Question

Assume A fixed income security is option-free. The par value (face amount) is $1,000. The coupons are paid on a semi-annual basis. The coupon rate is 4%. The current market yield for the security for the security is 3%. There are 8 years left to the maturity date. Deliverable Excel spreadsheet items.

1. Calculate the price of the fixed income security. Show your work. a. Show the coupon payments in dollars each period. b. Show the principal payment in dollars (par value, face amount) at maturity. c. Show the present value of each cash flow payment. d. Sum the present values or each cash flow payment to obtain the price.

2. Calculate the duration of the fixed income security. Assume a 20 bps move up and a 20 bps move down to calculate the duration. Show your work.

3. If you changed to coupon rate to 2%, but kept the market yield to maturity at 3%, what happens to duration? Does it increase or decrease? Briefly explain why. No math is needed to explain why.

Answer 1

1. a - Coupon rate is 4% paid semiannuallly. So coupon paid each period would be 2% of face value. i.e. $20

1. b - Principal payment at maturity would be the face Value = $1000

1. c- Present Value of each cashflow.

Yield	1.50%	1.50%	1.50%	1.50%	1.50%	1.50%
Period	1	2	3	4	5	6
Cashflow	20	20	20	20	20	1020
Present value of each cashflow	19.70443	19.41323	19.12634	18.84368	18.56521	932.833

Formula

=cashflow/((1+Yield rate)^no of period))

1. d - Price of the security

Yield	1.50%	1.50%	1.50%	1.50%	1.50%	1.50%
Period	1	2	3	4	5	6
Cashflow	20	20	20	20	20	1020
Present value of each cashflow	19.70443	19.41323	19.12634	18.84368	18.56521	932.833
Total Present Value	1028.486
Formula	=cashflow/((1+Yield rate)^no of period))

Answer in 1.d can be calculated directly with excel formula as well.

Face Value	1000
Time for maturity	3
Frequency of coupon payment	2	Semiannual
Coupon Rate	4%
Coupon Payment (semiannually)	2%	Coupon Rate/ Frequency
Coupon (in $)	20	Coupon * Face Value
Yield	3%
Yield per period	1.5%	Yield/Frequency
PV	₹ -1,028.49	=PV(Yield per period, No. of period, Coupon per period, Faace Value, End of the period payment)

Note -

1. Negative sign with red font only signify that you will have to pay the amount in order to purchase the security.

2. I have answered only 1 question as it already has 4 parts.