Question

Basic Discounting

1.  A. What is the price of a 10-year, $1,000 face value zero-coupon bond using a 4% rate of discount?

B. What price results if the rate of discount is 5%?

. c.What is the YTM if this bond could be purchased for $600?

Answer 1

Answer 1

(A)

Price of this zero coupon bond will be the present Value of this Bond.

Present value of zero coupon bond or Price of the coupon Bond is given by :

PV = FV/(1 + r)ⁿ

where PV = Price of the Bond or present value of the bond, FV = Face Value = 1,000 , n = time period= 10 and r = discount rate = 4% = 0.04.

Hence Using above formula we get :

Price of this Bond = PV = FV/(1 + r)ⁿ = 1,000/(1 + 0.04)¹⁰ = $675.56

Hence, the price of a 10-year, $1,000 face value zero-coupon bond using a 4% rate of discount is $675.56

(B)

Price of this zero coupon bond will be the present Value of this Bond.

Present value of zero coupon bond or Price of the coupon Bond is given by :

PV = FV/(1 + r)ⁿ

where PV = Price of the Bond or present value of the bond, FV = Face Value = 1,000 , n = time period= 10 and r = discount rate = 5% = 0.05.

Hence Using above formula we get :

Price of this Bond = PV = FV/(1 + r)ⁿ = 1,000/(1 + 0.05)¹⁰ = $613.91

Hence, the price of a 10-year, $1,000 face value zero-coupon bond using a 5% rate of discount is $613.91

(C)

As Discussed above Present value of zero coupon Bond is given by :

PV = FV/(1 + r)ⁿ

where PV = Price of the Bond or present value of the bond, FV = Face Value, n = time period and r = discount rate ot YTM i.e. Yield to Maturity.

=> (1 + r)ⁿ = (FV/PV)

=> r = (FV/PV)^1/n - 1

Here FV = Future value or face value of this bond = 1,000 , PV = Present Value or Price of the bond = 600 , n = time = 10 and r = YTM = Discount rate that we have to calculate

Hence, r = (FV/PV)^1/n - 1 => r = (1,000/600)^1/10 - 1

=> R = 0.0524 = 5.24%.

Hence, the YTM if this bond could be purchased for $600 is 5.24%.