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Can I Retire (2020 edition), Investing Blog Roundup

Another book announcement for today: the 2020 edition of Can I Retire? is now available. Of the 2020 editions I’ve done this year, this is the book that received the most significant update. Some of the changes include:

  • The discussion of annuities has been adjusted, given the new environment in which inflation-adjusted SPIAs are no longer available;
  • There’s a new brief chapter on Social Security and how that fits into a broader retirement plan, especially in a “creating a floor of safe income” sort of context;
  • There’s a new chapter on retirement spending strategies; and
  • The discussion of asset location has been condensed somewhat, given its reduced importance in a consistently-low-yield environment.

You can find the print edition here and the Kindle edition here.

Other Recommended Reading

Thanks for reading!

Corporate Finance: Excel Examples

The following discussion is intended as a companion to my book Corporate Finance Made Simple: Corporate Finance Explained in 100 Pages or Less.

Click any of the links below to jump to the applicable part of this page.

Future Value

The “future value” of an asset is the amount that the asset will be worth at some specific point in the future, given a particular rate of return.

Example: We want to calculate the future value of a 7-year CD with an initial deposit of $1,000 and a 6% rate of return compounded annually.

We calculate present value as follows:

FV = PV x (1 + r)n

where:

  • FV is future value,
  • PV is present value,
  • r is the rate of return (as a decimal), and
  • n is the number of periods.

So you could calculate the future value manually by typing the following equation into a given cell:

= 1000*1.06^7

If you’ve done everything correctly, Excel should provide the result: $1,503.63.

Or you could enter the appropriate input values in cells in Excel, such as in the image below. (The text in column B isn’t necessary for the formula. Its purpose is simply to make it easier for you to remember what the number in each cell refers to.)

Then you could enter the following in a new cell, thereby calculating the FV by referencing your input cells rather than manually entering the values in your equation.

= A1*(1+A2)^A3

The above approach is often convenient, because it makes it easy to see how the result changes as you adjust one or more of the inputs. For instance if you change the cell that contains your rate of return from 6% to any other number, your calculated future value will immediately change accordingly.

Alternatively, you could use Excel’s built-in “FV” function, which requires the following parameters:

  • Rate (the rate of return)
  • Nper (the number of periods)
  • Pmt (the periodic payment)
  • PV (present value)
  • Type (either a zero or a one, to indicate the timing of any periodic payment; 1 indicates payment at the beginning of the period; 0 or leaving the field blank indicates payment at the end of the period)

You can access the FV function by clicking Insert -> Function -> FV. Then in your formula builder window, enter the following:

  • Rate = A2
  • Nper = A3
  • Pmt = 0 (We’re dealing with a CD for which there are no periodic payments at all.)
  • PV = -A1 (We enter a negative value here, because in Excel’s financial functions, a negative value indicates a cash outflow. We’re paying $1,000 to buy the CD in the first place, so we need a negative value in order to represent this outflow.)
  • Type = left blank

Click “done,” and you should see the appropriate future value ($1,503.63) appear in the cell.

If you click on the cell and look in your formula bar, you should see the following formula:

=FV(A2,A3,0,-A1)

Of note: If you prefer, you can enter the applicable values directly into the formula builder window rather than entering them by reference to cells. (For example, instead of entering A2 for the rate, you could enter 0.06.)

Present Value

The “present value” of a future cash flow is the amount that that future cash flow is worth today.

Example: How much would you be willing to pay for an investment that will pay you $10,000 five years from now, if you could earn a 9% rate of return per year, via other investments with similar risk? (That is, what is the present value of a $10,000 cash flow five years in the future, with a 9% discount rate?)

We calculate present value as follows:

PV = FV / (1 + r)n

where again:

  • PV is present value,
  • FV is future value,
  • r is the discount rate (as a decimal), and
  • n is the number of periods.

So you could calculate the present value manually by typing the following equation into a given cell:

= 10000/1.09^5

If you’ve entered your equation correctly, Excel should provide the result: $6,499.31.

Or you could enter the appropriate input values in cells in Excel, such as in the image below.

