# Finance: Net Present Value Essay

Submitted By silvesterrr
Words: 2128
Pages: 9

CAPITAL INVESTMENT DECISION

Chapter 13

Capital investment decision are those decisions that involve current outlay (i.e. capital) in return for a stream of benefits in future years. These decisions include:-

• Investments in plant and machinery

• Investments in research and development

• Investments in advertising and warehouse facility

The decision is based on the following assumptions:

• Cash inflows and outflows are known with certainty

• Sufficient funds are available to undertake all profitable investments

• There are no taxes

• There is no inflation

Opportunity cost of investment
This is the rate of return that are available from alternate investments. A firm should invest in capital projects only if they yield a return in excess of the opportunity cost of investment.

Compounding

Invest \$100,000 at 10% payable at the end of each year for 4 years with the interest re-invested (i.e. compounding interest)

Long Way
|End of Year |Interest earned |Total Invested |Accumulated Total |
|0 | |100,000 | |
|1 |0.10 x 100,000 |10,000 |110,000 |
|2 |0.10 x 110,000 |11,000 |121,000 |
|3 |0.10 x 121,000 |12,100 |133,100 |
|4 |0.10 x 133,100 |13,310 |146,410 |

Formula
FV = Vo(1 + K)n

FV = Future Value
Vo = Invested Sum
K = Interest rate n = Number of years

= (100,000)(factor using compound table for \$1 for 4 years @ 10%) you get
100,000 x 1.464 =\$146,410

Future Value of an Annuity
Invest an annuity of \$10,000 for 5 years at interest of 12% compounding

FV of Annuity = Annuity (PVIFA ) 5 years 10%
= 10,000 x 6.353 =\$63,530

Present Value
The concept that \$1 received in the future is not equal to \$1 received today is known as the ‘time value of money’.

The process of converting cash to be received in the future into value at the present time by the use of an interest rate is called ‘discounting’. Discounting is the opposite of compounding.

\$121,000 received at the end of year 2 @ 10%

Vo (present value)= FVn OR FV(PVIF) 10% for 2 years = 121,000 x 0.826 (from table) =\$100,000 (1 + K)n

Net Present Value
NPV = PV of Cash Flows - Cash Outlay –

A company is evaluating two projects with an expected life of 3 years and investment outlay of \$1million. The estimated net cash inflows of each project are as follows:-

| |Project A |Project B |
|Year 1 |300,000 |600,000 |
|Year 2 |1,000,000 |600,000 |
|Year 3 |400,000 |600,000 |

| |Project A 10% |Project B 10% |
| | |factor |PV | |factor |PV |
|0 |1,000,000 |1 |(1,000,0000 |1,000,000 |1 |(1,000,000) |
|Year 1 |300,000 |0.9091 |272,730 |600,000 |0.9091 |545,460 |
|Year 2 |1,000,000 |0.8264 |826,400 |600,000 |0.8264 |495,840 |
|Year 3 |400,000 |0.7513 |300,520 |600,000