Whenever Im about to fill up the family car at the gas station, I find myself experiencing a moment of hesitation. Should I purchase regular, or should I pay a little extra for premium?

Im not an automotive engineer, so I dont know exactly whylet alone by how muchpremium gasoline is better for my cars engine. I can read the higher octane number on the pump and am willing to believe that higher is better, but how much better? In what way?

In contrast to this uncertainty, I do know one thing for sure: a tank of premium will cost me more than the same tank of regular. If regular is $3.70 a gallon, and premium is $4.00 a gallon, I will get the same amount of fuel (16 gallons in my car) in either case, but pay an additional $4.80 if I buy premium. So my hesitation comes from trying to balance the certainty of a higher cost today against some not-very-well-quantified benefit in the long run. After this hesitation, nowadays I always decide to pay less and choose regular.

However, I did encounter a very different choice a few years back. While travelling in Iowa, I learned that due to an ethanol subsidy throughout the state, the higher-octane premium grade gasoline was no more expensive than regular!

So over the course of that trip, I repeatedly made the opposite choice: given the certainty of there being no greater cost, I always chose the premium for its real, but hard to quantify, benefit to my car. Wouldnt you?

Premium Bonds Dont Cost More than Regular Bonds!

When it comes to bond investing, the term premium is not an indicator of costit just sounds like it is. The term does refer to what we call the dollar price of the bonda premium bond has a higher price tag than par bonds (which have price tags of $100). So, for instance, bonds with price tags of $101, $103.5, and $122 are all premium bonds. Conversely, bonds with price tags of $99, $94.72, etc. are discount bonds.

The price tag of a bond, however, is simply a function of the size of the bonds coupon (interest payment) in relation to the yield (set by market forces). Bonds with coupons that are higher than

the current market yield are said to have premium coupons, and have corresponding premium price tags. However, it doesnt cost more to buy a premium bond than a par bond.

You might want to read that line again.

Although a premium bond has a higher price tag than a par bond, it doesnt cost more to buy a premium bond. Now how can I say that? When you buy a bond, what you are buying is a stream of future interest payments. If a premium bonds higher price tag bought you only the same set of future interest payments as a par bonds $100 price tag did, then the premium bond would cost you more (just as filling up the same 16-gallon tank with premium gasoline costs more than doing so with lower-priced regular).

But with bonds, thats not how it worksinstead, you get more in future interest payments from a premium bond than you do from a par bond.

In fact, you get enough in additional future payments, in exchange for your premium upfront price, that the two bonds earn you the same amount once all is said and done

To illustrate this, lets consider two hypothetical five-year maturity bonds, both with a current market yield of 3%. One has a coupon rate of 3%, and hence its price tag is by definition par, or $100. Well call this the Par Bond. The second bond has a coupon rate of 5%. A bond calculator would tell us that the price tag on this bond at a 3% yield would be about $109.16.* Well call this the Premium Bond. For simplicity, well use annual coupon payments for both bonds, well reinvest their coupons at the same yield, 3%, well invest the same amount, $1,000,000, in each bond, and after five years, well see how much total money we have in each case.

For the Par Bond (see Table 1, below), we can buy $1,000,000 face amount with our money, so our annual coupon payment will be $30,000 (3% of $1,000,000). After five years, we will have five coupon payments ($150,000), plus our $1,000,000 face amount back, and an additional $9,274.07 in interest from the reinvestment of the earlier coupon payments, for a total of $1,159,274.07 from our $1,000,000 investment in the Par Bond.

For the Premium Bond (Table 2 below), because its price tag is not $100 but $109.16, we can only buy $916,091.39 face amount with our $1,000,000, so our annual coupon annual payment will be $45,804.57 (5% times the face amount). After five years, we will have received five coupons (totaling $229,022.85), plus the $916,091.39 face amount back, and an additional $14,159.83

interest from reinvesting the earlier coupons at 3%. So, in this case, we get back a total of $1,159,274.07 from our $1,000,000 investment in the Premium Bond.

The Premium Bond did not cost the investor more than the Par Bond each cost the investor $1,000,000.

Since they have different price tags, that investment buys different face amounts and different coupon streams, but as you can see, they both ultimately returned exactly the same dollar amount to the investor, $1,159,274.07 (Compare the received amount in Tables 1 and 2). It sounds like the bond math operates like my trip to Iowa a few years back. You can indeed get premium for the same cost as regular!

Is There Anything Premium About a Premium Bond?

You may be wondering, given that premium bonds dont cost any more than par bonds, whether there is any benefit to these bonds over par, or regular. After all, in my gasoline example, I did concede there were some advantages to premium over regular gasoline, and when given the chance to buy premium at no greater cost than regular, I did so in a heartbeat.

It turns out that premium bonds, like premium gasoline, do convey additional benefits over par bonds, even though they dont cost more. You will note that in the calculations in Tables 1 and 2,

there was a difference in the timing of when the investor received cashthe premium bond returned higher coupons, which in turn increased the amount of reinvestment interest the premium bond earned over the five years ($14,159.83 vs. $9,274.07). In these calculations, we used 3% as our interest rate for these reinvested coupons, which corresponds to a situation in which interest rates dont rise over the life of the investment (recall the bonds were purchased at a yield of 3%).

However, if interest rates were to rise during the five year investment period, the investor would certainly prefer to get more of his or her cash back earlier, in order to reinvest at the newly available higher rates. If rates rise, both the Par Bond and the Premium Bond will make more money due to higher interest earned on their reinvested coupon payments, but in that case the outcome will no longer be identical.

The Premium Bond, which returns more of the cash earlier, is able to capture more of these higher rates and return more to the investor than the Par Bond, at no greater cost. The difference can be substantialin the thousands of additional dollars (see Table 3 below) Rather than avoiding bonds that have dollar prices above $100, investors should prefer them. Premium bonds dont cost more than Regularand if rates rise, they can deliver better economic results.