How to calculate money earned off bonds?
Question by Lauren: How to calculate money earned off bonds?
If you bought a bond for $ 102 with a 5.2% coupon rate that pays semi-annually with a maturity of one year, how much money would you make after that one year?
Best answer:
Answer by buz
You’d receive $ 10.40 in interest payments, but since you bought the bond at $ 102, you’d actually have only made $ 8.40
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There will be some kind of taxes and commissions on anything you buy and sell. The bond price may fluctuate with the bond market depending on what is going on with the company who issued the bonds.
The price that you pay isn’t the value that the coupon rate is based on. The coupon rate of 5.2% is from the face value which would be $ 100 in this case. The bond is simply being sold at a premium because the interest that it offers is higher than the prevailing interest rates available at the time (10 yr US Treasury bond rate). Semi annually means twice a year so therefore there are two coupons that year, one at the six month mark and the second redeemable when the bond matures and hence redeemed with the face value. This means that for your $ 102 investment, you will receive a payment of $ 2.60 at the six month mark and receive $ 102.60 when the bond matures. In order to compare this with other investment opportunities, you would do an internal rate of return calculation to figure out what the yield to maturity is, basically you would determine at what rate R does the following equation hold true:
$ 102 = $ 2.60 / R^(1/2) + $ 102.60 / R
Which is R = 1.0318 or 3.18%
Note that although you are receiving $ 2.60 + $ 102.60 which is $ 105.20 for your investment of $ 102, that first $ 2.60 came in six months so it’s more valuable cause you could reinvest it into another investment. Therefore although you can only say that you made $ 3.20 from your $ 102 investment, it’s really equivalent to $ 3.24 if you could reinvest that first payment of $ 2.60 at 3.18% which appears to be the risk free discount rate they used to calculate the $ 102 price.
Now corporate bonds do have risks in that the company may not be able to make the payments that they promised to make. The average lifespan of a company in the Fortune 500 is 40 years so there’s roughly a 2.5% chance that a company will go under per year. Moody’s places this at 2% and it varies widely company to company with a AAA rated company being 2 in 10,000 while a CCC rated company has a 4% chance of going under per year. Using the 2% value, we have a 0.9950% chance that the company will go under in six months, let’s have p = 0.009950. So we have a p chance ( 0.9950%) that you won’t receive any money at all, a ( 1 – p ) * p chance ( 0.9851% ) that you will receive $ 2.60 and nothing else and a ( 1 – p )^2 chance ( 98.02% ) that you’ll receive all the payments due to you. Therefore, using Fermats expected value theorem, and using 3.18% as the discount rate which seems to be what they used to calculate the $ 102 market price, you actually wouldn’t want to pay more than $ 100 for the bond despite the coupon rate being higher than the risk free rate as you would want a 2.02% risk premium in order to risk your money. But even at $ 100, I wouldn’t invest more than 72% of my money in the corporate bond, keeping the rest free of risk in the US Treasury bonds because there is still the risk of loss with the corporate bond.