Question

1. bank Is offering bonds with a face value of $10,000 and a coupon rate per year of 7%,good for 5 years and the Interest is paid quarterly. Blom bank Is offering bonds with a face value of $10,000 and a coupon rate of 8% paid every 6 months also good for 5

years. The purchasing cost for the Byblos bond is $9,500 and for the Blom bank Is $9,750

,if your Marr is 5% a year CMPOUNDED MONTHLY ,which is a better investment based on present worth analysis?

Answer 1

i = 5% / 12 = 0.4167% per month

Effective interest rate per quarter = (1+0.004167)^3 -1

= (1.004167)^3 -1

= 0.0125531 ~ 1.2553%

Effective interest rate per semiannual period = (1+0.004167)^6 -1

= (1.004167)^6 -1

= 0.0252639 ~ 2.5264%

Byblos Bank

t = 5*4 = 20 quarters

coupon payment per quarter = 0.07 * 10000 / 4 = 175

Present worth of investment = -9500 + 175*(P/A,1.2553%,20) + 10000*(P/F,1.2553%,20)

= -9500 + 175*(((1 + 0.012553)^20-1)/(0.012553*(1 + 0.012553)^20)) + 10000*((1 + 0.012553)^-20)

= -9500 + 175*(((1.012553)^20-1)/(0.012553*(1.012553)^20)) + 10000*((1.012553)^-20)

= -9500 + 175*17.590027 + 10000*0.779192

= 1370.17

Blom Bank

t = 5*2 = 10 semiannual periods

coupon payment per semiannual period = 0.08 * 10000 / 2 = 400

Present worth of investment = -9750 + 400*(P/A,2.5264%,10) + 10000*(P/F,2.5264%,10)

= -9750 + 400*(((1 + 0.025264)^10-1)/(0.025264 *(1 + 0.025264)^10)) + 10000*((1 + 0.025264)^-10)

= -9750 + 400*(((1.025264)^10-1)/(0.025264 *(1.025264)^10)) + 10000*((1.025264)^-10)

= -9750 + 400*8.740137 + 10000*0.779189

= 1537.94

As present worth of Blom bond is more, it should be selected