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.
If you're looking for some formula, I don't think one exists. People talk about this all the time and give conflicting advice. If there was a proven-accurate formula, they wouldn't be debating it. There are basically 3 reasons to do a home improvement project: (a) Correct a problem so that you prevent on-going damage to your home. For example, have a leaking roof patched or replaced, or exterminate termites. Such a job is worthwhile if the cost of fixing the problem is less than the cost of future damage. In the case of my termite and leaking roof examples, this is almost always worth doing. Lesser maintenance problems might be more debatable. Similarly, some improvements may reduce expenses. Like replacing an old furnace with a newer model may cut your heating bills. Here the question is: how long does it take to repay the investment, compared to other things you might invest your money in. Just to make up numbers: Suppose you find that a new furnace will save you $500 per year. If the new furnace costs $2000, then it will take 4 years to pay for itself. I'd consider that a good investment. If that same $2000 furnace will only cut your heating bills by $100 per year, then it will take 20 years to pay for itself. You'd probably be better off putting the $2000 into the stock market and using the gains to help pay your heating bill. (b) Increase the resale value of your home. If you are paying someone else to do the work, the harsh reality here is: Almost no job will increase the resale value by more than the cost of getting the job done. I've seen many articles over the years citing studies on this. I think most conclude that kitchen remodeling comes closet to paying for itself, and bathrooms come next. New windows are also up there. I don't have studies to prove this, but my guesses would be: Replacing something that is basically nice with a different style will rarely pay for itself. Like, replacing oak cabinets with cherry cabinets. Replacing something that is in terrible shape with something decent is more likely to pay back than replacing something decent with something beautiful. Like if you have an old iron bathtub that's rusting and falling apart, replacing it may pay off. If you have a 5-year-old bathtub that's in good shape but is not premium, top of the line, replacing it with a premium bathtub will probably do very little for resale value. If you can do a lot of the work yourself, the story changes. Many home improvement jobs don't require a lot of materials, but do require a lot of work. If you do the labor, you can often get the job done very cheaply, and it's likely that the increase in resale value will be more than what you spend. For example, most of my house has hardwood floors. Lots of people like pretty hardwood floors. I just restained the floors in two rooms. It cost me, I don't know, maybe $20 or $30 for stain and some brushes. I'm sure if I tried to sell the house tomorrow I'd get my twenty bucks back in higher sale value. Realtors often advise sellers to paint. Again, if you do it yourself, the cost of paint may be a hundred dollars, and it can increase the sale price of the house by thousands. Of course if you do the work yourself, you have to consider the value of your time. (c) To make your home more pleasant to live in. This is totally subjective. You have to make the decision on the same basis that you decide whether anything that is not essential to survival is worth buying. To some people, a bottle of fancy imported wine is worth thousands, even millions, of dollars. Others can't tell the difference between a $10,000 wine and a $15 wine.  The thing to ask yourself is, How important is this home improvement to me, compared to other things I could do with the money? Like, suppose you're considering spending $20,000 remodeling your kitchen. What else could you do with $20,000? You could buy a car, go on an elaborate vacation, eat out several times a week for years, retire a little earlier, etc. No one can tell you how much something is worth to you. Any given home improvement may involve a combination of these factors. Like say you're considering that $20,000 kitchen remodeling. Say you somehow find out that this will increase the resale value by $15,000. If the only reason you were considering it was to increase resale value, then it's not worth it -- you'd lose $5,000. But if you also want the nicer kitchen, then it is fair to say, Okay, it will cost me $20,000, but ultimately I'll get $15,000 of that back. So in the long run it will only cost me $5,000. Is having a nicer kitchen worth $5,000 to me? Note, by the way, that resale value only matters if and when you sell the house. If you expect to stay in this house for 20 years, any improvements done are VERY long-term investments. If you live in it until you die, the resale value may matter to your heirs. The value does change from 12.61% to 13.48%. The difference between re-investing cashflows at 14% vs 12% is not big enough to change the rounded value. Edit: The initial cashflow is discounted at t0, meaning it's already equal to its present value and the finance rate doesn't have an effect. It does impact future outgoing cashflows, as you've noted. i cannot directly tell from the provided information if it is already included in Net A/R but if there is a balance sheet you can check yourself if the Total Cash Flow matches the difference between cash position year 0&amp;1 and see if it is net or still to be included. The equation is the same one used for mortgage amortization.  