Question

Jamal just inherited some money from a distant cousin overseas. He would like to put some of it in a bond and is looking at two choices. Bond A has four years to maturity, a semiannual coupon of 5% and a face value of $1,000. Bond B has twelve years to maturity, an annual coupon of 4% and a face value of $1,000. Jamal knows that the rate expected in the marketplace for investments similar to these is 4.5%.


What is the present value of the coupon stream for each bond?
What is the present value of the face value for each bond?
What is the present total value of each bond?
If the prices in the Wall Street Journal are equal, which one should Jamal choose? _________
A or B

Ahmad just bought a certificate of deposit at his local bank. The rate printed on the front of the certificate is 6.8%, but Ahman knows that inflation is currently running at 2.15%.
What is the APPROXIMATE real rate of interest that Ahmad is getting?
What is the EXACT real rate of interest that Ahmad is getting? (Two decimal places, please)

Answer 1

1.Bond A
Semi annual coupon =5%*1000/2 =25
Number of Periods =4*2 =8
Semi annual YTM =4.5%/2 =2.25%
PV of coupons =PMT*((1-(1+r)^-n)/r =25*((1-(1+2.25%)^-8)/2.25% =181.80
.Bond B
Semi annual coupon =5%*1000/2 =25
Number of Periods =12*2 =24
Semi annual YTM =4.5%/2 =2.25%
PV of coupons =PMT*((1-(1+r)^-n)/r =25*((1-(1+2.25%)^-24)/2.25% =459.73

Bond A PV of Par Value =1000/(1+2.25%)^8 =836.94
Bond B PV of Par Value =1000/(1+2.25%)^24 =586.25

Present value of Bond A =25*((1-(1+2.25%)^-8)/2.25%)+1000/(1+2.25%)^8=1018.12
Present value of Bond B =25*((1-(1+2.25%)^-24)/2.25%)+1000/(1+2.25%)^24=1045.97

If Prices are equal Bond A must be chosen