Calculating theoretical Present Value
If you are using an Excel, the Function PV should be able to easily calculate this. Excel Formulae PV = (Rate,Nper,Pmt,Fv,Type)   Where Rate: Rate of return. In this case you can use Inflation or assumed rate that would cost you. Say 3-5%. Note the Rate has to be for Nper. i.e. in Nper if you are counting yearly payments, then rate is yearly, if you are counting as monthly, then the rate should be monthly.   NPer: Number of periods. If yearly in your case it would be 20. If Monthly 20*12, if Quarterly 20*4 etc.   Pmt: Expected Payments for Nper. If you are saying 20 million over 20 years, it would be 1 million per year. Fv and Type can be blank So assuming a rate of 3%, and yearly payments of 1 million over 20 years. PV = $14,877,474.86 [It would show negative, just ignore the sign] The example from the following website: Investopedia - Calculating The Present And Future Value Of Annuities  specifically the section 'Calculating the Present Value of an Annuity Due' shows how the calculation is made.  Using their figures, if five payments of $1000 are made over five years and depreciation (inflation) is 5%, the present value is $4545.95  There is also a formula for this summation, (ref. finance formulas)
"Bonds are valued based on all of this, using the concept of the ""time value of money"". Simply stated, money now is worth more than money later, because of what you can do with money between now and later. Case in point: let's say the par value of a bond is $100, and will mature 10 years from this date (these are common terms for most bonds, though the U.S. Treasury has a variety of bonds with varying par values and maturation periods), with a 0% coupon rate (nothing's paid out prior to maturity). If the company or government issuing the bonds needs one million dollars, and the people buying the bonds are expecting a 5% rate of return on their investment, then each bond would only sell for about $62, and the bond issuer would have to sell a par value of $1.62 million in bonds to get its $1m now. These numbers are based on equations that calculate the ""future value"" of an investment made now, and conversely the ""present value"" of a future return. Back to that time value of money concept, money now (that you're paying to buy the bond) is worth more than money later (that you'll get back at maturity), so you will expect to be returned more than you invested to account for this time difference. The percentage of rate of return is known as the ""yield"" or the ""discount rate"" depending on what you're calculating, what else you take into consideration when defining the rate (like inflation), and whom you talk to. Now, that $1.62m in par value may be hard for the bond issuer to swallow. The issuer is effectively paying interest on interest over the lifetime of the bond. Instead, many issuers choose to issue ""coupon bonds"", which have a ""coupon rate"" determining the amount of a ""coupon payment"". This can be equated pretty closely with you making interest-only payments on a credit card balance; each period in which interest is compounded, you pay the amount of interest that has accrued, to avoid this compounding effect.  From an accounting standpoint, the coupon rate lowers the amount of real monies paid; the same $1m in bonds, maturing in 10 years with a 5% expected rate of return, but with a 5% coupon rate, now only requires payments totalling $1.5m, and that half-million in interest is paid $50k at a time annually (or $25k semi-annually). But, from a finance standpoint, because the payments made in the first few years are worth more than the payments made closer to and at maturity, the present value of all these coupon payments (plus the maturity payout) is higher than if the full payout happened at maturity, and so the future value of the total investment is higher.  Coupon rates on bonds thus allow a bond issuer to plan a bond package in less complicated terms. If you as a small business need $1m for a project, which you will repay in 10 years, and during that time you are willing to tolerate a 5% interest rate on the outstanding money, then that's exactly how you issue the bonds; $1 million worth, to mature in 10 years and a 5% coupon rate. Now, whether the market is willing to accept that rate is up to the market. Right now, they'd be over the moon with that rate, and would be willing to buy the bonds for more than their face value, because the present value would then match the yield they're willing to accept (as in any market system, you as the seller will sell to the highest bidder to get the best price available). If however, they think you are a bad bet, they'll want an even higher rate of return, and so the present value of all coupon and maturity payments will be less than the par value, and so will the purchase price." Ok maybe I should have went into further detail but I'm not interested in a single point estimate to compare the different options.  