A 7.40 percent coupon bond with 12 years left to maturity is priced to offer a 8

Question

A 7.40 percent coupon bond with 12 years left to maturity is priced to offer a 8.1 percent yield to maturity. You believe that in one year, the yield to maturity will be 7.7 percent. What is the change in price the bond will experience in dollars? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

A 7.40 percent coupon bond with 12 years left to maturity is priced to offer a 8.1 percent yield to maturity. You believe that in one year, the yield to maturity will be 7.7 percent. What is the change in price the bond will experience in dollars? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Explanation / Answer

This is a present value (PV) problem. We will use to excel PV function. The syntax of the excel PV function is:

PV= (rate, nper, pmt,[FV],[type])

Where   rate= Discount rate or the opportunity cost

              nper= number of periods

              pmt= Dollar value of the coupon payments

FV= The principal that we will receive at maturity. Also referred to as the par amount.

Type=0 or 1. 0 means payments made at the end of the period while 1 means payment made at the beginning of the period. The default setting in excel is 0.

1st Part- We are going to assume that the bond makes semi-annual payments, and the FV of the bonds is $ 1,000. Therefore, price of the bond when yield is 8.1 %:

rate=8.10/2=4.05% (Divided by 2 as coupon payments made semiannually)

nper= 2×12=24 (12 years left to maturity and factor of 2 since semi-annual payment)

pmt= (7.40%×1000)/2= $ 37 ( Every six months I will get coupon payment of $ 37.)

FV=$ 1000

Type=0 (nothing is given in the equation so we will assume default)

PV= (0.0405,24,37,1000,0)

$946.9078

2nd Part: Now using the same concept we need to find PV of the bond after 1 year when yield of the bond is 7.7 %.

rate=7.7/2=3.85% (Divided by 2 as coupon payments made semiannually)

nper= 2×11=22 (11 years left to maturity after 1 year and factor of 2 since semi-annual payment)

pmt= (7.40%×1000)/2= $ 37 ( Every six months I will get coupon payment of $ 37.)

FV=$ 1000

Type=0 (nothing is given in the equation so we will assume default)

PV= (0.0385,22,37,1000,0)

$978.0092

Conclusion: Therefore, the change in bond price when the yield to maturity changes from 8.1 % to 7.7 % in one year is (978.0092 -$946.9078 ) = $31.1014 = $ 31.10 (rounded 2 decimal places)

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