432M4 SLP
Financialinvestments and decision making processes often require calculationsusing values obtained from the financial position of a company or aproject. Evaluating such a company or project may require calculatingvalues such as the net present value (NPV), rate of return oninvestment and profitability index [ CITATION Sam80 l 1033 ]. The complexity in such calculations is simplified by the use ofspreadsheets such as excel and other related packages.
Considera project with the following expected cash flows:Year Cashflow0 $549,0001 $91,0002 $182,0003 $374,000
Thenet present value of the project at 0% and 5% discounting rates canbe worked out from the excel spreadsheet giving results shown below:
year 
cash flow 
present value at 0% 
present value at 5% 
0 
549000 
$549,000.00 
$549,000.00 
1 
91000 
$91,000.00 
$86,666.67 
2 
182000 
$182,000.00 
$165,079.37 
3 
374000 
$374,000.00 
$323,075.26 
net present value 
$1,196,000.00 
$1,123,821.29 
Theresults show that the net present value is lower at a discounted rateof 5% than when there is zero discounting rate used. The formulaused can be obtained from the attached excel document. It isdeveloped from the compound interest formula but with reciprocalvalue for the returns [ CITATION Hae87 l 1033 ].
Incalculating the internal rate of return (IRR), the first value hasbeen assigned a negative sign indicating that this is a payment to bemade in the project. The IRR given below has been worked out usingexcel spreadsheet.
cash flow 
IRR 
549000 
7% 
91000 

182000 

374000 
Considera project with the expected cash flows given in the table below:Year Cash flow0 $51,0001 $51,0002 $87,0003 $87,000
Thecalculations in excel are given in the table below:
year 
cash flow 
present value at 4% 
0 
51000 
$51,000.00 
1 
51000 
$49,038.46 
2 
87000 
$80,436.39 
3 
87000 
$77,342.68 
net present value 
$257,817.54 
Theinternal rate of return for the cash flow above is given by
cash flow 
IRR 
51000 
116% 
51000 

87000 

87000 
Theprofitability index is given by the ratio of the gross present valueto the outlay [ CITATION Wik142 l 1033 ]. The gross present value is given by the net present value less theinitial outlay. Hence, a project requiring 1.26m and has aprofitability index of 0.96 will have a net present value as shown inthe working below:
outlay 
1260000 
profitability index 
0.96 
net present value 
50400 
Theformula (NPV + K)/ K = 0.96 was applied in this case where K is theinitial outlay of the project. NPV is worked out by substituting thevalue of K in the formula.
Ina case where one needs financing for a project where payments aremade in future, it is necessary to work out the present values of thefuture payments before deciding on the amount of loan to be givenout. For the repayment schedules given, we need to know the presentvalues of their respective future payments. This is given in thetable below:
year 
cash flow 
present value at 10% 
2 
15000 
$12,396.69 
4 
10000 
$6,830.13 
net present value 
$19,226.83 
Fromthe net present value obtained, and as a financier of the project, Iwould be willing to give $19227 as a loan for the project.
Theeffective annual rate of interest for a loan that has a 15% annualpercentagerate,compounded monthly can be worked out from the formula given as:
Effectiverate = e^{r}– 1 = e^{0.15}–1 = 16%.
References
Haeussler, E. F., & S, P. R. (1987). Introductory Mathematical Analysis. New Jersey: Prentice Hall.
Samuels, J. M., & Wilkes, F. M. (1980). Management of Company Finance. London: Butler and Tanner Ltd.
Wikipedia. (n.d.). Retrieved June 18, 2014, from Profitability Index: http:www.en.wikipedia.org/wiki/profitability_index