You first want to calculate the PV (present value) for a stream of $50K payments over 20 years at a10% rate.  Then that value is the FV (future value) that you want to save for, and you are looking to solve the payment stream needed to create that future value. Good luck achieving the 10% return, and in knowing your mortality down to the exact year. Unless this is a homework assignment, which need not reflect real life.  Edit - as indicated above, the first step is to get that value in 20 years:  The image is the user-friendly entry screen for the PV calculation. It walks you though the need to enter rate as per period, therefore I enter .1/12 as the rate. The payment you desire is $50K/yr, and since it's a payment, it's a negative number. The equation in excel that results is: =PV(0.1/12,240,-50000/12,0) and the sum calculated is $431,769 Next you wish to know the payments to make to arrive at this number:  In this case, you start at zero PV with a known FV calculated above, and known rate. This solves for the payment needed to get this number, $568.59 The excel equation is: =PMT(0.1/12,240,0,431769) Most people have access to excel or a public domain spreadsheet application (e.g. Openoffice). If you are often needing to perform such calculations, a business finance calculator is recommended. TI used to make a model BA-35 finance calculator, no longer in production, still on eBay, used.  One more update- these equations whether in excel or a calculator are geared toward per period interest, i.e. when you state 10%, they assume a monthly 10/12%. With that said, you required a 20 year deposit period and 20 year withdrawal period. We know you wish to take out $4166.67 per month. The equation to calculate deposit required becomes - 4166.67/(1.00833333)^240= 568.59  HA! Exact same answer, far less work. To be clear, this works only because you required 240 deposits to produce 240 withdrawals in the future. When calculating the NPV, is there anything I need to do in between the project start date outlay (Nov 2017), and the first cash inflow (July 2019). Do I need to discount the cashflow to the present, and if so, how? Yes, you need to discount every cash flow to the present time, not just the first one.   When discounting cash flows, the appropriate discount rate needs to represent the opportunity cost of the initial cash outlay.  Meaning if you were to use that money for something else, what rate of return would you expect? You could be safe and assume only a risk-free return (like 2-3%) or use the average rate of return of other investments (e.g. 10-15%). Another common approach is to use your cost of capital if you're raising funds for the project, or would instead have use the funds to pay off existing debt. Once you find a relevant discount rate, then just discount each cash flow by dividing them by e^rt, where r is the annualized discount rate (e.g. 0.10 for 10%) and t is the decimal number of years between now and the cash flow (e.g. 1.5 for 18 months) The bank I work with would be more inclined to expand an existing HELOC rather than write a new one. I think that would be your best bet if you decide to continue borrowing against your home. Consider that your own income would have to support the repayment of these larger homes. If it is, why didn't you buy a larger home to begin with? As far as increasing the appraisal, you don't usually get one dollar of increased appraisal for each dollar you spend on improvements unless you have a rundown house in a nice neighborhood; part of the appraisal comes from a comparison with the appraisals of the other homes nearby. Eventually you get close enough to par with the other houses that anyone looking for something more expensive will often choose a different neighborhood entirely. Update: To your edit that mentions the original lender will cap the amount you can borrow, you can take additional secondary mortgages/HELOCs, but the interest rate is usually higher because it is not the first mortgage. I don't generally recommend it, but the option is there. What you are looking here is the cost of capital, because that is what you are effectively giving up in order to invest in those loans. In a discounted cash-flow, it would be the *i* in the denominator (1+*i*). For instance, instead of purchasing those loans you could have lent your money at the risk-free rate (not 100% true, but typical assumption), and therefore you are taking a slight risk in those loans for a higher return.  