TIPS In-Depth

Let’s take a deep dive into the language of TIPS.

By David Enna, Updated Dec. 31, 2022

Treasury Inflation-Protected Securities are a complicated investment, and it’s hard to find plain-language explanations. I have a Q&A on TIPS that answers many questions, but I thought it would be helpful to discuss, in detail, the complex language of TIPS. If you understand the language, you will better understand TIPS.

Par value

Par value is the bedrock of a TIPS investment. At some point, when you buy a TIPS at auction or on the secondary market, you will enter a dollar amount in a box. The dollar amount you enter is the par value of the TIPS you are purchasing.

TreasuryDirect’s purchase form. Purchase amount = par value.

Par value, almost always, is not what you will actually pay for that TIPS. The actual cost will be determined by a combination of factors, but par value is 1) the amount the Treasury guarantees will be returned to you at maturity, no matter what happens with inflation, and 2) the base amount you will use to determine the current accrued value of your TIPS.

Coupon rate

After the initial auction of a TIPS, the Treasury sets its coupon rate at the 1/8th-percentage-point increment below the auctioned real yield. (All coupon rates are set at 1/8th percentage points … 0.125%, 0.250%, 0.375%, etc. If the TIPS auctions with a negative real yield, it gets a coupon rate of 0.125%, the lowest the Treasury will go for a TIPS.)

For example, at the July 21, 2022, auction of a new 10-year TIPS, the auctioned real yield was 0.630% and the coupon rate was set at 0.625%.

The coupon rate remains the same until that TIPS matures, even if the real yield to maturity rises or falls in the future. For example, that July TIPS later reopened in November with a a real yield of 1.485%, but its coupon rate remained at 0.625%.

The coupon interest on a TIPS is biannual, paid out every six months. It is not reinvested. But while the coupon rate remains the same, the amount actually paid will rise (or possibly fall) to match the accrued principal of the TIPS.

Real yield to maturity

What is it? It is the total return your TIPS investment will earn above (or below) official U.S. inflation for the term of the TIPS. The term “real yield” means “yield above inflation.” Other Treasury issues and bank CDs have a defined “nominal” yield, but investors can’t know the future real yield. TIPS have a defined real yield, but investors can’t know the future nominal yield. It all depends on future inflation.

The real yield of any TIPS is constantly changing, based on market sentiment. But the important factor is: When you buy a TIPS you plan to hold to maturity, you have set in stone your real yield to maturity. The market may reprice that TIPS, but your real yield doesn’t change, unless you sell before maturity.

A key thing to remember about the real yield: After you purchase a TIPS, and pay a premium or discount to par value to create the real yield to maturity, this is what you will earn going forward:

Inflation accruals + coupon rate

In other words, your real yield was set by the price you paid. After that, you earn the rate of inflation + future coupon payments.

Pricing of a TIPS

How is the price of a TIPS determined? At the original auction, investors bid based on the desired real yield to maturity, because at that point there is no set coupon rate. At a reopening auction or on the secondary market, investors know the coupon rate, so bidding is based on how much the real yield will vary from that coupon rate.

You will see TIPS prices based on $100 increments, and that is how much you will pay for $100 of the TIPS’ current value (par value + inflation accruals). If the coupon rate is below the market real yield, then the price of the TIPS will be lower than $100. If the coupon rate is higher than the market, the price of the TIPS will be higher than $100. Here’s an example of how that worked for the 10-year TIPS issued in July 2022:

Originating auction. Even at an original auction, the TIPS price is unlikely to be exactly $100. That’s because: 1) the coupon rate will be slightly below the auctioned real yield (when the real yield is above 0.125%), and that will slightly lower the price you pay, and 2) even a new TIPS will have some inflation and interest accruals. A new TIPS is issued on the 15th of the month, but the settlement date is on the last business day of the month. So an investor is getting about 15 days of accrued inflation and interest.

Take the July 2022 10-year TIPS as an example:

The auctioned real yield, called “high yield” in this chart, was 0.630%, so the Treasury set the coupon rate at 0.625%. That set the unadjusted price for par value at about $99.951. But then you have to calculate in the fact that this TIPS would have an inflation index of 1.00495 on the settlement date of July 29, plus it would earn a few cents of interest in those 14 days.

