Chapter 11, Problem 22PS

a)

Summary Introduction

To determine: Net present value (NPV).

Explanation of Solution

Given information:

Annual output is 100,000 tons

Operating cost are $0.90 per ton

Sale price is $1 per ton.

Cost of capital is 10%.

Calculation of net present value:

Net present value of such plant is probably going to zero, as a result of industry is competitive and, after two years no company would enjoy the technical benefits.

The present value of each of these plants would be $100,000 the cost is $100,000 and net present value is zero.

b)

Summary Introduction

To determine: Price of polysyllabic acid in 3 year and beyond

Explanation of Solution

Calculation of price by using net present value of new plant:

 $\begin{array}{c}\text{Present value}=\left(\frac{100,000\times \left(\text{Price}-0.85\right)}{0.10}\right)\\ \$100,000=\left(\frac{500,000\times \left(\text{Price}-0.85\right)}{0.10}\right)\\ \text{Price}=\$0.95\end{array}$

Therefore, the price of polysyllabic acid is $0.95

c)

Summary Introduction

To determine: Present value when the scrap value is $40,000 and $80,000 in 2 year.

Explanation of Solution

Calculation of net present value at year 2:

  $\begin{array}{c}\text{PV=}\left(\frac{100,000\text{tons}\times \left(\text{Price}-\text{cost}\right)}{0.10}\right)\\ =\left(\frac{100,000\times \left(\$0.95-\$0.90\right)}{0.10}\right)\\ =\$50,000\end{array}$

Therefore, when the existing plant can be scrapped at t=2 as long as the value of scrap at that point exceeds $50,000 that it’s expected to be.

d)

Summary Introduction

To discuss: Whether company U operate plants profitably after year 2 when plant is fully depreciated.

Explanation of Solution

Person X views that, company doesn’t operate them in profitably because book value is irrelevant and the net present value of the existing plant is negative after the second year.

e)

Summary Introduction

To discuss: Whether company scrap the new plant in year 2

Explanation of Solution

Person X views that, company should scrap the newly purchased plant in year 2 because sunk costs are irrelevant and the net present value of the existing plant is negative after the second year.

f)

Summary Introduction

To determine: Net present value.

Explanation of Solution

Company P’s project causes temporary excess capacity. Therefore the price for future 2 years should be specified the prevailing plant owners are indifferent between scrapping currently and scrapping at the end of 2 year.

Scrap value is $60,000 and also it is equal to present values of future cash flows. Therefore,

Calculation of net present value:

                             $\begin{array}{c}\text{Present value}=\frac{\text{Cash}\text{flows}}{{\left(1+\text{r}\right)}^{\text{n}}}\\ \$60,000=\left(\frac{100,000\times \left(\text{Price}-\$.90\right)}{1.10}\right)+\left(\frac{100,000\times \left(\text{Price}-\$.90\right)}{{1.10}^2}\right)\\ +\frac{\$57,900}{{1.10}^2}\\ \text{Price}=\$0.97\end{array}$

By using this value of price we can calculate the present value of new plant,

Calculation of present value of new plant:

             $\begin{array}{c}\text{Present value}=\frac{\text{Cash}\text{flows}}{{\left(1+\text{r}\right)}^{\text{n}}}\\ \$60,000=\left\{100,000\times \left[\left(\frac{\$0.97-0.85}{1.10}\right)+\left(\frac{\$0.97-0.85}{{1.10}^2}\right)+\frac{\left(\$0.95-0.85\right)}{\left(0.10\times {1.10}^2\right)}\right]\right\}\\ -\$100,000\\ \text{Present value}=\left\{100,000\times \left[0.10909+0.09917+0.82644\right]\right\}\\ -\$100,000\\ =\$103,470-\$100,000\\ =\$3,470\end{array}$

Therefore present value of new plant is $3,470.