Question

QUESTION 43 An analyst collects the following spot rates, stated as annual BEYS: • 6-month spot rate = 6%. • 12-month spot rate = 6.5%. • 18-month spot rate = 7% • 24-month spot rate = 7.5%. Given only this information, the price of a 2-year, semiannual-pay, 10% coupon bond with a face value of $1,000 is closest to: A) $918.30 B) $1,000.00 C) $1,046.77 ОА B oc

Answer 1

Present value of the bond for the first period :
FV = 1000 * 10% / 2 = 50
Rate = 6% / 2 = 3%
Nper = 1

Present value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(3%,1,0,-50)
= $48.54

Present value of the bond for the second period :
FV = 1000 * 10% / 2 = 50
Rate = 6.5% / 2 = 3.25%
Nper = 2

Present value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(3.25%,2,0,-50)
= $46.90

Present value of the bond for the third period :
FV = 1000 * 10% / 2 = 50
Rate = 7% / 2 = 3.5%
Nper = 3

Present value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(3.5%,3,0,-50)
= $45.10

Present value of the bond for the fourth period :
FV = 1000 + 50 = 1050
Rate = 7.5% / 2 = 3.75%
Nper = 4

Present value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(3.75%,4,0,-1050)
= $906.23

Total present value = $48.54 + $46.90 + $45.10 + $906.23 = $1,046.77

Price of the bond = $1,046.77