  • $100 par value x .99951 unadjusted price = $99.952
  • $99.952 x inflation index of 1.00495 = $100.446 adjusted price
  • Plus the investor would prepay for about 2 cents of accrued interest.

Reopening auction. Now let’s quickly look at the result of the 10-year TIPS reopening auction on Nov. 17 for this same TIPS, CUSIP 91282CEZ0. Over the four months from the originating auction, real yields soared higher, so the pricing was quite different.

Note that the coupon rate remained at 0.625%, set by the original auction. But the auction resulted in a much higher real yield to maturity, 1.485%. And because of that, the price paid by investors was deeply discounted.

  • $100 par value x .92312 unadjusted price = $92.3126
  • $92.3126 x inflation index of 1.02147 = $94.2946 adjusted price
  • Plus the investor prepaid for about 23 cents of accrued interest

The key factor here is that the real yield to maturity was created by market demand, and because the real yield was higher than the coupon rate, the price of the TIPS was lower. When you buy a TIPS, whether at an opening or reopening auction or on the secondary market, the real yield to maturity is the key factor to consider. If you hold to maturity, it sets your future return over U.S. inflation.

Non-competitive bidders — that’s all of us — at both new and reopened TIPS automatically get the high yield. Big-money investors make competitive bids, which could be rejected. All winning competitive bids also get the high yield.

Accrued interest. As a side note, you pay for the accrued interest after the sale closes, but this money is not added to the principal of the TIPS. You will get that money back at the next coupon payment; in the case of this July 2022 TIPS, on January 15, 2023.

Inflation accruals

Inflation accruals for TIPS are based on non-seasonally adjusted inflation from two months earlier. The Treasury takes that inflation number and creates an inflation index that changes every day, up or down depending on if inflation was positive or negative two months earlier. For example, non-seasonally adjusted inflation rose 0.41% in October 2022, so TIPS inflation accruals in December are rising 0.41.%. In November, non-seasonal inflation dropped 0.10%, so inflation accruals will decline 0.1% in January.

Each month, on the day the U.S. inflation report is released, the Treasury issues new inflation index ratios for all TIPS for the month two months ahead of the report. Here is the full list of January inflation indexes, based on November inflation. And here is how those numbers look for the TIPS issued in July, CUSIP 91282CEZ0:

In that chart, note that the index ratio for Jan. 1 is 1.02569 and through the month will decline to 1.02469 on Jan. 31 because November was a slightly deflationary month. These inflation indexes are crucial because they set the base principal amount for all TIPS, every single day. That means if you sell a TIPS on the secondary market, you will get the full value of your earned inflation.

Accrued principal value

TIPS have a “market value” — set by the market based on constantly changing real yields to maturity, but also a “current principal value,” which ignores the market shifts and simply measures the current total of par value + inflation accruals. If you are holding to maturity, you can simple track the current accrued principal value with this equation:

Par value x inflation index = Accrued principal

If you bought $10,000 par value of a TIPS and it currently has an inflation index of 1.05672, that TIPS now has $10,567.20 of accrued principal. That number is important because it is the base for the next coupon payment. As it rises, the coupon payment also rises.

At maturity, any TIPS will pay par value x inflation index, along with one final coupon payment. It’s not complicated if you hold to maturity.

Current market value

The accrued principal value is one factor used to determine the current market value of a TIPS on the secondary market. As market real yields rise and fall, the price of the TIPS rises and falls. So the price could be $90 for $100 of value, or $110 for $100 of value, depending on how much the coupon rate varies from the market-set real yield.

Secondary market purchase. When you purchase a secondary-market TIPS at a brokerage, you will be putting a dollar amount in a box, just like at TreasuryDirect. But that is not what you will pay. It is the par value you are purchasing. Your actual purchase would look something like this for a TIPS with a price of $95 and an inflation accrual of 1.15:

  • You place an order for $10,000 par value
  • Principal you are purchasing: $10,0000 x 1.15 = $11,500 accrued value
  • Your cost: $11,500 x .95 = $10,925
  • Plus some small amount of accrued interest.
  • And in some cases, a brokerage commission.

So, in this simplified example, you’d be paying $10,925 for $11,500 of principal. From that moment on, until maturity, you’d be earning inflation + coupon payments. You accepted a below-market coupon rate, but were rewarded with a price discount. It all balances out. Par value is $10,000, so even if severe deflation strikes, you are guaranteed to receive at least $10,000 at maturity, along with coupon payments along the way.