I want to look at the comparable NPVs for the two different options for a range of exit points (sell property / exit lease and sell equity shares). I want to graph the present values of each (y-axis being the PVs and x-axis being the exit date) and look at the 'cross-over' point where one option becomes better than the other (i'm taking into account all of the up front costs of the real estate purchase which will be a bit different in the first years).  i'm also looking to do the same for multiple real estate and equity scenarios, in all likelihood generate a distribution of cross-over points.  this is all theoretical, i'm not really going to take the results to heart. merely an exercise and i'm tangling with the discount rates at the moment. "Here's a link to an online calculator employing the Discounted Cash Flow method:  Discounted Cash Flows Calculator.  Description: This calculator finds the fair value   of a stock investment the   theoretically correct way, as the   present value of future earnings. You   can find company earnings via the box   below.   [...] They also provide a link to the following relevant article:  Investment Valuation: A Little Theory.  Excerpt: A company is valuable to stockholders   for the same reason that a bond is   valuable to bondholders: both are   expected to generate cash for years   into the future. Company profits are   more volatile than bond coupons, but   as an investor your task is the same   in both cases: make a reasonable   prediction about future earnings, and   then ""discount"" them by calculating   how much they are worth today. (And   then you don't buy unless you can get   a purchase price that's less than the   sum of these present values, to make   sure ownership will be worth the   headache.)   [...]" "One way to value companies is to use a Dividend discount model. In substance, it consists in estimating future dividends and calculating their present value. So it is a methodology which considers that an equity is similar to a bond and estimates its current value based on future cash flows. A company may not be paying dividends now, but because its future earnings prospects are good may pay some in the future. In that case the DDM model will give a non-zero value to that stock. If on the other hand you think a company won't ever make any profits and therefore never pay any dividends, then it's probably worth 0! Take Microsoft as an example - it currently pays ~3% dividend per annum. The stock has been listed since 1986 and yet it did not pay any dividends until 2003. But the stock has been rising regularly since the beginning because people had ""priced in"" the fact that there was a high chance that the company would become very profitable - which proved true in the long term (+60,000% including dividends since the IPO!)." what do you mean exactly?  Do you have a future target price and projected future dividend payments and you want the present value (time discounted price) of those? Edit: The DCF formula is difficult to use for stocks because the future price is unknown.  It is more applicable to fixed-income instruments like coupon bonds.  You could use it but you need to predict / speculate a future price for the stock. You are better off using the standard stock analysis stuff: Learn Stock Basics - How To Read A Stock Table/Quote The P/E ratio and the Dividend yield are the two most important.  The good P/E ratio for a mature company would be around 20.  For smaller and growing companies, a higher P/E ratio is acceptable.  The dividend yield is important because it tells you how much your shares grow even if the stock price stays unchanged for the year. HTH "Sometimes an assumptions is so fundamentally flawed that it essentially destroys the relevance and validity of any modelling outputs.  ""Obviously, we're assuming the company can pay it back""  Is one of those assumptions.  The person gets a notes stating that they will get $525 'IN ONE YEAR' You need to divide $525/(1+Cost of Capital)^n n being the number of periods to find out what the note will be worth today.  