What is a Discount Called in the Context of a Negative Interest Rate?
"Even though the article doesn't actually use the word ""discount"", I think the corresponding word you are looking for is ""premium"". The words are used quite frequently even outside of the context of negative rates. In general, bonds are issued with coupons close to the prevailing level of interest rates, i.e. their price is close to par (100 dollar price). Suppose yields go up the next day, then the price moves inversely to yields, and that bond will now trade at a ""discount to par"" (less than 100 dollar price). And vice versa, if yields went down, prices go up, and the bond is now at a ""premium to par"" (greater than 100 dollar price)" "Negative Yields on Bonds is opposite of Getting profit on your investment. This is some kind of new practice from world wide financial institute.  the interest rate is -0.05% for ten years. So a $100,000 bond under   those terms would be ""discounted"" to $100,501, give or take. No, actually what you are going to get out from this investment is after 10 years when this investment is mature for liquidation, you will get return not even your principle $100,000 , but ( (Principle $100,000) minus (Negative Yields @ -0.05) Times ( 10 Years ) ) assume the rates are on simple annual rate.  Now anyone may wander why should someone going to buy this kind of investment where I am actually giving away not only possible profit also losing some of principle amount!  This might looks real odd, but there is other valid reason for issuing / investing on such kind of bond.  From investor prospective: Every asset has its own 'expense' for keeping ownership of it. This is also true for money/currency depending on its size. And other investment possibility and risk factor. The same way people maintain checking account with virtually no visible income vs. Savings account where bank issue some positive rate of interest with various time factor like annually/half-yearly/monthly. People with lower level of income but steady on flow choose savings where business personals go for checking one. Think of Millions of Ideal money with no secure investment opportunity have to option in real. Option one to keeping this large amount of money in hand, arranging all kind of security which involve extra expense, risk and headache where Option two is invest on bond issued by Government of country. Owner of that amount will go for second one even with negative yields on bonds where he is paying in return of security and risk free grantee of getting it back on time.  On Issuing Government prospective: Here government actually want people not to keep money idle investing bonds, but find any possible sector to invest which might profitable for both Investor + Grater Community ultimately country.  This is a basic understanding on issue/buy/selling of Negative interest bearing bond on market.   Hope I could explain it here. Not to mention, English is not my 1st language at all. So ignore my typo, grammatical error and welcome to fix it.  Cheers!"
"The Dividend Discount Model is based on the concept that the present value of a stock is the sum of all future dividends, discounted back to the present. Since you said: dividends are expected to grow at a constant rate in perpetuity ... the Gordon Growth Model is a simple variant of the DDM, tailored for a firm in ""steady state"" mode, with dividends growing at a rate that can be sustained forever. Consider McCormick (MKC), who's last dividend was 31 cents, or $1.24 annualized. The dividend has been growing just a little over 7% annually. Let's use a discount, or hurdle rate of 10%. MKC closed today at $50.32, for what it's worth. The model is extremely sensitive to inputs. As g approaches r, the stock price rises to infinity. If g > r, stock goes negative. Be conservative with 'g' -- it must be sustainable forever.  The next step up in complexity is the two-stage DDM, where the company is expected to grow at a higher, unsustainable rate in the early years (stage 1), and then settling down to the terminal rate for stage 2. Stage 1 is the present value of dividends during the high growth period. Stage 2 is the Gordon Model, starting at the end of stage 1, and discounting back to the present. Consider Abbott Labs (ABT). The current annual dividend is $1.92, the current dividend growth rate is 12%, and let's say that continues for ten years (n), after which point the growth rate is 5% in perpetuity. Again, the discount rate is 10%. Stage 1 is calculated as follows: Stage 2 is GGM, using not today's dividend, but the 11th year's dividend, since stage 1 covered the first ten years. 'gn' is the terminal growth, 5% in our case. then... The value of the stock today is 21.22 + 51.50 = 72.72 ABT closed today at $56.72, for what it's worth." The IRR is the Discount Rate r* that makes Net Present Value NPV(r*)==0. What this boils down to is two ways of making the same kind of profitability calculation.  You can choose a project with NPV(10%)>0, or you can choose based on IRR>10%, and the idea is you get to the same set of projects.  That's if everything is well behaved mathematically. But that's not the end of this story of finance, math, and alphabet soup. For investments that have multiple positive and negative cash flows, finding that r* becomes solving for the roots of a polynomial in r*, so that there can be multiple roots.  Usually people use the lowest positive root but really it only makes sense for projects where NPV(r)>0 for r<r* and NPV(r)<0 for r>r*.   To try to help with your understanding, you can evaluate a real estate project with r=10%, find the sum future discounted cash flows, which is the NPV, and do the project if NPV>0.   Or, you can take the future cash flows of a project, find the NPV as a function of the rate r, and find r* where NPV(r*)==0. That r* is the IRR.  