There are several ways to compute that number, the one most often used would be the rate if the bank were to lend that money. In this way, it would be the Fed Funds rate plus some additional risk premium. "Yes, a HELOC is great for that. I just had my roof done last month (~$15K, ""ugh"") and pretty much every major contractor in my area had a 0% same-as-cash for at least 12 months. So that helps - any balance that I don't bank by 11/15/2015 will be on the HELOC." "I think the real problem here is dealing with the variable income. The envelope solution suggests the problem is that your brother doesn't have the discipline to avoid spending all his money immediately, but maybe that's not it. Maybe he could regulate his expenses just fine, but with such a variable income, he can't settle into a ""normal"" spending pattern. Without any savings, any budget would have to be based on the worst possible income for a month. This isn't a great: it means a poor quality of life. And what do you do with the extra money in the better-than-worst months? While it's easy to say ""plan for the worst, then when it's better, save that money"", that's just not going to happen. No one will want to live at their worst-case standard of living all the time. Someone would have to be a real miser to have the discipline to not use that extra money for something. You can say to save it for emergencies or unexpected events, but there's always a way to rationalize spending it. ""I'm a musician, so this new guitar is a necessary business expense!"" Or maybe the car is broken. Surely this is a necessary expense! But, do you buy a $1000 car or a $20000 car? There's always a way to rationalize what's necessary, but it doesn't change financial reality. With a highly variable income, he will need some cash saved up to fill in the bad months, which is replenished in the good months. For success, you need a reasonable plan for making that happen: one that includes provisions for spending it other than ""please try not to spend it"". I would suggest tracking income accurately for several months. Then you will have a real number (not a guess) of what an average month is. Then, you can budget on that. You will also have real numbers that allow you to calculate how long the bad stretches are, and thus determine how much cash reserve is necessary to make the odds of going broke in a bad period unlikely. Having that, you can make a budget based on average income, which should have some allowance for enjoying life. Of course initially the cash reserve doesn't exist, but knowing exactly what will happen when it does provides a good motivation for building the reserve rather than spending it today. Knowing that the budget includes rules for spending the reserves reduces the incentive to cheat. Of course, the eventual budget should also include provisions for long term savings for retirement, medical expenses, car maintenance, etc. You can do the envelope thing if that's helpful. The point here is to solve the problem of the variable income, so you can have an average income that doesn't result in a budget that delivers a soul crushing decrease in quality of living." "Re. question 2 If I buy 20 shares every year, how do I get proper IRR? ... (I would   have multiple purchase dates) Use the money-weighted return calculation: http://en.wikipedia.org/wiki/Rate_of_return#Internal_rate_of_return  where t is the fraction of the time period and Ct is the cash flow at that time period. For the treatment of dividends, if they are reinvested then there should not be an external cash flow for the dividend.  They are included in the final value and the return is termed ""total return"".  If the dividends are taken in cash, the return based on the final value is ""net return"". The money-weighted return for question 2, with reinvested dividends, can be found by solving for r, the rate for the whole 431 day period, in the NPV summation. Now annualising And in Excel" That's pretty typical for introductory problems.  It's leading you into an NPV question.  They're keeping the cash flows the same to illustrate the time value of money to show you that even though the free cash flow is the same in year 1 and year 4 or whatever when you discount it to present value today's stream is worth more than tomorrow's The Finance functions in spreadsheet software will calculate this for you.  The basic functions are for Rate, Payment, PV (present value), FV (Future value), and NPER, the number of periods.  The single calculation faces a couple issues, dealing with inflation, and with a changing deposit. If you plan to save for 30 years, and today are saving $500/mo, for example, in ten years I hope the deposits have risen as well. I suggest you use a spreadsheet, a full sheet, to let you adjust for this.  Last, there's a strange effect that happens. Precision without accuracy. See the results for 30-40 years of compounding today's deposit given a return of 6%, 7%, up to 10% or so. Your forecast will be as weak as the variable with the greatest range. And there's more than one, return, inflation, percent you'll increase deposits, all unknown, and really unknowable.  The best advice I can offer is to save till it hurts, plan for the return to be at the lower end of the range, and every so often, re-evaluate where you stand. Better to turn 40, and see you are on track to retire early, than to plan on too high a return, and at 60 realize you missed it, badly.  