Investment
Decisions
Present Value (PV)
Present
Value is the sum which would have to be invested today to amount to a given sum
at a rate of interest over a given time period.
=
Original Sum x (1+ rate of interest)Years at Interest
Rate
Calculate
present value of a sum payable or receivable sometime in the future at
10%. A sum of $121 receivable in two
years at 100 has a present value today of only $100.
$121
x 1
(1
+ 0.10)2
Net Present Value (NPV)
Net
present value approach takes all the cash flow associated with a project and
reduces them to a common denominator (present value) by using appropriate
interest rate (also called cost of capitol / or cost of finance)
Years |
Capital / Return |
Interest Rate 5% |
Net present value |
|
1 |
-300 |
1 |
-300 |
|
2 |
114 |
.952 |
108.5 |
|
3 |
114 |
.907 |
103.4 |
|
4 |
114 |
.864 |
98.6 |
|
Total |
42 |
.823 |
10.50 |
Total present value |
Of the income |
|
310.50 |
Internal Rate of Return
Example: What is rate of return on an investment of $1000 which generates cash flow of $420 per annum for the next three years.
Step
1 @ 10%
Years |
Capital / Return |
Interest Rate 10% |
Net present value |
|
0 |
-1000 |
1.000 |
-1000 |
|
1 |
420 |
.909 |
382 |
|
2 |
420 |
.826 |
347 |
|
3 |
420 |
.751 |
315 |
|
|
|
NPV |
44 |
Ø Rate
is too low
Step
2 @ 14%
Years |
Capital / Return |
Interest Rate 14% |
Net present value |
|
0 |
-1000 |
1.000 |
-1000 |
|
1 |
420 |
.877 |
368 |
|
2 |
420 |
.760 |
323 |
|
3 |
420 |
.675 |
284 |
|
|
|
NPV |
-25 |
Ø Rate
is too high.
Step
3 Interpolate
10%
+ 44 x 14% - 10%
44+25
=
10% +2.5%
=
12.5%
Payoff or Payback Period
Time
taken to recover original investment.
|
Year |
Capital / Return |
Cumulative cash flow |
|
|
1 Investment |
-50,000 |
|
|
|
1 cash flow |
13,000 |
(50,000
–13,000) |
-37,000 |
|
2 |
15,000 |
(37,000-15,000) |
-22,000 |
|
3 |
15,000 |
(22,000-15,000) |
-7,000 |
|
4 |
15,000 |
(7,000-15,000) |
8,000 |
Ø Payback
3+(7000/15000) = 3.5 years
Average Cost
Average
cost based on the relative proportions that are expected to be used.
Source of finance |
Optimum proportion % |
Estimated cost |
|
Long Term Loan |
30 |
8.75% |
|
Preference share capital |
5 |
10.50% |
|
Existing ordinary share capital |
20 |
10.00% |
|
New ordinary share capital |
10 |
10.50% |
|
Retained earnings |
35 |
10.00% |
Using optimum proportion as
weights, the average cost of capital can be calculated as:
Source of finance |
Optimum proportion % |
|
Estimated cost |
Average cost of capital |
|
Long Term Loan |
.30 |
x |
8.75 |
2.625 |
|
Preference share capital |
.05 |
x |
10.50 |
.525 |
|
Existing ordinary share capital |
.20 |
x |
10.00 |
2.000 |
|
New ordinary share capital |
.10 |
x |
10.50 |
1.050 |
|
Retained earnings |
.35 |
x |
10.00 |
3.500 |
Average cost of Capital |
9.700 |
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