As you go through the brokerage purchase process, you may see “yield to worst” listed as the yield. That is the real yield to maturity. This “worst” terminology refers to callable bonds, but TIPS aren’t callable and the worst yield is the actual real yield to maturity.

Inflation breakeven rate

This is a measure of market sentiment toward future inflation. It is calculated by subtracting the real yield of a TIPS from the nominal yield of a Treasury of the same term. For example, at the Dec. 20 market close, the 10-year inflation breakeven rate was 2.24%, based on Treasury estimates.

  • 10-year Treasury note was yielding 3.69%
  • 10-year TIPS had a real yield of 1.45%
  • 3.69% – 1.45% = 2.24%

Keep in mind that the inflation breakeven rate isn’t a great predictor of future inflation. It just measures market sentiment. Here is the trend in the 10-year inflation breakeven rate from 2003 to 2022. Look at the 2012 to 2108 era. Do you see any prediction or even hint of our current surge to 40-year-high inflation, topping 7% a year over the last two years?

Click on the image for a larger version.

The inflation breakeven rate is a useful tool, however, because it shows how “expensive” TIPS are versus a nominal Treasury. The lower the inflation breakeven rate, the cheaper the relative cost of a TIPS. Right now, with the 10-year at 2.24%, we are at the border of expensive, but the inflation trend has dramatically changed in the last two years. TIPS look attractive, in my opinion.

Final thoughts

I know that TIPS are an esoteric and confusing investment. I was at a party the other night and a friend told me, “I have TIPS in my portfolio but I have no idea how they work.” Yeah, I hear you. Things get less complicated if you invest in individual TIPS and hold to maturity, ignoring market swings. Then you can track current value with a simple Excel spreadsheet: Par value x inflation index.

I am sure I didn’t get close to answering all the possible questions or solving all the mysteries. I’ve been writing about TIPS for more than a decade and I still come across new concepts. It’s a learning process and I hope this article helps. If you did find this article helpful, please share it with friends who are new to investing in TIPS.

Confused by TIPS? Read my Q&A on TIPS

TIPS on the secondary market: Things to consider

Upcoming schedule of TIPS auctions

* * *

Feel free to post comments or questions below. If it is your first-ever comment, it will have to wait for moderation. After that, your comments will automatically appear.Please stay on topic and avoid political tirades.

David Enna is a financial journalist, not a financial adviser. He is not selling or profiting from any investment discussed. The investments he discusses can be purchased through the Treasury or other providers without fees, commissions or carrying charges. Please do your own research before investing.


29 Responses to TIPS In-Depth

  1. Craig says:

    Surely I’m overlooking it, but is there a resource that shows the overall yield performance of matured TIPS bonds? A 5 year TIPS bond I purchased at auction just expired – 9128284H0 – I downloaded the CSV and calculated the interest earned (0.00625/2 times the principal times the inflation factor at the time of the interest payment) – because that was easier than finding the interest payments in Fidelity’s site!!! My calculation yielded a 4.42% yield over the 5 years; this does not compound the interest earned.

    Comparing to other performance – STIP (~2.5 yr avg maturity) 5 year performance as of 3/31/23 was 3.01% and TIP (~7 yr avg maturity) was 2.75%. 5 year Treasury note yield was ~2.7% in April 2018.

    Anyway, it seems that there should be a resource that shows the historical and even the yield to date of TIPS bonds. Fidelity’s site is very confusing because it adjusts the cost basis of purchased bonds with the current inflation factor – I cannot find an apparent way to benchmark individual TIPS performance.

  2. Rob M says:

    Thank you for this excellent website. My question has to do with the ‘dreaded’ OID. I bought the 5 year TIP at auction issued Oct 22, 2022 and keep it in my US Treasury Direct personal taxable account. When I go to the Security Details for this TIP in my UST account, it states a Discount that is
    Discount = Par – price paid + accrued interest – accrued inflation compensation.
    That all makes sense to me.
    But, my 1099 OID states an amount in Box 8 that is ~20% higher than the Discount stated by the UST in my Security Details. What is driving this discrepancy?

