Chapter 6, Problem 22QP

Summary Introduction

To determine: Net present value to analyze the viability of the project.

Project Analysis:

Project analysis means analyzing the various related aspects of the project on the basis of the benchmarks previously decided by the firm and the deviations so located should be worked upon.

Net Present Value:

The net present value is the differential amount between the net cash inflows from future investments and net cash outflows in the form of costs that the company has to pay at present as initial cost of investment.

Explanation of Solution

Given,

The cost price of the facility is $750,000.

The estimated life of facility is 7 years.

The estimated revenue at the end of the first year is $635,000.

The current revenues are increased at 5% inflation rate per annum.

The estimated cost at the end of the first year of producing the units is $395,000.

The costs are increased at 4% per annum.

The real discount rate is 7%

The company falls under 34% of tax bracket.

Calculation of net present value,

Net Present Value
Particulars	Present Value factor @ 12.35%	Net Cash Flows ($)	Present Value ($)
Initial investment	1	(750,000)	(750,000)
Year 1	0.89	194,829	173,398
Year 2	0.792	205,356	162,642
Year 3	0.705	216,514	152,642
Year 4	0.628	228,337	143,396
Year 5	0.559	240,866	134,644
Year 6	0.497	254,137	126,306
Year 7	0.443	268,194	118,810
Net Present Value			261,838

Table (1)

Working notes:

Calculation of annual sales revenue for year 2,

$\begin{array}{c}\text{Sales revenue}=\text{Year1sales}+\left(\text{Year1sales}\times \text{Inflation rate}\right)\\ =\$635,000+\left(\$635,000\times 5\%\right)\\ =\$635,000+\$31,750\\ =\$666,750\end{array}$

Calculation of annual sales revenue for year 3,

$\begin{array}{c}\text{Sales revenue}=\text{Year 2 sales}+\left(\text{Year 2 sales}\times \text{Inflation rate}\right)\\ =\$666,750+\left(\$666,750\times 5\%\right)\\ =\$666,750+\$33,338\\ =\$700,088\end{array}$

Calculation of annual sales revenue for year 4,

$\begin{array}{c}\text{Sales revenue}=\text{Year 3 sales}+\left(\text{Year 3 sales}\times \text{Inflation rate}\right)\\ =\$700,088+\left(\$700,088\times 5\%\right)\\ =\$700,088+\$35,004\\ =\$735,092\end{array}$

Calculation of annual sales revenue for year 5,

$\begin{array}{c}\text{Sales revenue}=\text{Year 4 sales}+\left(\text{Year 4 sales}\times \text{Inflation rate}\right)\\ =\$735,092+\left(\$735,092\times 5\%\right)\\ =\$735,092+\$36,755\\ =\$771,847\end{array}$

Calculation of annual sales revenue for year 6,

$\begin{array}{c}\text{Sales revenue}=\text{Year 5 sales}+\left(\text{Year 5 sales}\times \text{Inflation rate}\right)\\ =\$771,847+\left(\$771,847\times 5\%\right)\\ =\$771,847+\$38,592\\ =\$810,439\end{array}$

Calculation of annual sales revenue for year 7,

$\begin{array}{c}\text{Sales revenue}=\text{Year 6 sales}+\left(\text{Year 6 sales}\times \text{Inflation rate}\right)\\ =\$810,439+\left(\$810,439\times 5\%\right)\\ =\$810,439+\$40,522\\ =\$850,961\end{array}$

Calculation of annual expenses for year 2,

$\begin{array}{c}\text{Expenses}=\text{Year 1 expenses}+\left(\text{Year 1 expenses}\times \text{Increase rate}\right)\\ =\$395,000+\left(\$395,000\times 4\%\right)\\ =\$395,000+\$15,800\\ =\$410,800\end{array}$

Calculation of annual expenses for year 3,

$\begin{array}{c}\text{Expenses}=\text{Year 2 expenses}+\left(\text{Year 2 expenses}\times \text{Increase rate}\right)\\ =\$410,800+\left(\$410,800\times 4\%\right)\\ =\$410,800+\$16,432\\ =\$427,232\end{array}$

Calculation of annual expenses for year 4,

$\begin{array}{c}\text{Expenses}=\text{Year 3 expenses}+\left(\text{Year 3 expenses}\times \text{Increase rate}\right)\\ =\$427,232+\left(\$427,232\times 4\%\right)\\ =\$427,232+\$17,089\\ =\$444,321\end{array}$

Calculation of annual expenses for year 5,

$\begin{array}{c}\text{Expenses}=\text{Year 4 expenses}+\left(\text{Year 4 expenses}\times \text{Increase rate}\right)\\ =\$444,321+\left(\$444,321\times 4\%\right)\\ =\$444,321+\$17,773\\ =\$462,094\end{array}$

Calculation of annual expenses for year 6,

$\begin{array}{c}\text{Expenses}=\text{Year 5 expenses}+\left(\text{Year 5 expenses}\times \text{Increase rate}\right)\\ =\$462,094+\left(\$462,094\times 4\%\right)\\ =\$462,094+\$18,484\\ =\$480,578\end{array}$

Calculation of annual expenses for year 7,

$\begin{array}{c}\text{Expenses}=\text{Year 6 expenses}+\left(\text{Year 6 expenses}\times \text{Increase rate}\right)\\ =\$480,578+\left(\$480,578\times 4\%\right)\\ =\$480,578+\$19,223\\ =\$499,801\end{array}$

Calculation of annual depreciation,

$\begin{array}{c}\text{Depreciation}=\frac{\text{Cost}}{\text{Estimated life}}\\ =\frac{\$750,000}{7\text{years}}\\ =\$107,143\end{array}$

Calculation of nominal interest rate,

$\begin{array}{c}\text{Real interest rate}=\frac{1+\text{Nominal interest rate}}{1+\text{Inflation rate}}-1\\ 0.07=\frac{1+\text{Nominal interest rate}}{1+0.05}-1\\ 1.07\times 1.05=1+\text{Nominal interest rate}\\ \text{Nominal interest rate}=12.35\%\end{array}$

Calculation of annual cash flows,

Conclusion

Thus, the net present value is $261,838.