Question

Ontario wants to raise $3,000,000 by issuing bonds. The coupon rate is set at 8% per annum with semi-annual payments. However, market interest rates have risen to 9%. If the bonds mature in 20 years, what is the current worth of the bonds?

        a) 3,000,000(P/F,4.0%,40) + 120,000(P/A,4.0%,40)

        b) 3,000,000(P/F,4.5%,40) + 120,000(P/A,4.5%,40)

        c) 3,000,000 + 120,000(P/A,4.5%,40)

        d) 3,000,000(F/P,4.5%,40) + 120,000(F/A,4.5%,40)

Answer 1

Ans:

since the coupons are paid semiannualy,

so Coupon amount = 4/100 * 3000000 = $120000.

time period = 2*20 = 40

discount factor = market rate @ semi annual basis = 4.5%

Also at the end of the period, the principal is paid back, so $3000000 is also paid back

calculating current value of bond,

= sum(PV of all future coupon payments )+ PV of principal amount paid at end of 40 time periods

(since, coupons are paid semi annualy, we keep 40 time periods @ 4.5% market rate on semi annual basis)

= 120,000*(P/A,4.5%,40) + 3,000,000*(P/F,4.5%,40) {OPTION B}

where,

(P/A,i,n) = Uniform series present worth factor =

(P/F,i,n) = Single payment present worth factor =