Question

1. Suppose Company Inc. would like to buy today a five-year, $1000 bond with a 5% coupon rate and semi-annual coupons. The bond was issued exactly one year earlier today. The current market interest rate on similar bonds is 6%. What should the price of this bond be today?

2. Suppose Company Inc. held the bond until maturity, what should be its total rate of return on this bond?

3. At maturity, what is the price of the bond, assuming the issuer were solvable? Provide a proof for your answer.

***SHOW ALL WORK***

Answer 1

Given information

Face value 1000

coupon rate 5%

semi annual

nper 5

interest rate 6%

Annual coupon (pmt) 50 = (1000*5%)

1) The bond maturity is 5 years. In the question it mentioned that the bond was issued one year earlier today. So we are in the second year of bond issue. We are buying the bond in year 2. Now we need to find the price of bond in year 2. That can found using FV function in excel.

In the image above i have plotted cash flow from year 1 to 5.

Price of the bond in year 2 =FV(G13/2,2*2,G15/2,H6,0)

= 1020.92

Few things to understand.

The bond is semi annual, so divide rate of interest by 2.

We are calculating the value of the bond in year 2, so take the number of years as 2. Then multiply number years with 2 since it is semi annual. ( 2*2 )

Divide pmt (coupon amount) by 2 since it is semi annual. i.e 50/2 = 25

2) To calculate total rate of return on bond first we need to calculate FV of the bond in year 5.

Price of bond in year 5 =FV(G13/2,4*2,G15/2,-I8,0)

= 1070.96

Things to keep in mind

Since it is semi annual payment divide coupon amount and interest rate by 2, and multiply number of year with 2.

Number years to be taken here is 4. We are buying the bond in year 2. So number of years remaining is 4 years.

PV of bond taken in the above excel equation is -1020.92. Since we are buying the bond in year 2 at that price.

ROR on bond at maturity = (coupon amount+(price on the bond at maturity-purchase price of the bond))/purchase price of the bond

= (50+(1070.96 - 1020.92))/1020.92

=9.80%

3) price of the bond at maturity = 1070.96

Price of the bond at maturity is the FV of the bond at year 5.