Question

3. Valuation of a semiannual payment bond (6 pts.) Assume a bond with a coupon rate of 11%, a par (maturity) value of $7,400, and a maturity term of 4 years. Assume also semiannual coupon payments at a compounding annual interest rate of 7.5%. Please compute the price for this bond. (Please show your work and round-off your calculations to four decimals)

Answer 1

Annual Coupon Rate of bond = 11%

Semi-annual coupon rate = 11% / 2 = 5.5%

Par Value = $7,400

Semi-annual coupon amount = 5.5% * 7,400 = $407

Annual YTM Rate = 7.5%

Semi-annual YTM rate = 7.5% / 2 = 3.75%

Maturity = 4 years

Let us show all the cash flows for this bond :-

A Period 00 vauw Cash Flows 407.00 407.00 407.00 407.00 407.00 407.00 407.00 7,807.00 13 14 15

To arrive at the bond price, let us discount the respective cash flows with their Present Value Factors (PV Factors).

PV Factors are arrived at using Semi-annual YTM Rates

For example,

PV Factor for period 1 = 1 / (1+3.75%) ^1 = 0.9638

PV Factor for period 2 = 1 / (1+3.75%) ^2 = 0.9290

And so forth..

Attaching all calculations and formulas used :-

B D Par Value Semi-annual coupon rate Semi-annual YTM Rate 7,400.00 5.50% 3.75% Period 00 Vauw Cash Flows PV Factor PV of Cash Flows 407.00 0.963855422 392.2892 407.00 0.929017274 378.1100 407.00 0.895438336 364.4434 407.00 0.863073095 351.2707 407.00 0.831877682 338.5742 407.00 0.801809814 326.3366 407.00 0.772828737 314.5413 7,807.00 0.744895168 5,815.3966 SUM 8,280.9620

Par Value 7400 Semi-annual coupon rate=11%/2 Semi-annual YTM Rate =7.5%/2 Cash Flows PV Factor PV of Cash Flows =C$3*C$2 =1/(1+$C$4)^B7 =C7*D7 =C$3*C$2 =1/(1+$C$4)^B8 =C8*D8 =C$3*C$2 =1/(1+$C$4)^B9 =C9*D9 =C$3*C$2 =1/(1+$C$4)^B10 =C10*D10 =C$3*C$2 =1/(1+$C$4)^B11 =C11*011 =C$3*C$2 =1/(1+$C$4)^B12 =C12*D12 =C$3*C$2 =1/(1+$C$4)^B13 =C13*D13 = (C$3*C$2)+C2 =1/(1+$C$4)^B14 =C14*D14 SUM =SUM(E7:E14)

Hence, Price of Bond = $ 8,280.9620