Question

Page 7 of 8 (14 points) Bond prices and yield to maturity: Note for this problem, it is ok to not calculate the exact numerica solution as long as you show in detail the formula you would use to calculate your answer suppose you buy a two-year bond that is issued today that has a face value of $1.000 and a coupon rate of a. What is the price of the bond today if the market interest rate on similar bonds is 52 points $1000-(1+0.57² = blonu $1000 / blank = answer b. What will be your rate of return if you decide to hold this bond till maturity? (3 points Suppose that the day after you purchase the bond, market interest rate on similar bonds rises to 7%. What is the price of your bond now? (4 points) d. Now suppose that one year has gone by and the market interest rates are still 7%. You have received one coupon payment. What price can you expect if you try to sell your bond now? (4 points)

Answer 1

Answer a. Remember that the price of any security is the present value of its cash flow. In a bond there are two types of cash flows, one is the lump sum amount = the face value of the bond and the second is the annual annuity payment in the form of coupon payment. thus to find the value of the bond, we need to find out the PV of both these cash flows.

PV of $1000 (face value) of the bond, we will use the formula PV= $\frac{FV}{(1+r)^{n}}$ Here FV=fave value=$1000, r=interest rate on similar bonds=5% and n=years to maturity of bond=2. Thus the PV= $907.03

the PV of annuity we will use the formula $C*\frac{1-(1+r)^{-n}}{r}$ here C=annuity amount=5%of FV=$50, r= 5%, n=number of years for the maturity of the bond=2

Thus putting the values we will get $50*\frac{1-(1+0.05)^{-2}}{0.05}$ = 50*1.86= $92.97

Thus the present value of the bond will be $907.03+$92.97= $1000

Answer b. The rate of return of the bond will be equal to the coupon rate of the bond =5% as the face value and present value of the bond is same.

Answer c. Here again we will find the PV of the cash flows of the bond and add them just the value of r will be equal to 7%. Thus formula used for PV of face value= $\frac{FV}{(1+r)^{n}}$ , Here FV=fave value=$1000, r=interest rate on similar bonds=7% and n=years to maturity of bond=2. Thus the PV= $873.44

the PV of annuity we will use the formula $C*\frac{1-(1+r)^{-n}}{r}$ here C=annuity amount=5%of FV=$50, r= 7%, n=number of years for the maturity of the bond=2

$50*\frac{1-(1+0.07)^{-2}}{0.07}$

on further calculation we will get the answer= $90.40

The value of the bond now will be $873.44 + $90.40= $963.84

Answer d. Here again we will find the PV of the cash flows of the bond and add them just the value of r will be equal to 7% and n=1 as one year of maturity of the bond is gone. Thus formula used for PV of face value= $\frac{FV}{(1+r)^{n}}$ , Here FV=face value=$1000, r=interest rate on similar bonds=7% and n=years to maturity of bond=1. Thus the PV= $934.58

the PV of annuity we will use the formula $C*\frac{1-(1+r)^{-n}}{r}$ here C=annuity amount=5%of FV=$50, r= 7%, n=number of years for the maturity of the bond=2

$50*\frac{1-(1+0.07)^{-1}}{0.07}$= $46.73

The value of the bond now will be $934.58 + $46.73= $981.31