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%**

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