TO:Mrs. Gram, Board Directors


DATE. : 3-3-2016


Thetime value of money is a significant concept to investors. Money inhand today is worth more than money to be received in future (Keown,Martin &amp Petty 2010). Investors use this concept while makingdecisions ininvestment securities, valuing their cash flowsandfinancing decisions like evaluating present value of costs betweentwo or more projects.


1.Discounting is a method used to calculate the present value of acsahflow associated with a project at prevailing interest (ordiscount) rate. Compounding&nbspmethod is used to determine thefuture&nbspvalue of an investment (Keown, Martin &amp Petty 2010).Both methods are useful in determing the worth of money at differentpoints in time.

2. The relationship between present value factor and annuity presentvalue factor. The present value factor calculates the value ofincoming cash flows. The annuity present value factor calculates thepresent value of future dollar cash flows. Both formulas rely on theconcept of time value of money.

3.Some of the formulas used for calculating future value and presentvalue of cash flows are as follows. Take for example:

  1. the future value of $5,000 compounded annually at an interest rate of 8% for 10 years is equal to $10,794.62. Using the formula FV=P (1+i)n, 5000(1.08)10.

  2. The number of years a $400reach $1,671 at interest rate of 10% can be calculated by the formulan= ln(FV/PV)/ln(1+r).Hence n= ln (1671/400)/ln(1.1) will be 15years.

  3. In a case where you have the PV say $1000 and an FV of $4046 and a time period of 10 years one can calculate the interest rate using the formula r= (FV/PV)1/10 – 1. In such a case the interest rate will be 15% that is r=[(4046/1000)1/10– 1] (Keown, Martin &amp Petty 2010).

4.When finding the PV of a specified FV=$1000, for 5years with aninterest rate of 10%, PV=FV/(1+r)n is the formula to use. Hence PV=1000/(1+ 0.1)5gives us $620.92.

5.Annuity due are annuities where payments are made at the beginning ofeach period. Ordinary annuity is where by payments are made at theend of each period (Keown, Martin &amp Petty 2010).. For example,bonds coupon payments are usually made at the end of each period. Anannuity due can also be described as an ordinary annuity that has itsterm beginning and ending one period earlier than an ordinary annuity(Keown, Martin &amp Petty 2010)..

6.PVof an ordinary annuity is calculated using PMT[{1-(1+i)^-n}/r]. Forexample an ordinary annuity whose payment is $1000 for a period ofseven years at a rate of 10% is 1000[{1-0.51315812}/0.1]= $4868.42.

Inthe case of the PV of an annuity due, PMT [{1- (1+i)^-n}/i] x (1+i)is used (Known, Martin &amp Petty 2010). Note that only (1+i) isadded at the end of the formula. Nothing else changes. It slightlydiffers because of payments are made the beginning of the period.Using the same values above, the PV of an annuity due will be$4868.42 × (1.1) = $ 5355.26.

7.Likewise to calculate the FV of an ordinary annuity PMT[{(1+I)^n-1}/I] is the formula to use. Still using the same figuresgiven in number six, 1000[{(1.1)^7 – 1}/ 0.1]results to $9487.1.Similarly to get the FV of an annuity due only (1+I) is added tolatter. So that the FV of an annuity due becomes 9487.1 × (1.1)which is equal to $10,435.81.

8.In a case where one borrowedmoney let say $100000 and makes paymentsfor a period of 25years at a rate if 10%. PMT will equalPV/[{1-(1+i)^-n}/r]. Therefore $100000/[{1-(1.1-25)}/0.1]will be $ 11016.73.

9.The Present Value of a perpetuity is calculated using the formula(PMT/i ). Assuming a perpetuity with an interest of 8% and payment of$1000, the PV becomes 1000/0.08 = $12500.

10.If payment made each period is $1000 for a period of 10 years at arate of 10% where first payment is made after ten years. The PV ofthe annuity is 1000[{1-(1.1)^-20}/0.1=$8513.60

11.A perpetuity with an interest rate of 10% and payments of $1000 whosepayment is made after ten years has a PV of 10,000i.e.1000/0.1

Timevalue of money calculates the interest one gains or is possiblysuppose to gain after a period of investment. In Mathew 25: 20 says&quotSo he who received five talents came back and bought five othertalents….He who had received two talents came back and gained twomore talents…in verse 27 it is stated &quotTherefore you ought todeposited my money with the bankers and at my coming I would havereceived back my own with interest” (American Bible Society1976).It is evident that an entrepreneur will always want to make profitand to avoid losses. Time value of money enables entrepreneurs andorganizations calculate their probable investment outcomes. Moneyinvested now reaps back interest and gains than money held.


Business,organizations and individuals need time value of money to evaluatetheir project cash flows and to make financial and investmentdecisions. It is clear that this concept is significant and should beadopted if not used by all investors.

Iused a memorandum relay this information because it’s precise andeasy understand. It is also used to convey large amounts ofinformation in an organized format.


AmericanBible Society. (1976). Good News Bible: Mathew 25 verse 14-30.

Keown.A., Martin. D. J, Petty. J. W. (2010).Foundations of Finance: TheLogic and Practice of financial management. Pearson Education. ISBN:9780135122365.