As far as the spreadsheet goes, this is for the Google Sheets -  Type this into a cell =nper(0.01,-100,0,1000,0) It represents 1% interest per month, a payment (deposit) of $100, a starting value of $0, a goal of $1000, and interest added at month end. For whatever reason, a starting balance must be entered as a negative number, for example - =nper(0.01,-100,-500,1000,0) Will return 4.675, the number of months to get you from $500 to $1000 with a $100/mo deposit and 1%/mo return. Someone smarter than I (Chris Degnen comes to mind) can explain why the starting balance needs to be entered this way. But it does show the correct result. As confirmed by my TI BA-35 financial calculator, which doesn't need $500 to be negative. "Value averaging has you shift the balance of your portfolio over time, not the amount of contributions.  So you can only do it if you have a portfolio holding both risky assets (shares etc) and some cash. You start out by making a plan about how much you will contribute every month and at what rate you expect the share part of the portfolio to grow.  Perhaps based on 20th century data you think an 8% growth rate is reasonable.  Or alternatively if you know your desired final amount obviously you can work backwards to a desired rate from that. If in any month the share part is falling below its expected growth path, you would put more money into it: possibly your whole paycheck contribution plus some from the savings cash account.  On the other hand if the share component is growing ""too fast"" you would put all your additional savings into cash.  So if your investments are doing well, you're not supposed to spend the excess money, but rather to put it aside into a dedicated cash account to top up your share component when prices fall. In theory, this has the auto-levelling benefit of Dollar Cost Averaging, but even better: when prices are high, you'll automatically buy fewer shares, or even sell some; conversely when prices are low you'll buy extra shares from your reserve account. If it turns out your estimate was unreasonably optimistic, and over your lifetime shares only ever average 3%, you'll end up with an entirely share portfolio, and a bumpier ride than you might have liked.  If you have horrible luck and over your entire investing life shares return less than cash (which has happened, though not yet in the USA), then this will be worse than a standard balanced portfolio. The original book Value Averaging by Edelson has a pretty good explanation of various cases, though I would say some of the examples are worked in excessive detail. I have not implemented this myself, one reason being that the amount I'm able to save from year to year varies, as it probably does for you, and so predicting a path is not quite so simple as he assumes.  You could still do it I suppose. I think you could get a very crude approximation to this by simply directing your savings into cash when the share market's rate of growth over the last several years is above what you think is the long term average." someone is paid a certain sum each month, and wants to spend only a certain amount each month, can he spend more and then take it out of next month's payment? Using the example 100 month 1, 60 first month. Save 40 Second Month, 100 salary, spend 70. Save 30. Overall Savings 70 Third month, 100 salary, spend 50. Save 50. Overall Savings 120 So in short term or once a while doing this is fine. However if [and this depends on individuals] it goes beyond control, i.e. you keep spending say 90 every month, you would have to save for quite a few months to get back to normal. A better way would be to reverse this. Using the example 100 month 1, 60 first month. Save 40 Second Month, 100 salary, spend 50. Save 50. Overall Savings 90 Third month, 100 salary, spend 70. Save 30. Overall Savings 120 i.e. save more first and then spend, rather than spending now and saying you will save in future. Generally this is the trap quite a few fall into specially when saving for retirement, they keep putting it to future and very soon realize that they can't get back to the goal. I would not claim to be a personal expert in rental property. I do have friends and family and acquaintances who run rental units for additional income and/or make a full time living at the rental business.  As JoeTaxpayer points out, rentals are a cash-eating business. You need to have enough liquid funds to endure uncertainty with maintenance and vacancy costs. Often a leveraged rental will show high ROI or CAGR, but that must be balanced by your overall risk and liquidity position. I have been told that a good rule-of-thumb is to buy in cash with a target ROI of 10%. Of course, YMMV and might not be realistic for your market. It may require you to do some serious bargain hunting, which seems reasonable based on the stagnant market you described. Some examples: The main point here is assessing the risk associated with financing real estate. The ROI (or CAGR) of a financed property looks great, but consider the Net Income. A few expensive maintenance events or vacancies will quickly get you to a negative cash flow. Multiply this by a few rentals and your risk exposure is multiplied too!  Note that i did not factor in appreciation based on OP information. Cash Purchase with some very rough estimates based on OP example Net Income = (RENT - TAX - MAINT) = $17200 per year Finance Purchase rough estimate with 20% down Net Income = (RENT - MORT - TAX - MAINT) = $7500 per year