Question

Compute the present values of the following. Bond using three different rates

Face Value= $1,000

Coupon rate= 12%

Coupons. Are paid once in. A year

Compute the PV of the bond using

I Discount rate of 14%

ii Discount rate of 12%

iii Discount rate of 10%

iv Discuss the relationship between PV of bond and different rates

no years to maturity given. assume a year to maturity if neccesasry

Answer 1

Answer :i) Calculation of PV of Bond using Discount rate of 14%

PV = [Coupon * PVAF @discount% for n years] + [Face Value * PVF @Discount rate for nth year]

n is the number of years to maturity and since it is missing I assume it to be 2

Coupon = 1000 * 12% = 120

PV = [120 * PVAF @14% for 2 years] + [1000 * PVF @14% for 2th year]

= [120 * 1.64666051091] + [1000 * 0.76946752846]

= 967.07

ii.) Calculation of PV of Bond using Discount rate of 12%

PV = [Coupon * PVAF @discount% for n years] + [Face Value * PVF @Discount rate for nth year]

n is the number of years to maturity and since it is missing I assume it to be 2

Coupon = 1000 * 12% = 120

PV = [120 * PVAF @12% for 2 years] + [1000 * PVF @12% for 2th year]

= [120 * 1.69005102039] + [1000 * 0.79719387754]

= 1000

iii) Calculation of PV of Bond using Discount rate of 10%

PV = [Coupon * PVAF @discount% for n years] + [Face Value * PVF @Discount rate for nth year]

n is the number of years to maturity and since it is missing I assume it to be 2

Coupon = 1000 * 12% = 120

PV = [120 * PVAF @10% for 2 years] + [1000 * PVF @10% for 2th year]

= [120 * 1.73553719008] + [1000 * 0.82644628099]

= 1034.71

iv) If the discount rate is more than Coupon rate , then Present value of bond is less than face value .

If the discount rate is equal than Coupon rate , then Present value of bond is equal than face value .

If the discount rate is less than Coupon rate , then Present value of bond is more than face value .