If IRR=r*>10% and the NPV function is well behaved as above, you can also do the project. When we don't have to worry about multiple roots, the preceding two paragraphs will select the same identical sets of projects as meeting the 10% return requirement. Unless stated otherwise, these terms apply to all bonds. The par value or face value of a bond refers to the value of the bond when it's redeemed at maturity. A bond with a par value of $10,000 simply means that if you purchase the bond and hold it until the maturity date specified in the contract, you receive $10,000.  The purchase price, however, is exactly that: it's what you paid for the bond. Bonds may sell below, at, or above par. Continuing the example from above, if you paid $9,800 for a bought a bond with a $10,000 par value, you bought the bond below par. A bond selling below par is said to be selling at a discount. For bonds selling above bar, they're selling at a premium. If the purchase price and the par value are the same, the bond is selling at par. These terms apply to callable bonds only, which are bond contracts that allow the issuer of the bond (in the case of municipal bonds, the institution or agency who created the contract) to buy back from bond holders at a given date (the call date) and at a given price (the call price) before the bond reaches maturity and pays the holder the full par value.  Yes, the coupon rate is essentially the interest paid. It's usually represented as a percent of the par value, so if the $10,000 in the example above had a 5% coupon rate, this means that it paid out 0.05 * 10,000 = $500 each year. Usually, this payment is made as two semi-annual payments of $250. Some bonds are zero-coupon bonds, which means exactly what you would think; they don't make any coupon payments. U.S. Treasury Bills are one example of a zero-coupon bond. All of these factors are linked, because the coupon rate, callable provisions, and par value, along with the overall economic environment, can affect the purchase price of a bond. Yeah it's called the Fed buying shit mortgages that the banks invented to make money, then got bailed out on 100 cents on the dollar for, and with an underhanded deal that the banks will then buy Treasury bills with the magically prestidigitated money the Fed creates out of nothing that the banks receive in order to prop up federal debt prices, and thus keep interest rates down, so the dollar can limp along a little while longer until the bottom drops out because they are out of ways to keep the money cheap because at some point government debt will become massively discounted no matter what they do.  Only, how does this bizarre circlejerk process end?  It ends with consumption ramped up consuming things for a large war, is how it ends.  Edit: I'm wasted.  Fuck you. When he says shitty, he means less likely to actually pay back the money.   If I have a company that's not doing well enough, and I have already issued $100,000 in bonds onto this market, and I want to pay back all my bond-holders, maybe I convince a near-bankrupt company to give me $100,000 of bonds in their company for $50,000 in goods. I then repay my bondholders with the $100,000 in shitty bonds.  Or maybe I give them $300,000 in goods and they give me $600,000 in their shitty bonds (since thier company is about to fall apart and they know I'll give them a kickback down the line). Then I pay back my 100k bonds with the new shitty bonds, and I go buy $500k worth of raw material for my company and pay for them using almost-bankrupt-company's shitty bonds .   Then I have no debt, $500k worth of raw material, the people I used to owe money to (AND my suppliers) now hold a total of $600k in shitty bonds, and then my friend's almost-bankrupt-company DOES go bankrupt.... and my suppliers and old lenders realize the paper I just gave them is worthless. In the equity world, if a stock trades at 110 and is going to pay a dividend of 10 in a few days, an option expiring after the ex date would take the dividend into account and would trade as if the stock were trading at 100. (Negative) interest rates may also lead to a similar effect. In the commodity world the cost of carry needs to be taken into account. "The interest rate offered by a bond is called the nominal interest rate.  The so-called real interest rate is the nominal interest rate minus the rate of inflation. If inflation is equal to or greater than the nominal rate at any given time, the REAL interest rate is zero or negative. We're talking about a ten year bond. It's possible for the real interest rate to be negative for one or two years of the bond's life, and positive for eight or nine.  On the other hand, if we have a period of rising inflation, as in the 1970s, the inflation rate will exceed the (original) interest rate in most years, meaning that the real interest rate on the ten year bond will be negative over its whole life. People lost ""serious"" money on bonds (and loans) in the 1970s. In such situations, the BORROWERS make out. That is, they borrow money at low rates, earn inflation (plus a little more) pay back inflated dollars, and pocket the difference. For them, the money is ""free.""" Interest is a fee that you pay in order to use someone else's money. Once you've made the deal, pretty much anything you do that reduces the total interest that you pay does so by reducing the time for which you get to use their money. As an extreme example, consider a thirty-year interest-only loan, with a balloon payment at the end. If you pay it off after fifteen years you pay half as much interest because you had the use of the money for half as long. The same thing happens when you make biweekly payments: you reduce the total interest that you pay by giving up the use of some of the borrowed money sooner. That's not necessarily bad, but it's also not automatically good.