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Presentvalue (PV) of a lump sum

PresentValue is the current net worth of cash flow. As an organization whenwe want to find the present value of a lump sum in a project forecastwe use the future value lump sum formulae given below (Eugene& Michael, 2008).

PV= FV /

Wheren represents the period where the future earning is located

ris the interest rate

FVis the future value

Lettake a case in the next two years I am planning to buy a house worth$20000 I need that cash a down payment. If I decide to purchase acertificate of principle for two years that pays at a rate of 5% perannum, I need to determine how much I need to invest now so that Ican meet my goal.

Solution

Inthis case, $20000 is the future value the time frame is 2 years atan interest rate of 5% so we can determine the present value as

PV= = $ 18140.59

Soin order to earn $20000 we need to invest $ 18,140.59 now.

Insteadof keeping $ 20,000 I can invest $18, 140.59 saving around $ 1859.41

Incase the periods are non-annual, I will be divided by 24 and n willbe 24.

*FutureValue (FV) of a lump sum*

Thishelps us know how much a single amount will grow after a given periodit`s calculated using the formulae given below (Eugene& Michael, 2008).

FV= PV (1+r)^{n}

WherePV is the present value

Letuse the above example where I have $18,140.59 which I need to investin two years at a rate of 5%, I will be able to know the future valueof my investment as follow

PV= $18, 140.59 (1.05)^{2}= $ 20, 000.00

Thismeans that if I invest $18, 140.59 at a rate of 5% will have $20,000as my future value of an investment in two years.

*Futurevalue of an annuity*

Thisis the value of the payment made on a specific date they are set ofcash flows. The future value annuity can bethe future value of anordinary annuity. This helps us know how much we can invest perperiod. It helps us know how much we will have in the future wheninvested at a given rate. In case of a loan repayment, it helps usknow how much we can pay.

Wecan use the following formulae

FVordinary Annuity= C

WhereC is the cash flows (Annuity), r is the interest and n is the numberof payments (Brigham & Houston, 2006).

Example

Lastfrom January this year, I ventured into bond where I am to receivecoupons, and I agreed that I will be making an annual payment of $1000 at the end of every year. I need to tell how much money I willhave if I pay an annuity of $1000 in the next five years at a rate of5%.

FVordinary annuity = $1000

=$ 1000*[5.53] = $ 5525.63

Incase it`s an annuity due we will use the following formulae sincepayments are made at the start of the month. Let’s use the abovecase but assume that payments were made at the start of the periodi.e. in January

Inthis case, the formulae will be the same but we multiply the answerin the above case by (1+i) where I is the interest in his case itwill be

=C

=

$1000*5.53* 1.05 = $ 5801.91

Inboth cases, we put into consideration the time when payment was madeeither at the start or the end.

Presentvalue of an annuity

Thishelps us know the current value of future payments in a series wewill use the following formula (Brigham & Houston, 2006).

PVordinary annuity = C

=$1000= $ 4329.48

Presentvalue annuity due we calculate the discount, but one period aheadsince payment are held for a lesser period.

Inthis instance, we will use the same formulae but we will multiply theanswer in the ordinary above by (1+r)

Hencethe amount will be $ 4329.48* 1.05 = $ 4545.95

Thishelps us in calculating the present and future values of theannuities of the money we have invested.

References

Brigham,F. & Houston, F. (2006). *Fundamentalsof financial management (14th ed.).*Boston, MA: Cengage Learning.

EugeneB. & Michael E.(2008).*FinancialManagement: Theory & Practice *Branzil:Amazon.