Question

Please show all work

Present Value and Yield to Maturity. (a) A 15 year coupon bond with face value $250,000 and a 5% coupon rate has a yield to maturity i = 0.06. What is the value of the annual coupon payment? What is the price of this coupon bond?

Answer: C = $12,500 and PCB = $225,719.39

(b) A 10 year coupon bond with a 4% coupon rate and yield to maturity i = 0.05 sells for a price of $9,227.8245. What is the face value of the bond?

Answer: FV =$10,000

Answer 1

A: Annual coupon = Coupon rate*face value

= 5%*250000

= 12500

Using financial calculator

Input: PMT = 12500

N =15

FV = 250000

I/Y = 6

Solve for PV as $225,719.38

B: Let the FV be 100, hence Coupon = 4%=$4

PV as a percentage will be 9227.8245/100 = 92.278245

FV of bond = Present value*(1+Rate)^number of periods + Future Value of annuity ( A* ((1+rate)^n-1)/rate)

100 = -92.278245*1.05^10 + 4*(1.05^10-1)/0.05

Which is true

Hence Fv of the bond will be 100*100 = 10,000