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 five years to maturity, a semiannual coupon of 6% and a face value of $1,000. Bond B has ten 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 5%.
1. What is the present value of the coupon stream on each bond?
2. What is the present value of the face value on each bond?
3. What is the total value of each bond?
4. If Jamal sees the two bonds in the Wall Street Journal and they are both priced at 99, which bond should he buy?

Answer 1

Answer:

i. = $262.56 , = $308.87

ii. = $781.198 , = $613.91

iii. Bond A = $1,043.76 ,  Bond B = $922.78

Explanation:

(i) Present Value of Coupon Payment

Bond A :- Semiannual Coupon Amount = $1,000 * 6% * 6 / 12 = $30

Total Semiannual Period = 5 * 2 = 10

Semiannual Interest = 5% / 2 = 2.5%

Present Value of Coupon Payment = $30 * PVAF (2.5% , 10)

= $30 * 8.752

= $262.56

Bond B :- Annual Coupon Amount = $1,000 * 4% = $40

Annual Periods = 10

Annual Interest = 5%

Present Value of Coupon Payment = $40 * PVAF ( 5% , 10)

= $40 * 7.72

= $308.87

(ii) Present Value of Face Value of Bond

Bond A = $1,000 * PVF (2.5% , 10 periods)

= $1,000 * 0.7812

= $781.198

Bond B = $1,000 * PVF (5% , 10)

= $1,000 * 0.6139

= $613.91

(iii) Total Value of Each Bond

Bond A = $262.56 + $781.198 = $1,043.76

Bond B = $308.87 + $613.91 = $922.78

(iv)If Jamal sees the two bonds in the Wall Street Journal and they are both priced at 99, he should consider:

If the Bond Current Price is lower than Bond Fair Price then he should Buy the Bond

If the Bond Current Price is higher than Bond Fair Price then he should not buy  the bond

Market Price of Bond = $99

He should buy Bond A  But not Bond B