FINANCIAL MANAGEMENT

‘TIME VALUE OF MONEY’

MBA (FM/HR/IT) III- Trimester

INTRODUCTION In projects companies invest a sum of money in anticipation

of benefits spread over a period of time in the future If we borrow `100 today @ 10% (i.e. 09-Aug-10) from SBI

than we will have to pay `110 (08-Aug-11), the additional `10 is called interest or time value of money

Required rate of return = Risk free rate of return + risk premium

Decision can be made by two methods: Compounding method Discounting method

FUTURE VALUE OF A SINGLE CASH FLOW

It is the process of determining the future value of a lump sum amount invested at one point of time.

We calculate the future value of a single cash flow compounded annually by

FV = PV(1+i) n

FV= Future valuePV = initial cash flowi = interest rate per annumn = the number of compounding periods

EXAMPLE

Suppose ` 1100 are placed in the saving account of a bank at 5% pa. how much shall it grow after 2 years if interest is compounded annually

If compounding is done for shorter compounding period, then:

FV = PV (1+ ) m x n

FV= Future valuePV = initial cash flowi = interest per annumm = number of times compounding is done in a yearn = the number of compounding periods

m

i

EXAMPLE

Suppose Vijaya Bank gives 10% pa interest and interest is compounded quarterly then calculate the return after two years if Harsh deposit ` 1000 today in Vijaya Bank

SOLUTION

FV = PV (1+ ) m x n

= 1000(1+0.10/4) 4 x 2

= 1000(1+0.025) 8

= 1000 x 1.2184 = ` 1,218

FV= ?PV= 1000m= 4n= 2

m

i

FUTURE VALUE OF MULTIPLE FLOWS Instead of investing lump sum at one time if money is invested in

multiple flows then how value of money will be affected?

Suppose Mr Paw Invests ` 1,000 now (at the beginning of one year), ` 2,000 at the beginning of year 2 and ` 3,000 at the beginning of year 3, how much these flows accumulate to at the end of year 3 at a rate of 12% pa?

SOLUTION

FV3 = ` 1000 x FVIF(12,3) + ` 2000 x FVIF(12,2) + ` 3000 x FVIF(12,1)

=`[(1000x1.405)+(2000x1.254)+(3000x1.120)]

= ` 7273

FUTURE VALUE OF ANNUITY Annuity is the term used to describe a series of

periodic flows of equal amounts. The example of payment of Life insurance premium (`

2000 per annum) for next 20 years can be classified as an annuity.

The future value of a regular annuity for a period of n years at a rate of interest ‘i’ is given by the formula:

])1)1(

[ii

AFVAn

A= Amount deposited at the end of every yeari= Interest raten= Time HorizonFVA= Accumulation at the end of n year

),( niAxCVFAFVA

EXAMPLE

Suppose Mr Jain deposits ` 2000 at the end of every year for 10 years at the interest rate of 10% per annum, then how much will be his corpus after 20 years?

SOLUTION

),(])1)1(

[ ni

n

AxCVFAi

iAFVA

]10.0

)1)10.01([2000

10 FVA

= 2000x 15.94

= ` 31880

SINKING FUND

It is used when we want to calculate how much we have to deposit every year for ‘X’ years at the interest rate of i% pa to receive amount ‘Y’ at the end of ‘X’ year.

We know that FVA=A x CVFA(i,n)

A= FVA x 1/CVFA(i,n)

EXAMPLE Suppose we want to accumulate ` 500,000 at the end of 10

years. How much should we deposit each year at an interest rate of 10% per annum so that it grows to ` 500,000.