Google 'Present Value of an Annuity' to deal with debt that is more complex than you have $500 now and give me $525 in a year..." "Below I will try to explain two most common Binomial Option Pricing Models (BOPM) used. First of all, BOPM splits time to expiry into N equal sub-periods and assumes that in each period the underlying security price may rise or fall by a known proportion, so the value of an option in any sub-period is a function of its possible values in the following sub period. Therefore the current value of an option is found by working backwards from expiry date through sub-periods to current time. There is not enough information in the question from your textbook so we may assume that what you are asked to do is to find a value of a call option using just a Single Period BOPM. Here are two ways of doing this: First of all let's summarize your information: Current Share Price (Vs) = $70 Strike or exercise price (X) = $60 Risk-free rate (r) = 5.5% or 0.055 Time to maturity (t) = 12 months Downward movement in share price for the period (d) = $65 / $70 = 0.928571429 Upward movement in share price for the period (u) = 1/d = 1/0.928571429 = 1.076923077 ""u"" can be translated to $ multiplying by Vs => 1.076923077 * $70 = $75.38 which is the maximum probable share price in 12 months time. If you need more clarification here - the minimum and maximum future share prices are calculated from stocks past volatility which is a measure of risk. But because your textbook question does not seem to be asking this - you probably don't have to bother too much about it yet. Intrinsic Value: Just in case someone reading this is unclear - the Value of an option on maturity is the difference between the exercise (strike) price and the value of a share at the time of the option maturity. This is also called an intrinsic value.  Note that American Option can be exercised prior to it's maturity in this case the intrinsic value it simply the diference between strike price and the underlying share price at the time of an exercise. But the Value of an option at period 0 (also called option price) is a price you would normally pay in order to buy it. So, say, with a strike of $60 and Share Price of $70 the intrinsic value is $10, whereas if Share Price was $50 the intrinsic value would be $0. The option price or the value of a call option in both cases would be fixed.  So we also need to find intrinsic option values when price falls to the lowest probable and rises to the maximum probable (Vcd and Vcu respectively) (Vcd) = $65-$60 = $5 (remember if Strike was $70 then Vcd would be $0 because nobody would exercise an option that is out of the money) (Vcu) = $75.38-$60 = $15.38 1. Setting up a hedge ratio:  h = Vs*(u-d)/(Vcu-Vcd) h = 70*(1.076923077-0.928571429)/(15.38-5) = 1 That means we have to write (sell) 1 option for each share purchased in order to hedge the risks. You can make a simple calculation to check this, but I'm not going to go into too much detail here as the equestion is not about hedging. Because this position is risk-free in equilibrium it should pay a risk-free rate (5.5%). Then, the formula to price an option (Vc) using the hedging approach is: (Vs-hVc)(e^(rt))=(Vsu-hVcu) Where (Vc) is the value of the call option, (h) is the hedge ratio, (Vs) - Current Share Price, (Vsu) - highest probable share price, (r) - risk-free rate, (t) - time in years, (Vcu) - value of a call option on maturity at the highest probable share price. Therefore solving for (Vc): (70-1*Vc)(e^(0.055*(12/12))) = (75.38-1*15.38) => (70-Vc)*1.056540615 = 60 => 70-Vc = 60/1.056540615 => Vc = 70 - (60/1.056540615)  Which is similar to the formula given in your textbook, so I must assume that using 1+r would be simply a very close approximation of the formula above. Then it is easy to find that Vc = 13.2108911402 ~ $13.21 2. Risk-neutral valuation: Another way to calculate (Vc) is using a risk-neutral approach. We first introduce a variable (p) which is a risk-neutral probability of an increase in share price. p = (e^(r*t)-d)/(u-d) so in your case: p = (1.056540615-0.928571429)/(1.076923077-0.928571429) = 0.862607107 Therefore using (p) the (Vc) would be equal: Vc = [pVcu+(1-p)Vcd]/(e^(rt)) => Vc = [(0.862607107*15.38)+(0.137392893*5)]/1.056540615 => Vc = 13.2071229185 ~ $13.21 As you can see it is very close to the hedging approach. I hope this answers your questions. Also bear in mind that there is much more to the option pricing than this. The most important topics to cover are: Multi-period BOPM Accounting for Dividends Black-Scholes-Merton Option Pricing Model" But how do I bring the initial deposit into the equation? Basically, you can't.  Unless you combine two different formulas from Math of Finance into a single expression. The single initial deposit of $1000 will compound for 20 years at 5% compounded annually. The final amount for this part of the deposit will be: V1 = 1000 x (1.05)^20 In addition the series of 20 payments will be an ordinary annuity with a regular payment of $100, with the value on the occasion of the 20th payment given by:  So the final total amount in the account at the end of 20 years will be the sum of these two values...