Introduction
In the event of making a choice between the two options, of which bonds to buy, the Johnson’s family has the task of determining the benefit they are likely to get in each case. This involves either calculating for the future value attached to the bond or the present value. Future value will weigh the two based on how much the investment will give in a particular a number of years. However, in this case we chose to use present value, which weighs the option based on the amount that should be spent in getting each at a particular interest rate. The present value is important because it predicts the amount of yield to be received in case a bond is to be purchased. Usually, the best option will be to choose the bond that has a higher value of investment today than that with the lower value, because this will give the investor a higher chance for bargain. This is especially true for cases where the investments give the same amount of interest to the bond holders with the same maturity periods. The case of Johnson’s family requires a closer look into the present value, as can be evident in the difference portrayed within the redemption value.
Methodology
The price of a bond is to be determined by finding the sum of all the Present Value of the future cash flows. In which case, this involves discounting all the given future cash flows. The formula to be used as follows:
Whereby C= coupon payment n is the number of payments; i is the interest rate or the yield required, M is the amount at maturity also known as the par value.
Price of a bond = present value on interest rate + present value of redemption value
Calculations for Johnson family’s case
For the two options
The option have the same present value of interest rate paymentnt.
Option A: Bond A is a $40000 10% 10 year bond paying annual coupons with redemption value $2000, which can be purchased at a premium for $3000.
Present value of redemption value = 30001+0.1010 = 1158.30
Present value of interest payment = 10%*4000+ 1-1+0.1-100.1=406.14
Hence total present value = 406.14 + 1158.30 = 1564.44
For option 2
Option B: Bond B is a $40000 10% 10 year bond paying annual coupons with redemption value $3000, which can be purchased at a premium for $2000.
Present value of redemption value = 20001+0.1010 = 772.20
Present value of interest payment = 10%*4000+ 1-1+0.1-100.1=406.14
Hence total present value = 406.14 + 772.2 = 1178.34
As can be seen from the above calculation, it comes out that the alternative 1 has a higher present value than the alternative 2. The difference comes because of the difference in present value of the redemption value for the two.
Conclusion
The calculations done indicate that alternative 1 is far much better than the alternative 2. This is because, when looking at the present value of their investments, it gives a higher value. This happens if we choose to ignore the option of exercising the put option. It comes out that Johnson family have to choose between receiving $1564.44 (for option 1) or 1178.34 (for option 2) today. This insinuates that the higher the face value of the redemption so does the present value of a bond goes higher. This is true for two scenarios where the bonds have the same interest rates.
