Chapter 6, Problem 36QP

Summary Introduction

To determine: Bid price.

Capital Budgeting:

Decision related to the investment for the long run is called capital budgeting. Capital budgeting includes the investment in the heavy machinery and information technology.

Net Present Value(NPV):

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

Explanation of Solution

Given,

Cost of the investment is 145,000,000.

Estimated life of the investment is 4 year.

Selling price of the project is $435.

Labor cost is 16.25 per hour.

Labor cost is increased by 2%.

Energy cost per physical unit is $3.80.

Energy cost is increased by 3%.

Inflation rate is 5%.

Tax rate is 34%.

Discount rate is 4%.

Formula to calculate the Net present value,

Working notes:

Calculate the depreciation for the 1^st year,

$\begin{array}{c}\text{Depreciation}=\frac{\text{Investment}}{\text{Estimated}\text{life}}\times \frac{1}{1+\text{Inflation}\text{rate}}\\ =\frac{\$145,000,000}{4\text{years}}\times \frac{1}{\left(1+0.05\right)}\\ =\$36,250,000\times 0.952\\ =\$34,510,000\end{array}$

Calculate the depreciation for the 2^nd year,

$\begin{array}{c}\text{Depreciation}=\frac{\text{Investment}}{\text{Estimated}\text{life}}\times \frac{1}{{\left(1+\text{Inflation}\text{rate}\right)}^2}\\ =\frac{\$145,000,000}{4\text{years}}\times \frac{1}{{\left(1+0.05\right)}^2}\\ =\$36,250,000\times 0.907\\ =\$32,878,750\end{array}$

Calculate the depreciation for the 3^rd year,

$\begin{array}{c}\text{Depreciation}=\frac{\text{Investment}}{\text{Estimated}\text{life}}\times \frac{1}{{\left(1+\text{Inflation}\text{rate}\right)}^3}\\ =\frac{\$145,000,000}{4\text{years}}\times \frac{1}{{\left(1+0.05\right)}^3}\\ =\$36,250,000\times 0.864\\ =\$31,320,000\end{array}$

Calculate the depreciation for the 4^th year,

$\begin{array}{c}\text{Depreciation}=\frac{\text{Investment}}{\text{Estimated}\text{life}}\times \frac{1}{{\left(1+\text{Inflation}\text{rate}\right)}^4}\\ =\frac{\$145,000,000}{4\text{years}}\times \frac{1}{{\left(1+0.05\right)}^4}\\ =\$36,250,000\times 0.823\\ =\$29,833,750\end{array}$

Calculate the labor cost per hour for 2 years,

$\begin{array}{c}\text{Lobor}\text{cost}=\left(\text{Year}\text{1}\text{labor}\text{cost}\times \text{growth}\text{rate}\right)+\text{Year}\text{1}\text{labor}\text{cost }\\ =\left(\text{\$16}\text{.25}\times 0.02\right)+\$16.25\\ =\text{\$0}\text{.325}+\text{\$16}\text{.25}\\ =\text{\$16}\text{.58}\end{array}$

Calculate the labor cost per hour for 3 years,

$\begin{array}{c}\text{Lobor}\text{cost}=\left(\text{Year}2\text{labor}\text{cost}\times \text{Growth}\text{rate}\right)+\text{Year}\text{1}\text{labor}\text{cost}\\ =\left(\text{\$16}\text{.58}\times 0.02\right)+\$16.25\\ =\text{\$0}\text{.3316}+\text{\$16}\text{.58}\\ =\text{\$16}\text{.91}\end{array}$

Calculate the labor cost per hour for 4 years,

$\begin{array}{c}\text{Lobor}\text{cost}=\left(\text{Year}3\text{labor}\text{cost}\times \text{growth}\text{rate}\right)+\text{Year}\text{1}\text{labor}\text{cost}\\ =\left(\text{\$16}\text{.91}\times 0.02\right)+\$16.25\\ =\text{\$0}\text{.3382}+\text{\$16}\text{.58}\\ =\text{\$17}\text{.25}\end{array}$

Calculate the energy cost for the 2 years,

$\begin{array}{c}\text{Energy}\text{cost}=\text{Year}\text{1}\text{energy}\text{cost}+\left(\text{Year}\text{1}\text{energy}\text{cost}\times \text{Growth}\text{rate}\right)\\ =\$3.80+\left(\$3.80\times 3\%\right)\\ =\$3.91\end{array}$

Calculate the energy cost for the 3 years,

$\begin{array}{c}\text{Energy}\text{cost}=\text{Year}2\text{energy}\text{cost}+\left(\text{Year}2\text{energy}\text{cost}\times \text{Growth}\text{rate}\right)\\ =\$3.91+\left(\$3.91\times 3\%\right)\\ =\$4.03\end{array}$

Calculate the energy cost for the 4 years,

$\begin{array}{c}\text{Energy}\text{cost}=\text{Year}3\text{energy}\text{cost}+\left(\text{Year}3\text{energy}\text{cost}\times \text{Growth}\text{rate}\right)\\ =\$4.03+\left(\$4.03\times 3\%\right)\\ =\$4.15\end{array}$

Conclusion

Hence, net present value of the project is $22,418,247.