    • Tipswatch says:

      When I look at the current value of one of my TIPS in TreasuryDirect, it shows me the inflation-adjusted value as Oct. 17, 2022 because (I assume) that is the last time that TIPS compounded the inflation accruals. But the 1099-OID will show the full accruals through December 2022. This could be the reason for the differing amounts?

  3. Ben Ethridge says:

    Hi. I think I basically understand the above, but I’m not understanding why the various TIP funds (VTAPX or VTIP for example) paid such a low dividend amount for the first quarter of 2023.

    Average dividend payment has been about 30 to 40 cents per share for a few years, but in first quarter of 2023 it dropped to about a penny a share. Looking over the dividend history, I don’t see it ever dropping this low.

    I’ve spoken with three different advisors at Vanguard (in three different departments) and none of them have a clue as to why this sudden drop occurred.

    They suggest that I write a letter to the fund manager for VTAPX and ask him, but they freely admit that he probably won’t respond to my letter. Since (they also said) I can neither email or call him, my only other alternative would be to drive up to Pennsylvania and try to get an appointment with him or one of his analysts/accountants.

    As to why the question matters: People in retirement count on dividend payouts for ongoing living expenses. I thought I could at least count on the weighted average coupon rate amount for that. Apparently that is not the case for TIP funds/ETFs.

    • Tipswatch says:

      It looks like the March dividend for VTAPX is always the smallest of the year. It was only 0.047 in March 2021 and it looks there was no March dividend in 2020 and several other years. I wonder what months of inflation are used to pay that dividend. Looking back to late 2022, we had inflation rates of 0.41% in October, -0.1% in November and -0.31% in December. That works out to flat inflation for three months, but the fund paid a decent dividend in December (0.559). So it could because there is a lag between inflation reports and the dividend payments.

      • Ben Ethridge says:

        That is a good observation, thanks. Here is corroborating evidence for what you say:

        I can’t find it now, but yes, I do remember reading somewhere that the underlying bonds have a few months delay in the CPI calculation for the principal adjustment…but I thought that was the underlying bond, so surely the fund wouldn’t be applying that as well.

        I do notice that about one-third of the underlying bonds in VTAPX were bought in January of the various years. (Random buys each quarter would be more like one-fourth from statistical probability.)

        At first I thought that Vanguard was using some kind of formula to “smooth” the dividend payments for each quarter…but then that wouldn’t make sense if March is typically zero or near zero, and the rest of the months are relatively high. If there is no smoothing formula from Vanguard, then the formula would just be the government’s, which is published…so we’re back to lack of randomness?

        Another thought is that maybe Vanguard is having to sell some pieces of bonds in certain months to savvy investors who sell after taking their cyclical high dividend payment, and that temporarily cuts the dividend for the rest of us who hold the fund for the long-term? but then they make it up in other quarters to get the Vanguard-published yearly dividend rates?

        At this point, I have more questions than answers, and the only person whom Vanguard staff says knows the answer is the fund manager (Joshua C. Barrickman), as I discussed above.

    • Tipswatch says:

      Ben, all TIPS issues get a daily inflation adjustment base on inflation two months earlier (this is the only way it could be done, since the inflation report lags by a month, and then the Treasury has to set the inflation adjustment for the next entire month.) The March inflation report will come out April 12 and will set the inflation accruals for May. So it is possible the TIPS funds have another lagging factor on top of that delay.

      • Ben Ethridge says:

        Ya. Here is the article I read on that subject (confirming what you also say above), i.e. delay in dividend payout due to the CPI calculation months. Notice that this is for TIP ETFs, not the underlying TIP bonds:

        Click to access mechanics-of-tips-en-us.pdf

        However, this still doesn’t explain why dividends in the first quarter are almost invariably zero or near zero for TIP funds, right?

        I would love to get my hands on that formula from Vanguard or Fidelity et al, wouldn’t you?


  4. Ahura says:

    I purchased CUSIP: 91282CDC2 directly from Treasury Direct at auction on 10-15-2021. At that time I paid a premium to purchase this 5 years TIP (Paid $10,950.93 for $10,000.00 par value).

