Question

Henry is planning to purchase a Treasury bond with a coupon rate of 2.67% and face value of $100. The maturity date of the bond is 15 May 2033.

(c) If Henry purchased this bond on 2 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 4.80% p.a. compounded half-yearly. Henry needs to pay 28.3% on coupon payment and capital gain as tax payment. Assume that all tax payments are paid immediately.

Select one:

a. 65.4393

b. 78.5573

c. 56.3634

d. 64.3298

Answer 1

No of periods = (15 years * 2) + 1 = 31 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Par value

Coupon per period = (2.67% / 2) * $100

Coupon per period = $1.335

Let us compute the Bond price on 15^th November 2017

Bond Price = Coupon / (1 + YTM / 2)^period + Par value / (1 + YTM / 2)^period

Bond Price = $1.335 / (1 + 4.80% / 2)¹ + $1.335 / (1 + 4.80% / 2)² + ...+ $1.335 / (1 + 4.80% / 2)³¹ + $100 / (1 + 4.80% / 2)³¹

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $1.335 * (1 - (1 + 4.80% / 2)^-31) / (4.80% / 2) + $100 / (1 + 4.80% / 2)³¹

Coupons value = $1.335 * (1 - (1 + 4.80% / 2)^-31) / (4.80% / 2)

Coupons value = $28.9582

After tax coupon value = Coupons value * (1 - tax rate)

After tax coupon value = $28.9582 * (1 - 28.3%)

After tax coupon value = $20.7630

Par value = $100 / (1 + 4.80% / 2)³¹

Par value = $47.9404

After tax Par value = Par value * (1 - tax rate)

After tax Par value = $47.9404 * (1 - 28.3%)

After tax Par value = $34.3732

Bond Price = After tax coupon value + After tax Par value

Bond Price = $20.7630 + $34.3732

Bond Price = $55.1362

Days between 15^th November 2017 to 2^nd May 2018 = 15(Nov) + 31(Dec) + 31(Jan) + 28(Feb) + 31(Mar) + 30(Apr) + 2(May) = 168 days

Days between 15^th November 2017 to 15^th May 2018 = 15(Nov) + 31(Dec) + 31(Jan) + 28(Feb) + 31(Mar) + 30(Apr) + 15(May) = 181 days

Full Bond price = Bond price * (1 + YTM / 2)^{(Days between 15th November to 2nd May / Days between 15th November to 15th May)}

Full Bond price =  $55.1362 * (1 + 4.80% / 2)^{(168 / 181)}

Full Bond price = $56.3634