In: Finance
A corporate bond has a face value of $1 000, a coupon rate of interest of 10.5% per annum, payable semi-annually, and 20 years remaining to maturity. The market interest rate for bonds of similar risk and maturity is currently 8.5% per annum. Required:
i. What is the coupon payment of the bond? (1 mark)
ii. What is the present value of the bond?
iii. If the coupon payment is payable annual (based on the same information), what is the value of the bond?
i] | Coupon payment = 1000*10.5%/2 = $52.50 | |
ii] | PV of the bond is the PV of the maturity value of $1,000 | |
and the coupon payments of $52.50 for 40 half years. | ||
The discount rate is 8.5%/2 = 4.25% half yearly. | ||
Price = 1000/1.0425^40+52.50*(1.0425^40-1)/(0.0425*1.0425^40) = | $ 1,190.77 | |
iii] | Value of the bond with annual coupons = | |
= 1000/1.085^20+105*(1.085^20-1)/(0.085*1.085^20) = | $ 1,189.27 |
Explanation for the formula:
The price of a bond is the sum of the following:
1] PV of the maturity value of the bond. Here it is $1,000 receivable after 40 half years [or 20 years]. Its PV = 1000/1.0425^40 [For annual coupons the PV of the maturity value = 1000/1.085^20.
2] PV of the semiannual interest of $52.5 [yearly $105]. It is an annuity. Using the formula to find PV of annuity, the PV of semi annual coupons = 52.5*(1.0425^40-1)/(0.0425*1.0425^40). For annual coupons the PV of annual interest = 105*(1.085^20-1)/(0.085*1.085^20).