    Today the same TIP is being sold in secondary market on for:

    Price (Bid) 95.799
    Price (Ask) 95.998
    Ask Yield to Worst 1.271%
    Ask Yield to Maturity 1.271%
    Current Yield 0.130%
    Inflation Factor 1.09035
    Inflation Adjusted Price 104.671419
    Third Party Price 95.834
    Inflation Adjusted Third party Price 104.465
    Spread to Treasuries -2.433
    Treasury Benchmark 3 YR.(1.625% 10/31/2026)

    I assume the par value is $100 for the quoted price above. Need to understand:

    The difference between Inflation Factor of 1.09035 versus Inflation Adjusted Price of 104.671419. why are they different? Shouldn’t the Inflation Adjusted Price be approximately 109.00?

    Inflation Factor of 1.09035., sounds correct as the inflation rate was over approximately 8% in 2022.

    Is it a better deal to buy the same TIPS in an IRA at the Ask Price of 95.998, instead of what I paid 109.509.

    Would you consider “Yield to Maturity” of 1.27% as the yield above inflation rate?

    Thank you

    • Tipswatch says:

      The inflation factor tells you simply the amount of accrued inflation, and 1.09035 means that your $10,000 par purchase now has accrued inflation value of $10,903.50. Multiply that by the price factor (0.95988) and you get a current market value of about $10,466 (which matches the inflation-adjusted price). If you decide to hold to maturity, you can ignore the market value and know you have $10,903.50 in inflation-adjusted value at this point.

      • Ahura says:

        Thank you for the explanation. Currently, the above TIPS have $10,903.50 in inflation-adjusted value at this point. With the price factor of 0.95988 I can purchase the same TIPS today for $10,466 (Approx. 4% discount.)
        Am I right in saying that today I can buy the same TIPS at discount of 4% with full forward Inflation adjustments to maturity and a low coupon rate of 1/8% (fixed at the auction).

  5. Roy says:

    I’m looking at 91282CFR7, issued on 10/31/22. The 3/31/23 Index Ratio is 1.00967. So after 5 months the inflation accrual is less than 1%. Seems very low given the inflation environment we’re in. Please help me understand. Thank you.

    • Tipswatch says:

      OK. The index ratio on the settlement date of Oct 31 was 0.99982 based on inflation of -0.04% in August. After that non-seasonally adjusted inflation was 0.22% in September (applied to November), 0.41% in October (applied to December), -0.10% in November (applied to January), -0.31% in December (applied to February) and then 0.80% in January (with 9 days applied to March). Add it up and you only get to 1.00399 on March 9.

      • Roy says:

        I’m sure you’re correct but I was unable to arrive at 1.00399. I started by subtracting .0004 from 1 then multiplying by 1.0022, 10041, .9990 etc.. Obviously I’m off base but I see the monthly adjustments are lower than I expected. Thank you.

  6. daanzu says:

    I’m still a bit perplexed why two TIPS with similar maturities have such different YTMs. It seems to me like the chance of overall deflation having an impact over a multiyear time frame would be negligible. What is the logic behind the coupon rate having a significant effect? Possible tax implications? I also don’t understand why the premium/discount would really matter (other than the trivial calculation necessary for determining how much/many you want to purchase), when it seems to me like the YTM would be the overriding concern. Thanks for your wonderful site/analysis/explanations!

    • Tipswatch says:

      The yield differences aren’t that great, really. Usually about 10 basis points or less. Today I happened to be looking at TIPS maturing from 2032 to 2033. There are four issues. One of them is 912810FQ6, with a coupon rate of 3.375%, an inflation factor of 1.673, and a buy price of 115.042. That means this TIPS is going for a whopping 92% above par value. The other three are selling at a discount and the yield difference is only about 6 basis points.

  7. Tom says:

    Thank you for all your great information!

    One clarification on the guaranteed yield to maturity.

    I purchased 9128286N5 with the following:
    Price: 97.4646
    Inflation Factor: 1.18076
    Settlement Date: 1/23/2023
    Maturity Date: 4/15/2024
    YTM at purchase: 2.62%

    My question is this: Since I know that the inflation factor on 2/28/2023 will be 1.17692 based on the -0.31% CPI drop in Dec 2022, would not a more accurate YTM be 2.35% factoring in the negative inflation adjustment that I know will happen between the settlement date of my purchase and the end of February?

    After that we do not know what the inflation will be so we can assume it will be unchanged till maturity.