Then you could enter the following equation in another cell, thereby calculating the present value by referencing your input cells:

= A1/(1+A2)^A3

Or you could use Excel’s built-in “PV” function, which requires the following parameters:

  • Rate
  • Nper
  • Pmt
  • FV
  • Type (again, either a zero or a one; 1 indicates payment at the beginning of the period; 0 or leaving the field blank indicates payment at the end of the period)

You can access the PV function by clicking Insert -> Function -> PV. Then in your formula builder window, enter the following:

  • Rate = A2
  • Nper = A3
  • Pmt = 0 (In our example there are no periodic payments at all.)
  • FV = A1
  • Type = left blank (Again, there are no periodic payments, so the timing of the nonexistent payments doesn’t matter. We could enter a one, a zero, or leave it blank, and we’d get the same answer regardless.)

Click “done,” and if you’ve done everything correctly, you should see the present value (-$6,499.31) appear in the cell. (Note that it’s a negative value, simply to indicate a cash outflow again. That is, you’d have to pay $6,499.31 today, in order to have $10,000 after five years, given a 9% rate of return.)

If you click on the cell and look in your formula bar, you should see the following formula:

=PV(A2,A3,0,A1)

Again, if you prefer, you can enter the applicable values directly into the formula builder window rather than entering them by reference to cells. (For example, instead of entering A2 for the rate, you could enter 0.06.)

Net Present Value (NPV)

The “net present value” of an investment is the sum of the present values of each of the cash inflows, minus the sum of the present values of each of the cash outflows.

Example: We want to calculate the NPV for a project with an initial cost of $1,000, which is projected to provide the following annual cash inflows, given a 7% discount rate.

  • End of year 1: $200,
  • End of year 2: $300,
  • End of year 3: $400,
  • End of year 4: $500.

We could manually calculate the net present value, by calculating the present value of each individual cash flow, then summing those present values. But that would be inconvenient, to say the least. (And with more complex streams of cash flows, it becomes thoroughly impractical.)

A much faster approach is to use Excel’s “NPV” function. The NPV function requires the following parameters:

  • Rate (the discount rate)
  • Value1 (the future value of the first cash flow)
  • Value2 (the future value of the second cash flow)
  • etc

We begin by entering our relevant inputs:

Then we choose Insert -> Function -> NPV.

An important point about the NPV function is that it assumes that cash flows happen at the end of each period. So if you have any cash flow that occurs at the beginning of the first period, you have to exclude it when using the NPV function, then manually add/subtract the initial cash flow in question. So in our example, we will not be including the value in cell A2 in our NPV function. Rather, we’ll calculate the NPV without it, then we will manually subtract $1,000 from the calculated NPV to arrive at the actual NPV for our investment.

In the formula builder window, you can manually enter A3 for Value1, A4 for Value2, A5 for Value3, and so on. A faster approach, however, is to enter a range of cells for Value1. That is, for Value1 you would select (highlight) the entire range from A3 to A6. Or you could type A3:A6 as the value for Value1.

When you click “done,” the NPV for the cash inflows should appear: $1,156.91. But remember, that does not account for the present value of the cash flow at the beginning of the first period. We have to subtract that manually. When we do so, we see that the NPV for the investment is $156.91.

Internal Rate of Return (IRR)

The “internal rate of return” (IRR) for an investment is the discount rate at which net present value of the cash flows is zero (i.e., it is the discount rate at which the present value of the cash outflows is equal to the present value of the cash inflows).

Example: We want to calculate the IRR for a project with an initial cost of $1,000, which is projected to provide the following annual cash flows:

  • End of year 1: $200,
  • End of year 2: $300,
  • End of year 3: $400,
  • End of year 4: $500.

There’s no practical way to calculate IRR manually, as the only way to do it is by trial and error. Fortunately, Excel can do the math instantly via the IRR function, which takes in the following parameters:

  • Values: (the range of cells that contain the cash flows in question)
  • Guess: (your guess as to the IRR — basically you’re telling Excel where to begin the trial and error process. If you leave this blank, Excel will start with 0.1 (i.e., 10 percent)).

Your first step would be to enter each of the cash flows, including the initial outflow (which, again, must be negative to indicate that it’s an outflow). Like so:

Then you can select another cell (wherever you want the IRR to appear) and click Insert -> Function -> IRR. Then in your formula builder window, provide the following inputs:

  • Values = A1:A5
  • Guess = left blank

When you click “done,” Excel should give you the calculated IRR (in this case, 12.8%, which may appear as 13% depending on how many decimals you currently have it set to show).

