Question

How to solve using financial calculator

16. In order to pay for all of its Super Bowl commercials, assume that Anheuser-Busch issued a bunch of bonds on January 1, 2019 with the following terms:
          Par Value                                                        $10,000,000
          Maturity                                                          20 years (January 1, 2039)
          Annual Coupon                                               6% annual rate
          Market Required Yield-to-Maturity               6% annual rate (at time of issuance)
          Payment frequency                                         Semi-annual (every 6 months)
                                                                                                                                              (8 points)
    
    1. How much cash did Anheuser-Busch receive upon issuance in January? (Ignore any possible fees or transaction costs – what was the market value of the bonds?)
       
       
       
       
       
       
       
    2. Now assume that the annual coupon rate was 8% instead of 6%. How much would Anheuser-Busch have received at issuance in this case (and all other terms were the same as above)?
       
       
       
       
       
       
       
       
       
       
    3. Now imagine it’s January 1, 2024. What would be the market value of the bonds if the annual yield-to-maturity has increased to 8% (and the annual coupon rate were 6%, with semi-annual payments)?
       
       
       
       
       

Answer 1

Solution for A)

The market required yield-to-maturity was equal to the coupon rate. When this happens, the bond's market rate = bond's par value.

Hence, in this case, Anheuser-Busch would have received the par value of all the bonds, which is $10,000,000

Solution for B

Now, the coupon rate is 8%. To find out the current price of the bond, we will use a financial calculator and input details. Let's assume the price of 1 bond = $1,000

Currently, there are 20 years till maturity. hence, since the bond pays coupons semiannually,

n = 20 * 2 = 40,

I/Y is YTM/2 = 6/2 = 3

PMT = (8%/2) * $1,000 = $40

FV = future value = par value of the bond = $1,000

inputting all these details into your financial calculator, you will get, PV = $1,231.14772

Next, we calculate how much Anheuser-Busch would have received under these conditions

for every $ 1,000 worth of bond par value Anheuser-Busch is getting $1,231.14772. Hence for total par value of $10,000,000, Anheuser-Busch will get, $10,000,000 *$1,231.14772/$1,000 = $12,311,477.2 (without rounding up intermediate calculations)

Solution for C

In this case, the coupon rate remains at 6%, but YTM is 7%. To find out the current price of the bond, we will use a financial calculator and input details. Let's assume the price of 1 bond = $1,000

In 2024, there are 15 years till maturity. hence, since the bond pays coupons semiannually,

n = 15 * 2 = 30,

I/Y is YTM/2 = 8/2 = 4

PMT = (6%/2) * $1,000 = $30

FV = future value = par value of the bond = $1,000

inputting all these details into your financial calculator, you will get, PV = $827.079667

Next, we calculate how much Anheuser-Busch would have received under these conditions

for every $ 1,000 worth of bond par value Anheuser-Busch is getting $827.079667. Hence for total par value of $10,000,000, Anheuser-Busch will get, $10,000,000 * $827.079667/$1,000 = $8,270,796.67