    • Tipswatch says:

      YTM is real yield to maturity in this case, but that number is fairly irrelevant to what you will actually earn between now and when this TIPS matures in April 2024. It was based on the discount you paid at purchase. Keep in mind that real yield is the yield above inflation, and if inflation goes down, so does your return. That TIPS has a coupon rate of 0.5%, so from this point forward you are going to earn inflation accruals + 0.25% coupon payments on April 15 and Oct 15, 2023, and the last one one April 15, 2024.

      • Tom says:

        Thank you for your reply.

        To clarify: The real yield to maturity of 2.62% assumes that the inflation factor of 1.18076 stays unchanged through maturity, but we already know that this factor will decrease every day through the end of February as this has already been determined, so wouldn’t the inflation factor that is known furthest in the future (in this case Feb 28th) at the time of purchase be a more accurate reflection of real yield to maturity?

    • Tipswatch says:

      I repeat: The real yield is the yield above inflation. Inflation goes down, and your nominal yield goes down, but your real yield remains the same in relation to inflation. Let’s say that you bought $100 of principal. You got it at a 2.54% discount, plus you will earn 0.50% annually. At maturity, you’ll get that $100, plus any inflation accruals (up or down) and 0.50% annual interest. The real yield was set by the discount you paid at purchase. After that, your return is inflation accruals + coupon payments.

  8. David says:

    Hi David,

    Thanks again for a great posting. One thing I don’t understand are the actual mechanics/rules of the auction. What exactly are the “Big Money” actors bidding on? If the real yield, wouldn’t they just bid it up to infinity?

    Or is it like a silent auction and there are a fixed & limited number of $100 TIPs available to be sold to the lowest bidders? So if you bid too high — no TIPs for you. If someone made a very large bid at a low rate would that effectively be a shill and tank the auction for everybody else? In this model would there a certain amount set aside for “Big Money” and then non-competitive? Does the re-issue auction just get whatever is left over after the intro auction?

    If this is already explained somewhere else in a comprehensible way, please just link to it.



    • Tipswatch says:

      Basically, the Treasury sorts all the competitive bids from high to low. It starts accepting the lowest ones and moves up the yield ladder until it fills the auction funding level, which is $17 billion at the Jan. 19 auction. Once it fills its funding need, it sets the high yield and accepts every bid up to that level. All bidders below that point end up getting the high yield. Of course, all non-competitive bidders (like us) also get the high yield. But bidders above that high yield get rejected. There is more to the process, but that is the basic procedure.

      • Jody Swanson says:

        Thank you David-Tipswatch for helping me, a CPA, understand the TIPS bidding yield, etc. process. Even though I have been investing in TIPS on & off for decades.

  9. Naren Malayath says:

    Firstly, thanks for doing such a great service to individual investors. If anyone wants to do a financial blog, TIPS watch should be the template.

    I have a question related to pricing of the TIPS in secondary market. I see that the yield to maturity swings wildly for bonds that are very close to each other in maturity date. I see that the higher the accrued principal lower is the yield.

    (on Jan 16th 2023)
    2032 Apr 15 – with an accrued principal of 1678 – Yield is 1.427%
    2032 Jul 15 – with an accrued principal of 1025 – Yield is 1.306%

    Surely the the difference in 3 months is not driving the yield difference.
    Is the higher amount of principal that is at risk of deflation that is driving the higher yield?

    • Tipswatch says:

      Definitely, if two TIPS have very similar maturities, the one with the higher accrued principal will generally demand a higher real yield to maturity. But in this particular case, you need to also look at the coupon rate. The Apr 15 has a coupon rate of 3.375%, so it has more principal and a PREMIUM price ($116.21). The July 15 TIPS has coupon rate of 0.625%, so it has less principal and a DISCOUNTED price ($93.25).

  10. Jim says:

    Great analysis of TIPS! Could you explain the inverse relationship between TIPS real YTM and price. It seems as the YTM increases so too the price.

    • Tipswatch says:

      It is all about the coupon rate of the TIPS, versus the market real yield. If the real yield rises above the coupon rate, then the market price of the TIPS is going to fall below $100. As real yields rise higher, the price of the TIPS falls more. This is why the TIPS funds did so poorly in 2022; the real yield of a typical TIPS rose more than 250 basis points. …. Of course, the reverse is true. If the real yield falls below the coupon rate, then the price of the TIPS rises above $100, and will continue to rise if the real yield falls more.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s