If you click on the cell and look in your formula bar, you should see the following formula:

=IRR(A1:A5)

Excel’s XIRR Function

One limitation of Excel’s IRR function is that it only works if the cash flows occur at regular intervals (e.g., monthly or annually).

If you have a series of cash flows in which there is no regular interval, you can use Excel’s XIRR function to calculate the internal rate of return for the series.

The XIRR function requires the following parameters:

  • Values (the dollar amounts of the cash flows in question)
  • Dates (a range of cells with the dates on which the cash flows will occur)
  • Guess (your guess as to the IRR)

Example: We want to know the IRR for the following series of cash flows:

  • $5,000 outflow on 1/1/2021
  • $1,000 inflow on 10/15/2021
  • $1,500 inflow on 3/10/2022
  • $3,000 inflow on 8/20/2022
  • $2,000 inflow on 6/15/2023

You would begin by typing the relevant inputs into cells, like so:

Then you can select another cell (wherever you want the IRR to appear) and click Insert -> Function -> XIRR. Then in your formula builder window, provide the following inputs:

  • Values = A1:A5
  • Dates = B1:B5
  • Guess = left blank

When you click “done,” Excel should give you the calculated IRR (in this case, 28.6%).

If you click on the cell and look in your formula bar, you should see the following formula:

=XIRR(A1:A5,B1:B5)

Yield to Maturity (YTM)

Yield to maturity (YTM) is the rate of return that a bond buyer would earn if he/she buys the bond at today’s price, holds the bond to maturity, and receives all the promised payments on time (i.e., there is no default).

Example #1: A three-year bond has a $1,000 par value and a 6% coupon rate, with interest paid annually ($60 every 12 months). The bond is currently selling for $960. What is the bond’s YTM?

To find the YTM, we can use Excel’s “Rate” function. The Rate function requires the following parameters:

  • Nper (the number of periods)
  • Pmt (the periodic payment)
  • PV (present value)
  • FV (future value — in this case, the face value of the bond)
  • Type (either a zero or a one, to indicate the timing of any periodic payment; 1 indicates payment at the beginning of the period; 0 or leaving the field blank indicates payment at the end of the period)
  • Guess (your guess as to the YTM. If you leave this blank, Excel will start with 0.1 (i.e., 10 percent))

We could provide our inputs in a spreadsheet as follows:

Then you would select another cell (wherever you want the YTM to appear) and click Insert -> Function -> Rate. Then in your formula builder window, provide the following inputs:

  • Nper = A2
  • Pmt = A3
  • PV = -A4 (Again, we use a negative value here to reflect the fact that purchasing the bond would reflect a cash outflow.)
  • FV = A1
  • Type (zero or left blank to indicate that coupons are paid at the end of each period)
  • Guess (left blank)

When you click “done,” Excel should give you the calculated YTM (in this case, 7.54%).

Things are slightly more complicated in a case in which interest payments are made more often than annually. And this is important, because most bonds in the US pay interest semiannually — every six months. When a bond pays interest more often than once per year, the quoted YTM represents the actual rate per payment period, multiplied by the number of payment periods per year.

Example #2: A three-year bond has a $1,000 par value and a 6% coupon rate, with interest paid semiannually ($30 every 6 months). The bond is currently selling for $960. What is the bond’s YTM?

In this case we could provide our inputs as follows:

And in our formula builder window for the Rate function, we would provide the following:

  • Nper = A2*2 (i.e., six semiannual periods)
  • Pmt = A3
  • PV = -A4 (Again, we use a negative value here to reflect the fact that purchasing the bond would reflect a cash outflow.)
  • FV = A1
  • Type (zero or left blank to indicate that coupons are paid at the end of each period)
  • Guess (left blank)

When you click “done,” Excel should give you the calculated rate (in this case, 3.757%). But this is the semiannual rate. To annualize it, we would multiply this figure by two (to reflect that there are two semiannual periods per year). The result would be the bond’s YTM: 7.514%.

To Learn More, Check Out the Book:

Corporate Finance Made Simple: Corporate Finance Explained in 100 Pages or Less

Topics Covered in the Book:
  • The difference between finance and accounting
  • Raising capital by borrowing or by selling equity
  • Cost of capital
  • Net present value, IRR, and other capital budgeting metrics
  • Click here to see the full list.

