# capital budgeting

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 valueP = present value or principal

r = interest raten = 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 similar consecutive payments or receipts.

Example

Assume that an investor deposits Sh.1,000 at the end of every year into an account earning 10% p.a. How much will he have at the end of four years?

Solution

At the end of the1st year = 1,000

2nd year= 1.1 x 1,000 = 1,100 + 1000= 2,100

3rd year= 1.1 x 2,100 = 2,310 + 1000 = 3,310

4th year= 1.1 x 3,310 = 3,641 + 1000 = 4,641

Using tables:

FVA= A x (l+r)n - l)

(r)

= 1000 x {(l.1)4 - l} = 100 x 1.4641 = l = 4,641

0.1 0.1

= 1000 * FVIFA r%,n

FVA = Annuity X FVIFA r%,n

iv/ Present Value of an Annuity

Example: Assume that you are investing in a project that gives you Sh.1000 at the end of every year for 4 years. What is the maximum amount you would be willing to pay for that project if the required rate of return is 10%.

Solution:

1000 +

1000 +

1000 +

1000

1.1

(1.1)2

(1.1)3

(1.1)4

909.1

826.4

751.3

683

= 3,169.8

PVa = A x (1 – 1/(1+r)n)

r

= 1000 x (1 – 1/(1.1)4 = 1000 x 3.1699 = 3169.9

0.1

= 1000 * PVIFr% ,n yrs

Using tables

PVA = Annuity x PVIFA r%, n yrs.

v/ Compound or Future Value of An Annuity Due

The concepts of compound or present value of an annuity assumes that payments and receipts at the year end. In practise payment may be made at the beginning of the year. A series of similar consecutive payments or receipts starting at the beginning of each year for a specified number of years is known as an annuity due.

Example:

Suppose you were to deposit Sh.1000 at the beginning of each year for four years at an interest rate of 10%. How much would you have at the end of the 4 years.

Solution:

(1000x1.1) + (2100x1.1) + (3310x1.1) + (4641x1.1)

1100 2310 3641 5105.1

FVAdue = A x ((1+r)n-1) (1+r)...

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