In: Finance
Henry is planning to purchase a Treasury bond with a coupon rate of 2.22% and face value of $100. The maturity date of the bond is 15 May 2033.
(c) If Henry purchased this bond on 4 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 1.84% 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. 96.8161
b. 105.9890
c. 95.8030
d. 76.0108
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 = (2.22% / 2) * $100
Coupon per period = $1.11
Let us compute the Bond price on 15th November 2017
Bond Price = Coupon / (1 + YTM / 2)period + Par value / (1 + YTM / 2)period
Bond Price = $1.11 / (1 + 1.84% / 2)1 + $1.11 / (1 + 1.84% / 2)2 + ...+ $1.11 / (1 + 1.84% / 2)31 + $100 / (1 + 1.84% / 2)31
Using PVIFA = ((1 - (1 + Interest rate)- no of periods) / interest rate) to value coupons
Bond Price = $1.11 * (1 - (1 + 1.84% / 2)-31) / (1.84% / 2) + $100 / (1 + 1.84% / 2)31
Coupons value = $1.11 * (1 - (1 + 1.84% / 2)-31) / (1.84% / 2)
Coupons value = $29.8198
After tax coupon value = Coupons value * (1 - tax rate)
After tax coupon value = $29.8198 * (1 - 28.3%)
After tax coupon value = $21.3808
Par value = $100 / (1 + 1.84% / 2)31
Par value = $75.2845
After tax Par value = Par value * (1 - tax rate)
After tax Par value = $75.2845 * (1 - 28.3%)
After tax Par value = $53.9790
Bond Price = After tax coupon value + After tax Par value
Bond Price = $21.3808 + $53.9790
Bond Price = $75.3598
Days between 15th November 2017 to 2nd May 2018 = 15(Nov) + 31(Dec) + 31(Jan) + 28(Feb) + 31(Mar) + 30(Apr) + 4(May) = 170 days
Days between 15th November 2017 to 15th 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 = $75.3598 * (1 + 1.84% / 2)(170 / 181)
Full Bond price = $76.0108