Question

A 22-year bond pays 4 coupons of 7 KRW per year for each 100 KRW of face value. The present value of the principal amount this bond will pay at maturity is 10.22 KRW per 100 KRW of par value. What is this bond's market price per 100 KRW of par value?

Answer 1

Sol:

Face value (FV) = 100 KRW each

Period (n) = 22 x 4 = 88 (Compounded quarterly)

rate (r) = (Compounded quarterly)

Present value (PV) = 10.22 KRW per 100 KRW of par value

To determine (r) compounded quarterly we will use PV of the principal.

PV = FV/(1+r)^n

PV = 100/(1+r)^88

10.22 = 100/(1+r)^88

(1+r)^88. = 100/10.22 = 9.78

1+r = 1.02625725

r = 2.625% (quarterly)

To determine market Price of the bond

FV = 100

Period (n) = 88,

Rate (r) = 2.625%

PMT = 7/4 = 1.75

PV = PMT [(1-(1/(1+i)^n))/i] + FV/ (1+i)^n

PV = 1.75[(1-(1/(1+2.625%)^88))/2.625%] + 100/ (1+2.625%)^88

PV = 1.75[(1-(1/(1+ 0.02625)^88))/0.02625] + 100/ (1+0.02625)^88

PV = 1.75[(1-(1/(1.02625)^88))/0.02625] + 100/ (1.02625)^88

PV = 1.75[(1-(1/(1.02625)^88))/0.02625] + 100/ (1.02625)^88

PV = 59.8491 + 10.2264

PV = 70.08

Therefore bond's market price per 100 KRW of par value will be 70.08 KRW