Given a certain yearly savings, how much can I spend on a capital improvement? NPV of future cash flow
This investment does not have a payback period as the net present value of your investment is negative. Your investment requires an initial cash outlay of $40,000 followed by annual savings of $2060 for the next 20 years. Your discount rate is 5% at which the NPV is $-14327.85 as calculated below by using this JavaScript financial functions library tadJS that is based on a popular tadXL add-in for Excel 2007, 2010 and 2013. For this, the internal rate of return is preferred. In short, all cash flows need to be discounted to the present and set equal to 0 so that an implied rate of return can be calculated. You could try to work this out by hand, but it's practically hopeless because of solving for roots of the implied rate of return which are most likely complex. It's better to use a spreadsheet with this capability such as OpenOffice's Calc. The average return on equity is 9%, so anything higher than that is a rational choice. Example Using this simple tool, the formula variables can easily be input. For instance, the first year has a presumed cash inflow of $2,460 because the insurance has a 30% discount from $8,200 that is assumed to be otherwise paid, a cash inflow of $40,000 to finance the sprinklers, a cash outflow of $40,000 to fund the sprinklers, a $400 outflow for inspection, and an outflow in the amount of the first year's interest on the loan. This should be repeated for each year.  They can be input undiscounted, as they are, for each year, and the calculator will do the rest. The question states :- Our insurance company is offering a 30% discount on an $8200/year   commercial policy, if we install sprinklers. The insurance is paid in   two installments. ... This appears to mean six-monthly payments, so I'll make some comparison calculations using six-monthly loan repayments to keep things simple. Without the loan or sprinklers the insurance costs $4100 every six months. Using this loan payment formula, the calculation below shows, with the 30% discounted insurance, sprinkler maintenance and loan repayment, you would be paying $4655.28 every six months.  The discount required to break even is 43.5%.  I.e. rearranging the equation :-  Alternatively, with the discount of 30% you would break even if the six-monthly repayment amount was $1030.  Solving the payment equation for s gives an equation for the loan :-  So with the 30% discount you would break even if the loan required was $25989. Checking by back-calculating the periodic payment amount, a :-  Likewise we can keep the loan at $40000 and solve for t to find the break-even loan term :-  (Note, in this formula Log denotes the natural logarithm.)  Now we can set some values :-  So with break-even payments the $40000 loan is paid off in just under 65.5 years.  I.e. checking :-  This just beats the $4100 cost of proceeding without the sprinklers. Notes If your loan repayment was monthly it would reduce the cost of the loan slightly.  The periodic interest rate is calculated from the APR according to the method used in the EU and in some cases in US.  The calculations above were run using Mathematica.
Lazy man's budget.  Four separate accounts for timing of expenses: short (monthly; utilities etc.), medium (quarterly+; property taxes), long (yearly+; house improvements) and retirement.   Set target levels for each account, to cover 1 full cycle.  The short target is smallest; it should comfortably cover a month.  For me each target is about 10x larger than the last.  (Cycles & targets for a homeowner w/ family; YMMV).   All income goes in short term.  When an account gets above target level, the excess gets swept up to the next longer term account.  That's all I keep firm track of; takes just a few minutes a month. Watching the account balances vs. their targets (and how short some of them are of target) keeps me focused on spending, and thinking about how much I can sweep (or can't) next paycheck. "Yes I thought his flow charts did a nice job with a complex system.  Some thoughts:  * he makes the ""if your house ran a blah blah blah"".  That is a horrible analogy to make for an economy.  * He quotes the revenue to debt ratio as if it is static.  We are spending much more now then we traditionally do at the same times as revenues are lower than historic levels.  Ratios change over time.  * Either he chooses to ignore, or doesn't know, that a lot of the issues with the PIIGS comes from the aggressive use of derivative products to clean their books for the joining of the EU.  Like his ARM example, now the rates have changed and those trades have moved against the sovereigns.   * His lists the outcome of current monetary policy as binary.  Either we inflate to infinity, and the world explodes, or we default and the world explodes.  One outcome that comes to my mind is that we ease out of aggressive capital injection and move through this liquidity issue.  We then pay back our debt and live on.  I am sure there are many other outcomes  * Almost all the problems seemed to be supply side ideas.  ""banks just won't lend"".  I would argue banks and even corporations have cash, but lack demand for NPV positive projects and thus are sitting on it.  And or they are waiting for things to play out so they can invest with better certainty.  * I thought his discussion on Current accounts was very good.  We also need to remember in many of these countries you have weak and corrupt tax systems which make it hard to fund your way out of these issues.   I only point these things out for others who may watch the video and want some counter points to what the speaker says." I have a discounted cash flow that's monthly.  My annualized discount rate is 8%.    1)What is the formula to turn the annualized rate into a monthly rate?  2)What is the formula to find out the NPV of monthly cash flows?   