Question

Clarrie has just bought a 14-year Treasury bond paying coupon semi-annually at j2 = 5% p.a. The bond matures at par.

a. Find Clarrie’s purchase price (per $100 face value, rounded to 3 decimal places) of this Treasury bond, allowing for a 30% tax on interest only, to give a yield of j2 = 3.2% p.a. (net). Draw a cash flow diagram that models this scenario to accompany your answer.

b. Find Clarrie’s purchase price (per $100 face value, rounded to 3 decimal places) of this Treasury bond, allowing for a 30% tax on interest only. The tax on interest is paid one year later (e.g., for the coupon payment at t = 0.5 year, the tax payment will be paid at t = 1.5 years.), to give a yield of j2 = 3.2% p.a. (net). Draw a cash flow diagram that models this scenario to accompany your answer.

c. Justify the difference in your answers to parts a. and b. above.

d. If Clarrie paid $95.268 per $100 face value for the bond, and was exempt from tax, what yield was associated with his purchase? Use linear interpolation to find this yield and express your yield as a j2 rate, to one decimal place.

Its all question information

Answer 1

a. We will use PV function in excel to calculate the price of bond

Yield = Rate = 3.2% per annum = 1.60% per half year

Maturity = NPER = 14 years = 28 half years

Coupon (Interest) = PMT = 5%/2 x 100 = $2.5

Net Coupon after tax = 2.5 X (1- Tax rate) = 2.5 X (1-0.30) = 2.5X 0.7 = $1.75

FV = 100

Type = 0 (Coupon received at the end)

Price of the bond = PV = PV(1.60%,28,1.75,100,0) = - $103.364 (Negative sign indicates, it is a cash outflow to purchase the bond)

Alternatively,

We can also solve it by first calculating the present value of bond using the coupon payment and then reducing the Present value of tax paid on coupon ($0.75 for 28 terms)

= PV(1.6%,28,2.50,100,0) - PV(1.6%,28,0.75,0,0)

= $120.184 - $16.820

= $103.364

Cash Flow timeline

Time	Cash Flow
0	Paid 103.36
1	1.75
2	1.75
27	1.75
28	100

b)

Cash Flow from bond would look like this (as tax is paid a year after receiving the interest.

Time	Cash Flow in $
0	103.36
1	2.5
2	2.5
3	2.5 - 0.75
4	2.5 - 0.75
27	2.5 - 0.75
28	100 + 2.50 - 0.75
29	- 0.75
30	- 0.75

The price of bond = PV of All cash flows (Coupon and maturity value) - PV of all tax paid on interest

From the values above

Yield = Rate = 3.2% per annum = 1.60% per half year

Maturity = NPER = 14 years = 28 half years

Coupon (Interest) = PMT = 5%/2 x 100 = $2.5

Tax = PMT (for PV of tax) = 2.5 x 30% = $0.75

FV = 100

Type = 0 (Coupon received at the end)

The price of bond = PV of All cash flows (Coupon and maturity value) - PV of all tax paid on interest

= PV(1.60%,28,2.50,1000,0) - PV of all tax paid (one year later)

= PV(1.60%,28,2.50,1000,0) - PV of PV(1.60%,28,0.75,0,0)

= $120.184 - PV of $16.820 to be paid 1 year later

= $120.184 - PV(1.60%,2,0,16.820,0)

= $120.184 - $16.294

= $ 103.890

c. Here, we have to find the yield

Maturity = NPER = 14 years = 28 half years

Coupon (Interest) = PMT = 5%/2 x 100 = $2.5

PV = - $95.268 (We use a negative sign to indicate this is a cash outflow to purchase the bond)

FV = $100

Type = 0 (Coupon received at the end)

Half yearly yield = Rate(28,2.50,-95.268,100,0)

= 2.744%

Annual Yield = 2.744% x 2 = 5.489%