# capital budgeting

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TIME VALUE OF MONEY

Time value of money refers to an individual preference of a given amount of cash now rather than the same amount at some future time. The reasons why an individual would prefer cash now:

i) Subjective preference for present consumption – one may prefer present consumption over future consumption of goods and services because of the urgency of present wants or the risk of not being in a position to enjoy future consumption. ii) Availability of investment opportunities – individuals prefer money now because of the availability of present opportunities to which they can put present cash to earn returns. iii) Uncertainties – one may not be certain of future amount of cash receipts and would rather receive cash now than in future.

Time Value of Money Computations

i/ Compound or Future value of A Simple Amount

This is the future value of a given amount that is allowed to grow at a constant interest rate for a given period of time.

Sn = P (1+r)n where:
Sn = Future value P = present value or principal r = interest rate n = number of years or time period.

Example

Suppose you have Sh.1000 and you are promised 10% for the next four years, how much will you have at the end of the four years.

Solution; Sn = P (1+r)n = 1000 (1+0.1)4 = 1000 x 1,4641 = 1464.10 or tables FV = P x Future Value Interest Factor (FVIF) = 1000 x 1.4641 = 1464.10

ii/ Present Value of A Simple Amount

This is the present value (value today or now) for a given future value.

Example

Suppose you were to receive 1464.10 four years from now and the required rate of return is 10%, What amount would you require to receive today to be indifferent?

Solution

P = Sn (1+r)n

P = 1464.10 = 1000 1.4691

P = Sn(1) PVIF r%, n yrs = 0.683 PVIF r%, n yrs

Using Tables = Sn x PVIF r%, n yrs

iii/ Compound or Future Value of An Annuity

An annuity is a series of

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