Question

Hi,

I am solving this problem right now.

I assume that the red colored fields are wrong, and the orange ones are probably correct. Green is given by the professor.

I would appreciate some help.

Thank you very much. I RATE in return.

Last year you bought a bond. Bond characteristics as of the time of bond purchase are given below. a) What was the bond price last year, when you bought it? What was the coupon yield? b) What are the current bond price and coupon yield if YTM did not change? c) What taxes would you pay after holding bond for a year? What is your after-tax cash flow? The tax rate is given below. Color Coding Numbers given Numbers calculated automatically Student's Calculations/Answers Score (filled by professor) Time to maturity o Face Value 1 Coupon Rate 2 YTM 3 Payments per year 4 Personal tax rate 5 Annual Coupon 10 years $1,000 4.00% 3.00% 22.00% 40.00 20 Score Maximum 3.5 7 a) What was the bond price last year, when you bought it? What was the 8 coupon yield? 1 Price last year (when bought) 2 Coupon Yield 3 Per period rate $747.51 5.35% 1.50% 4.5 + b) What are the current bond price and coupon yield? 7 New time to maturity 9 years 9 Remaining number of periods 18 $769.22 Current Bond Price (one year later) 1 Coupon Yield 5.20% 3 c) What taxes would you pay after holding bond for a year? What is your after- 4 tax cash flow? The tax rate is given at the top. Assume that YTM did not 5 change. 7 Coupons received over the year $40.00 8 o Taxes paid 1 After-tax Cash Flow $8.80 $31.20 2

Answer 1

Calculation of Bond Price for Last year (when purchased) and current (after 1 year)

Bond Price =

Cx 1-(1+r) -n - + - (1+r)n

C = Coupon payment = 40 / 2 = 20

R = yield = YTM / 2 = 3% / 2 = 1.5%

n = number of periods = 10 years* 2 coupons every year = 20

F = Face Value

Bond Price When purchased = [20 * {(1-(1+1.5%)^-20)/1.5%}] + [1000 / ((1+1.5%)^20)]

= [20 * {0.257529581776227/1.5%}] + [1000 / 1.34685500655005]

= [20 * 17.1686387850818] + 742.470418223773

= 343.372775701636 + 742.470418223773

= 1085.84

Current Bond Price (1 year later) = [20 * {(1-(1+1.5%)^-18)/1.5%}] + [1000 / ((1+1.5%)^18)]

= [20 * {0.235088413385414/1.5%}] + [1000 / 1.30734063583203]

= [20 * 15.6725608923609] + 764.911586614586

= 313.451217847218 + 764.911586614586

= 1078.36

Note: Always remember when Yield is less than coupon rate, bond price is more than face value. Reason being you are getting more return than expected.

Good Luck.