How Do Social Security Inflation Adjustments Work?

A reader writes in, asking:

“I’d be interested in an article on the specifics of Social Security inflation adjustments. I have a vague awareness that my wages are indexed so that my wages from early years count for more than just the actual dollar amount earned. And I also know that the SSA publishes a COLA figure every year for people already receiving benefits. Are those the same thing? And does a person have to file for benefits in order to start getting the COLA?”

The indexing of prior-year earnings is completely separate from the annual cost-of-living adjustments. Let’s discuss how each works.

Wage/Earnings Indexing

Wage indexing occurs at one point in time: in the year you turn 62 — or the year in which you die or become disabled if such happens before you reach age 62.

All of your wages (and net earnings from self-employment) up to 2 years prior to the year in question are indexed based on the national average wage index (NAWI) — sometimes just referred to as the average wage index (AWI). This can be roughly thought of as adjusting your old earnings for “wage inflation” up to age 60.

Example: Bob (alive and not disabled) turns 62 in 2020. All of Bob’s historical earnings up to 2018 are indexed based on the ratio of NAWI in 2018 to NAWI in the year of the earnings in question. So for example if Bob’s earnings in a given earlier year were exactly twice the NAWI figure for that year, then his earnings for that year would essentially “count for” twice the 2018 NAWI.

In the year 2000, NAWI was $32,154.82. If Bob earned twice that amount (i.e., $64,309.64) in the year 2000, then his 2000 earnings would be adjusted to twice the 2018 NAWI when originally calculating his benefit. In 2018, NAWI was $52,145.80, so Bob’s year-2000 earnings would count for $104,292 in 2018 dollars.

Earnings after age 60 are not indexed. In most cases this means that earnings after age 60 actually count for more than they would if they were indexed — because if they were indexed, they’d have to be indexed downward to age-60 dollars, given that NAWI usually grows over time. (There are exceptions of course. NAWI shrank in 2009 with the recession, and it’s certainly going to be lower for 2020 than it was for 2019.)

Another relevant point here — one you may have seen discussed in the news lately — is that your Social Security benefit is ultimately rather dependent on the NAWI figure in the year you turn age 60. If NAWI is low in that year, all of your prior earnings will be multiplied by the low age-60 NAWI. While we won’t know 2020 NAWI until (roughly) September 2021, it’s clear that the figure will be unusually low, given the dramatic amount of earnings loss this year. This is not a good thing for people born in 1960. (And to the extent that it doesn’t recover by 2021, this is not a good thing for people born in 1961.)

Cost-of-Living Adjustments (COLA)

The second type of indexing is the annual cost-of-living adjustment based on actual price inflation. Beginning with the year you turn 62 (or, if earlier, the year you die or become disabled), each year, your primary insurance amount is indexed upward based on the Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W).

Specifically, the COLA for a given year is based on the average of the CPI-W for the third quarter of the prior year, divided by the average of the CPI-W for the third quarter of the year before that. For example, the average CPI-W from July-Sept of 2019 was 1.6% higher than the average CPI-W from July-Sept of 2018, which is why we had a 1.6% COLA in 2020.

If the calculated figure is negative (i.e., CPI-W went down), then there is no COLA rather than there being a negative COLA. And in the following year, the denominator in the calculation will be the third quarter CPI-W from the last year for which there was an inflation adjustment. For example, in 2015, the third quarter average CPI-W was lower than in 2014. So there was no COLA for 2016. Then, in 2017, the COLA was calculated based on the ratio of average CPI-W from third quarter 2016 relative to third quarter 2014 (rather than being compared to 2015 as would typically be the case).

Finally, to answer the reader’s second question, a critical point about Social Security cost-of-living adjustments is that they do not depend on whether or not you have claimed your retirement benefit. That is, you will get the applicable COLAs beginning age 62 onward, regardless of the age at which you file for your retirement benefit.

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Topics Covered in the Book:
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  • How to decide the best age to claim your benefit,
  • How Social Security benefits are taxed and how that affects tax planning,
  • Click here to see the full list.

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Investing Blog Roundup: Downsizing, How to Get Rid of Stuff

Over a lifetime, we accumulate a lot of stuff. If you’ve lived in the same home for many years — and it’s therefore been quite a while since you’ve gone through the forced purge of moving — it’s probably a lot of stuff.

