Question

A government issues $6000000 of serial bonds paying interest at j12 = 9%, of which $1000000 is redeemed in 15 years, $1500000 is redeemed in 20 years and $3500000 is redeemed in 30 years. Determine the purchase price on the day that the bonds were issued, in order for investors to receive a yield of j12 = 7%.

Answer 1

Computation of Issue price Semi- Date Annuals 1-15 Interest Cash flow PV factor at 7% Disc. cash flow $ $ 4,918,271 $ 15th 16-20 Redemption Interest $ $ 362,450 668,745 es 540,000 9.10791 (6000000*9%) 1,000,000 0.36245 450,000 1.48610 (5000000*9%) (PVAF at n=20 - PVAF at n=15) 1,500,000 0.25842 315,000 1.81503 (3500000*9%) (PVAF at n=30 - PVAF at n=20) 3,500,000 0.30832 $ 20th 21-30 Redemption Interest $ $ 387,630 571,734 $ Redemption $ 20th Issue Price $ $ 1,079,120 7,987,950 The bonds shall be issued at $7,987,950 in order to yield the investor at 7%.