Question

1. Byblos 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?

2. The manager of a company is trying to select the most economic among three machines:

Machine         A               B          c

Initial cost    $5000 $6000 $7000

Annual cost    500     500 200

Savage value   300     800 1800

Useful life         6years         4yeas   1 2 years

the Marr value is 7%, which machine is the most economic?

3. A bond is good for 10 years. The coupon rate is 8% a year ,and the interest is paid every 3 months,the face value is $5000 and the purchasing cost is $4600. Find the nominal annual rate of return of this investment.

Answer 1

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

2.

Analysis period = 12 yrs

NPW of A = -5000 - 500*(P/A,7%,12) - (5000-300)*(P/F,7%,6) + 300*(P/F,7%,12)

= -5000 - 500*7.942686 - (5000-300)*0.666342 + 300*0.444012

= -11969.95

NPW of B = -6000 - 500*(P/A,7%,12) - (6000-800)*(P/F,7%,4) - (6000-800)*(P/F,7%,8) + 800*(P/F,7%,12)

= -6000 - 500*7.942686 - (6000-800)*0.762895 - (6000-800)*0.582009 + 800*0.444012

= -16609.63

NPW of C = -7000 - 200*(P/A,7%,12) + 1800*(P/F,7%,12)

= -7000 - 200*7.942686 + 1800*0.444012

= -7789.32

As Net present cost of C is lowest, it should be selected

3.

Coupon payment = 8% / 4 * 5000 = 100

t = 10 * 4 = 40 quarters

Let ROR be i%, then

-4600 + 100*(P/A,i%,40) + 5000*(P/F,i%,40) = 0

Dividing by 100

(P/A,i%,40) + 50*(P/F,i%,40) = 46

Using trail and error method

When i = 2%, value of (P/A,i%,40) + 50*(P/F,i%,40) = 27.355479 + 50*0.452890 = 50

When i = 3%, value of (P/A,i%,40) + 50*(P/F,i%,40) = 23.114772 + 50*0.306557 = 38.4426

using interpolation

i = 2% + (50 - 46) /(50-38.4426)*(3%-2%)

i = 2% + 0.3% ~ 2.3% (Approx)

Nominal return = 2.3% * 4 = 9.2% (Approx)