$             100.00	0.6663	1(1.07)^6	$               66.63
			Net present value	$               95.23

hence we should purchase bond at $95.23.

Answer for (2)

Since there will be tax on interest and tax is paid immediately cash flow for the every year will be coupone received - tax i.e. 30% of coupone received. For the final year there will be two cash flow coupone after tax and principle payment.

Calculation of Bond price with the yeild of 7%.

Year	Cash flows		Discounting factor @ 7%		Present Value
1	$                 4.20	6*(1 - 30%)	0.9346	1(1.07)^1	$                 3.93
2	$                 4.20	6*(1 - 30%)	0.8734	1(1.07)^2	$                 3.67
3	$                 4.20	6*(1 - 30%)	0.8163	1(1.07)^3	$                 3.43
4	$                 4.20	6*(1 - 30%)	0.7629	1(1.07)^4	$                 3.20
5	$                 4.20	6*(1 - 30%)	0.7130	1(1.07)^5	$                 2.99
6	$                 4.20	6*(1 - 30%)	0.6663	1(1.07)^6	$                 2.80
6	$             100.00		0.6663	1(1.07)^6	$               66.63
				Net present value	$               86.65

hence we should purchase bond at $86.65.

Answer for (3)

Since there will be tax on interest and tax is paid after one year cash flow for the first year will be the coupone received and for the every year there after will be coupone received - tax i.e. 30% of coupone received. For the final year there will be two cash flow coupone after tax and principle payment. There will be 7th year in which we will pay tax on coupone for 6th year and capital gain tax.

Calculation of Bond price with the yield of 7%.(Ignoring capital gain tax)

Year	Cash flows		Discounting factor @ 7%		Present Value
1	$                 6.00		0.9346	1(1.07)^1	$                 5.61
2	$                 4.20	6 - 6*30%	0.8734	1(1.07)^2	$                 3.67
3	$                 4.20	6 - 6*30%	0.8163	1(1.07)^3	$                 3.43
4	$                 4.20	6 - 6*30%	0.7629	1(1.07)^4	$                 3.20
5	$                 4.20	6 - 6*30%	0.7130	1(1.07)^5	$                 2.99
6	$                 4.20	6 - 6*30%	0.6663	1(1.07)^6	$                 2.80
6	$             100.00		0.6663	1(1.07)^6	$               66.63
7	$                -1.80	6*30%	0.6227	1(1.07)^7	$                -1.12
				Net present value	$               87.21

Since we have ignored the capital gain tax we will deduct it from the above price derived as follow:

Let the price of the bond be "x":

x = $87.21 - [($100 - x)*30%*0.6227]

x = $84.27

hence we should purse bond at $84.27

Answer for (4)

Since there will be tax on interest and tax is paid after one year cash flow for the first year will be the coupone received and for the every year there after will be coupone received - tax i.e. 30% of coupone received. For the final year there will be two cash flow coupone after tax and principle payment. There will be 7th year in which we will pay tax on coupone for 6th year and capital gain tax. cash flow for the 7th = -[6+(100-97.447)]*30% = -$2.5659

since bond price with yield of 7% = $84.27 which implecates that the yield of IRR of the bond with purchase price of 97.447 will be lower than 7%

by interpolating we arrive at rate 4.66891%

Calculating bond price with 4.66891% yield:

Year	Cash flows		Discounting factor @ 4.66891%		Present Value
1	$                 6.00		0.9554	1(10.466891)^1	$                 5.73
2	$                 4.20	6 - 6*30%	0.9128	1(10.466891)^2	$                 3.83
3	$                 4.20	6 - 6*30%	0.8721	1(10.466891)^3	$                 3.66
4	$                 4.20	6 - 6*30%	0.8332	1(10.466891)^4	$                 3.50
5	$                 4.20	6 - 6*30%	0.7960	1(10.466891)^5	$                 3.34
6	$                 4.20	6 - 6*30%	0.7605	1(10.466891)^6	$                 3.19
6	$             100.00		0.7605	1(10.466891)^6	$               76.05
7	$                -2.57	6*30%	0.7266	1(10.466891)^7	$                -1.86
				Net present value	$               97.45

There for net annual yield is 4.67% approx.