SOLUTION

PRESENT VALUE OF A SINGLE FLOW With this approach, we can determine the present value of a

future cash flow or a stream of future cash flows This is mostly used for evaluating the financial viability of

projects. Suppose if we invest `1000 today at 10% pa for a period of 5

years, we know that we will get ` 1000 x FVIF(10,5) =`1000x1.611 =`1,611 at the end of 5 years

So, the present value of `1,611 is `1000 Formula of calculating present value of a single flow is:

FV= PV x FVIF(i,n) ; PV =FV/FVIF(i,n) PV=

PV = FV x PVIF(i,n)

niFV

)1(

PRESENT VALUE OF AN ANNUITY

The present value of an annuity ‘A’ receivable at the end of every year for a period of n years at a rate of interest ‘i’ is equal to:

PVA= A x PVIFA(i,n)

])1(

1)1([

n

n

iii

APVA

EXAMPLE

Suppose Mrs Ravina deposits ` 1000 every year for 8 years with 15% interest rate per annum, then what is the present value of her deposits?

SOLUTION

A = ` 1000

n= 8 years

i= 12%

PVA=?

PVA= A x PVIFA(i,n)

PVA = 1000 x PVIFA(12,8)

PVA = 1000 x 4.968

PVA = 4968

CAPITAL RECOVERY AND LOAN AMORTIZATION

If HDFC housing finance gives home loan to a person then they will decide the EMIs through this method.

P= A x PVFA(i,n)

Suppose Mr X takes a loan of ` 50,000 today to buy a motor-cycle for his son. If interest rate is 10%, how much Mr X will have to pay per year to repay his loan in 3 equal end of year repayments? [`20104.543]

,

1=

PVAFn iA P

= × CRFn,iA P

PRESENT VALUE OF PERPETUITY Perpetuity is an annuity that occurs indefinitely. It tells that how much shall we invest today so that we can

get equal amount every year for indefinite time

Present Value of Perpetuity = Perpetuity ÷ Interest rate

For example If Hari expects ` 5,000 from his investments then how much he will have to invest today, if rate of interest is 10% per annum

Present Value = 5000/0.10 = ` 50,000

VALUES OF AN ANNUITY DUE

When annuity is calculated from the beginning of the year it is called annuity due

In the case of annuity due or when payment

is made at the beginning of the year, which means last payment has completed one year at the time of calculation

FUTURE VALUE OF ANNUITY DUE Suppose that you deposit ` 1000 in saving account at

the beginning of each year for 5 years to earn 4% interest rate

Future value of an annuity due= future value of an annuity x (1+i)

= A x CVFA(I,n) x (1+i)

= 1000 x 5.416 x 1.04

= ` 5632.64

)1]()1)1(

[ ii

iAFVA

n

PRESENT VALUE OF ANNUITY DUE Suppose you deposit ` 500 at the beginning of each

year for 5 years at 10% interest rate. Calculate the present value of annuity.

Present Value of Annuity due = present value of annuity x (1+i)

PVA = A x PVFA(I,n) x (1+i)

= 500 x 3.791 x 1.10 = ` 2085.05

])1(

1)1([

n

n

iii

APVA

NET PRESENT VALUE (NPV)

Net Present Value (NPV) of a financial decision is the difference between the present value of cash inflows and the present values of cash outflows.

NPV = PV of Cash Inflows – PV of Cash Outflows

If NPV is negative, it means investment in project higher than the return. So, project will be rejected.

EXAMPLE Reliance industries is planning to start a project which

requires ` 1000 Cr at the beginning year and ` 200 Cr at the beginning of second year. They are expecting to get a return of ` 250 Cr at the end each year for next 5 years. Suggest whether reliance should go for the project or not, If interest rate in the market is 10% per annum.

Year Out flow (Cr)

PV Factor1/(1.10)T

Present Value (Cr)

Inflow PV Factor1/(1.10)T

Present Value (Cr)

T=0 `1000 1 `1000 0 1 0

T=1 `200 0.909 `181.8 `250 0.909 `227.25

T=2 `250 0.826 `206.5

T=3 `250 0.751 `187.75

T=4 `250 0.683 `170.75

T=5 `250 0.621 `155.25

Total `1181.8 `947.5

NPV = 947.5- 1181.8 = - ` 234.3 Cr

SOLUTION