At some point, all of that stuff will have to go. Maybe that job will be yours if you do end up moving, or maybe the job will ultimately fall to your children or some other designated party. But, eventually, none of your stuff will remain in (what is currently) your home.

This week I encountered an interview of David Ekerdt about the findings from his new book, Downsizing: Confronting Our Possessions in Later Life. For the book Ekerdt conducted extensive interviews with people ages 50+ about their experiences getting rid of their stuff. The interview below shares many of the lessons and insights gained from that research.

Other Recommended Reading

I hope you’re well, and thanks for reading!

How Does the Fed “Prop Up” the Stock Market? (Interest Rates and Stock Prices)

A reader writes in, asking:

“I’ve read over and over this year that the Fed is ‘propping up’ the stock market by keeping interest rates low. How does that work?”

Broadly, there are two ways in which low interest rates help to keep stock prices high.

Firstly, to the extent that corporations are borrowers, keeping interest rates low reduces their costs and therefore directly improves their profitability, which of course helps keep their share prices higher. In the case of a struggling corporation, having access to low-cost capital can even make the difference between declaring bankruptcy or not. And of course avoiding bankruptcy proceedings is good for shareholders.

The second effect has to do with the way stocks are priced. (I think it’s actually easier to understand this effect from the perspective of increases in interest rates. So we’ll start with that.)

Stocks are quite a bit riskier than Treasury bonds. So why do you own stocks at all, rather than just buying Treasury bonds with all of your savings? Presumably, you own stocks because you hope to earn additional returns beyond what Treasury bonds earn. That additional return that you hope to earn is known as a risk premium (i.e., additional return to compensate you for the additional risk).

The price of a stock reflects the (market’s consensus as to the) present value of the future cash flows from the stock. And the discount rate used in that present value calculation is usually something along the lines of “whatever we could earn from bonds, plus a risk premium.”

So when interest rates go up, the necessary discount rate goes up. A higher discount rate means a lower present value, which means stock prices go down.

Or you can think of it this way: imagine that TIPS yields suddenly went way up to 3%, rather than the roughly -1% range where they are right now. Maybe you had been estimating that stocks would earn a 4% real return going forward. Before, that was a 5% risk premium. But with TIPS yielding 3%, a 4% real return would only be a 1% risk premium. Maybe you decide that a 1% expected risk premium isn’t high enough to justify the additional risk from owning stocks, so you sell your stocks to buy TIPS.

Collectively, lots of people would be selling stocks to buy bonds in such a scenario. So the price of stocks would fall. When the price falls, the expected return going forward goes up (because a new buyer is paying a lower price for a given amount of dividends/earnings). And the price would continue to fall (i.e., people would keep selling stocks) until the price was low enough that the expected return was high enough to earn whatever the market collectively decided was a sufficient risk premium over bonds.

So that’s what happens when interest rates go up: it has a downward effect on stock prices.

When governments or central banks make efforts to keep interest rates low, the opposite occurs: it exerts an upward pressure on stock prices. That is, low interest rates make the alternatives to stocks not look very appealing — and that helps keep stock prices high.

To be clear though, while low interest rates have an upward effect on stock prices (i.e., they make stock prices higher than they would otherwise be, all else being equal), they do not prevent stock prices from falling. When events occur that worsen the outlook for corporate profitability, stock prices will still fall.

Investing Blog Roundup: Why the Market Doesn’t Care that the Economy Stinks

This week Barry Ritholtz tackled the question of why the stock market is doing reasonably well when the economy, clearly, is not.

One critical point, as we discussed recently, is that the stock market and the economy are not the same thing. The stock market isn’t even supposed to reflect the economy. (Rather, the market’s value at any time is a prediction, not a reflection of current status. And it only reflects a prediction regarding publicly traded companies, which are only a piece of the broader economy. Further, it only reflects how profitable those companies are predicted to be, not anything regarding how well their employees — or, ahem, former employees — are predicted to fare.)

Ritholtz also points out that it’s easy to overestimate how badly publicly traded companies, on the whole, are doing. Many very visible sectors (e.g., airlines) are doing horribly, but if such sectors make up only a small portion of the overall market capitalization, how well/poorly they perform doesn’t have a very large impact on the overall market performance.

Recommended Reading

I hope you are well, and thanks for reading!

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