Time Value Problems

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Bond Practice Problems II

1. Seven years ago your firm issued $1,000 par value bonds paying a 7% semi-annual coupon with 15 years to maturity. The bonds were originally issued at par value.

a. What was the original yield to maturity on the bonds? They were issued at par…so the YTM = Coupon rate: 7%

b. If the current price of the bonds is $875, what is the yield to maturity of the bonds TODAY?
1000 FV
.07(1000)÷2= PMT
(15-7)*2 = N
-875 PV I/Y = 4.623*2 = 9.25%

c. If the yield to maturity computed in part b remains constant, what will be the price of the bonds three years from today?
Leave everything the same, just change N to (8 – 3)*2 = 10
PV = $911.70 2. You are looking to invest some money and identify two $1,000 par bonds with the same risk, both with 12 years to maturity and paying semi-annual coupons. Each of the bonds has a required return of 7%, but one bond is priced at $839.42 and the other at $1,120.44.

Compute the annual coupon rates for each bond.
1000 FV Only difference is price for second one
12*2 N -1120.44 PV
3.5 I/Y
-839.42 PV PMT = 42.5*2 = 85

PMT = 25*2 = 50 C. Rate = 85/1000 = .085 = 8.5%
C . Rate = 50/1000 = .05 = 5%

3. A $1,000 par bond has a 5% semi-annual coupon and 12 years to maturity. Bonds of similar risk are currently yielding 6.5%.

a. What should be the current price of the bond?
1000 FV
.05(1000)÷2= PMT
12*2 = N
6.5/2 = I/Y PV = $876.34
b. If the bond’s price five years from now is $1,105, what would be the yield to maturity for the bond at that time?
Just change N again, to…(12-5)*2 = N -1105 PV I/Y = 1.634*2 = 3.31%
c. What will the price of this bond be 1 year prior to maturity if its yield to maturity is the same as that computed in part b?
Just change N = 1*2….PV =…...

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