Question

Today is 1 January 2019. Lucy is planning to purchase a 10-year 4.15% p.a. Treasury bond with a face value of $100. The maturity date of the treasury bond is 1 January 2029. The bond is redeemable at par. (25 marks) a. [12 marks]

• Use Goal Seek to find Lucy’s yield to maturity (express your answer as a j2), if the purchase price is $96.5.

• Use Goal Seek to find Lucy’s net yield to maturity, that is after tax rate, (express your answer as a j2), if the purchase price is $95.5. Given that Lucy needs to pay 30% tax on coupon payment (interest payment) only.

• Use Goal Seek to find Lucy’s net yield to maturity, that is after tax rate, (express your answer as a j2), if the purchase price is $94.5. Given that Lucy needs to pay 30% tax on coupon payment (interest payment) and capital gain.

Answer 1

(a) Face Value = $ 100, Coupon Rate = 4.15 %, Tenure = 10 years

Annual Coupon = 0.0415 x 100 = $ 4.15

Price = $ 96.5

Let the yield to maturity be y1

Therefore, 96.5 = 4.15 x (1/y1) x [1-{1/(1+y1)^(10)}] + 100 / (1+y1)^(10)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y1 = 0.04594 or 4.594%

(b) Face Value = $ 100, Coupon Rate = 4.15 %, Tenure = 10 years

Annual Coupon = 0.0415 x 100 = $ 4.15

Price = $ 95.5

Let the yield to maturity be y2

Therefore, 95.5 = 4.15 x (1/y2) x [1-{1/(1+y2)^(10)}] + 100 / (1+y2)^(10)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y2 = 0.04725 or 4.725 %

Tax Rate = 30 %

After-Tax Yield = (1-0.3) x 4.725 = 0.03308 or 3.08% ~ 3.1 %

(c)

Face Value = $ 100, Coupon Rate = 4.15 %, Tenure = 10 years

Annual Coupon = 0.0415 x 100 = $ 4.15

Price = $ 94.5

Let the yield to maturity be y3

Therefore, 94.5 = 4.15 x (1/y3) x [1-{1/(1+y3)^(10)}] + 100 / (1+y3)^(10)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y3 = 0.04857 or 4.857%

After-Tax Yield = (1-0.3) x 4.857 = 3.4 %