Question

Question 24 Suppose that, several years ago, the Canadian government issued three very similar bonds; each has a $1,000 face value and a 8-percent coupon rate and will mature in 5 years. The only difference between the bonds is the frequency of the coupon payments. If the market yield is now 6.3 percent. Determine the price of the bond that pays coupons annually. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answer to 2 decimal places, e.g. 1564.25.) Price of bond Determine the price of the bond that pays coupons semi-annually. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answer to 2 decimal places, e.g. 1564.25.) Price of bond Determine the price of the bond that pays coupons monthly. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answer to 2 decimal places, e.g. 1564.25. Round intermediate calculations to 6 decimal places, e.g. 1.251246.) Price of bond

Answer 1

Answer (a):

Annual coupon:

Face value = $1,000

Annual coupon = 1000* 8% = $80

Number of periods in Years = 5

PV factor for Annuity = (1 - 1 /(1 + 6.3%)^5)/6.3% = 4.17821

PV factor = 1 / (1 + 6.3%)^5 = 0.73677

Bond Price = 80 * 4.17821 + 1000 * 0.73677 = $1071.03

Bond Price = $1,071.03

Answer (b):

Semiannual coupon:

Face value = $1,000

Semiannual coupon = 1000* 8%/2 = $40

Number of periods in semiannual periods = 5 * 2 = 10

PV factor for Annuity = (1 - 1 /(1 + 6.3%/2)^10)/(6.3%/2) = 8.46527

PV factor = 1 / (1 + 6.3%/2)^10 = 0.73334

Bond Price = 40 *8.46527+ 1000 *0.73334 = $1071.95

Bond Price = $1,071.95

Answer (c):

Monthly coupon:

Face value = $1,000

Monthly coupon = 1000* 8%/12 = $80/12

Number of periods in months = 5 * 12 = 60

PV factor for Annuity = (1 - 1 /(1 + 6.3%/12)^60)/(6.3%/12) = 51.35420

PV factor = 1 / (1 + 6.3%/12)^60 =0.73039

Bond Price = 80/12 *51.35420+ 1000 *0.73039 = $1072.75

Bond Price = $1,072.75