For example, if I get $1000, $2000, and $3000 in months 1, 2, and 3, how do I calculate how much each of those are equal to as a present value if the annual discount rate is 8%? But their strategy is not debt spending to increase demand. Every time we start getting anywhere near a balanced budget they cut taxes again so that they can continue blaming the deficit on pork barrel spending. Forcing ever more draconian budget cuts that will never ultimately balance the budget. It's called a [starve the beast](https://en.wikipedia.org/wiki/Starve_the_beast) strategy.   Deficit spending does drive demand short term. But as this debt rises so does the rent seeking cost of that debt. After some point this debt cost exceeds the benefits derived from the debt incurred in any given year. Just because you cab say the debt incurred this year exceeds the cost of the debt incurred this year does not mean that these benefits will remain positive overall as the debt remains on the books indefinitely, not just for the year they were incurred. This is not to claim that all debt is bad, but you can't make broad statements about the benefits of debt in general.  Most such debt spending is a complete waste. Because your taxes are not defined by how much they take from your paycheck alone. When debt is used for consumption spending, rather than investment spending that increases productive capacity, this consumption leaves fewer goods and services remaining on the market for the rest of the consumers competing for it. Raising your cost of living. Your tax rate is not determined by how much money the government takes from you. It's determined by how much they spend. That is how much they are taking from the consumer market.   Granted, given the [low wages relative to capital returns](http://www-tc.pbs.org/prod-media/newshour/photos/2012/12/06/Andrew_Smithers_chart_blog_main_horizontal.JPG), demand (consumption) is overly suppressed. Resulting in an [overproduction](https://en.wikipedia.org/wiki/Overproduction) problems. Which makes debt spending look even more financially appealing, because it's not actually suppressing the already excessive demand constraints. But this is because you wages have been suppressed. So instead of paying taxes you are working for a lower income. In fact the loss of wages, relative to capital returns, i.e., your cost of living, actually well exceeds your tax cut. Your just paying those taxes through lower wages, or an increased cost of living, instead of taxes out of your paycheck. So your being conned out of that money while the people doing it are pretending to cut taxes.  The same [applies to the rich (PDF)](https://www.gsb.stanford.edu/sites/gsb/files/jmp_simcha-barkai.pdf) in a different way. There is a limit to how rich you can get from a population of poor people. When you cut wages too far below productive capacity to save cost it dries up demand. People can't afford as much of your product as you can produce. So they cut jobs, i., production, to match market demand, which drives demand even lower. Pushing inflation and the velocity of money to historic lows in spite of an increased money supply. This also makes it unprofitable to invest in new productive capacity when market demand is already saturated. Wages, relative to capital returns, must increase to fix it. But if you take it too far it drives inflation to unacceptable levels. But, at the present ratio, we are a long ways from that. "One thing that's often overlooked is that cash reserves are also a long-term investment.  Anything can be a long-term investment if it's expected to appreciate or pay interest/dividends.  So it's not either/or.  Stocks are but one way to do long-term investments. Having said that, taking on less debt for a consumer good is never a bad idea.  Your primary residence is a consumer good, regardless of those who would say that ""your home is your biggest investment.""  So, there's my vote for a larger down-payment. Beyond that, a couple of outside-the-box comments:" Each situation is different, but it has to do with assessing what the Company is trying to do. People always talk about WACC, but in reality, WACC is less important than figuring how how much debt a Company can support (determined by leverage and solvency statistics).  Here are a few things to think about:  -How stable are the Company's cash flows? (big difference between a Company that has multi-year contracts locked in place vs. variable/cyclical revenue streams; what type of Capex requirement is there?)  -What is the purpose of raising the capital? (growth vs. recapitalization; where are the proceeds going?)  -What collateral is available for creditors?  -What does working capital look like? (is there seasonality?) The goal of the kelly criterion strategy is to find a balance between preservation of starting capital and returns. One of extreme you could bet the entirety of your account on one trade, which would maximize your returns if you win, but leave you unable to further invest if you lose. On the other extreme, you could bet the smallest amount of capital possible over the course of several trades to increase the probability that you'll even out to 70% accuracy over time. But this method would be extremely slow.  So for your case, investing 40% each time is one way to find an optimal balance between these two extremes. Use this as a rule of thumb though, because your own situation and investing goals may differ from the goal of  optimal growth. You need the Present Value, not Future Value formula for this. The loan amount or 1000 is paid/received now (not in the future). The formula is $ PMT = PV (r/n)(1+r/n)^{nt} / [(1+r/n)^{nt} - 1] $  See for example http://www.calculatorsoup.com/calculators/financial/loan-calculator.php With PV = 1000, r=0.07, n=12, t=3 we get PMT = 30.877 per month