Question

In: Finance

Henry is planning to purchase a Treasury bond with a coupon rate of 2.22% and face...

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

Solutions

Expert Solution

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


Related Solutions

Henry is planning to purchase a Treasury bond with a coupon rate of 2.22% and face...
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. (b) 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 as tax payment and tax are paid immediately. Select one: a. 97.5012 b. 97.5946...
Henry is planning to purchase a Treasury bond with a coupon rate of 1.69% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 1.69% and face value of $100. The maturity date of the bond is 15 May 2033. (b) If Henry purchased this bond on 2 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 3.97% p.a. compounded half-yearly. Henry needs to pay 23.2% on coupon payment as tax payment and tax are paid immediately. Select one: a. 70.5649 b. 70.5665...
Henry is planning to purchase a Treasury bond with a coupon rate of 3.02% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 3.02% and face value of $100. The maturity date of the bond is 15 May 2033. (a) If Henry purchased this bond on 3 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 2.39% p.a. compounded half-yearly. Select one: a. 107.8175 b. 109.3277 c. 109.3263 d. 109.11
Henry is planning to purchase a Treasury bond with a coupon rate of 3.02% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 3.02% and face value of $100. The maturity date of the bond is 15 May 2033. (b) If Henry purchased this bond on 3 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 2.39% p.a. compounded half-yearly. Henry needs to pay 21.8% on coupon payment as tax payment and tax are paid immediately. Select one: a. 100.7470 b. 100.7556...
Henry is planning to purchase a Treasury bond with a coupon rate of 3.48% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 3.48% and face value of $100. The maturity date of the bond is 15 May 2033. (a) If Henry purchased this bond on 6 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 4.61% p.a. compounded half-yearly.  
Henry is planning to purchase a Treasury bond with a coupon rate of 2.67% and face...
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....
Henry is planning to purchase a Treasury bond with a coupon rate of 4.86% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 4.86% and face value of $100. The maturity date of the bond is 15 May 2033. (a) If Henry purchased this bond on 6 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 4.35% p.a. compounded half-yearly. (b) If Henry purchased this bond on 6 May 2018, what is his purchase price (rounded to four decimal places)? Assume a...
Henry is planning to purchase a Treasury bond with a coupon rate of 2.12% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 2.12% and face value of $100. The maturity date of the bond is 15 May 2033. (a) If Henry purchased this bond on 5 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 3.62% p.a. compounded half-yearly.
Henry is planning to purchase a Treasury bond with a coupon rate of 2.05% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 2.05% and face value of $100. The maturity date of the bond is 15 May 2033. (a) If Henry purchased this bond on 7 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 2.31% p.a. compounded half-yearly. (a) If Henry purchased this bond on 7 May 2018, what is his purchase price (rounded to four decimal places)? Assume a...
Henry is planning to purchase a Treasury bond with a coupon rate of 4.71% and face...
Henry is planning to purchase a Treasury bond with a coupon rate of 4.71% and face value of $100. The maturity date of the bond is 15 May 2033. (a) If Henry purchased this bond on 3 May 2018, what is his purchase price (rounded to four decimal places)? Assume a yield rate of 3.12% p.a. compounded half-yearly. (b) If Henry purchased this bond on 3 May 2018, what is his purchase price (rounded to four decimal places)? Assume a...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT