Chapter 10, Problem 34QP

a)

Summary Introduction

To find: The net present value and determine what the answer states about the net present value. The number of cartons that can be sold and still break even; also find the cost level.

Introduction:

The price that a buyer is ready to pay for a security is the bid price.

Answer to Problem 34QP

The net present value is $861,836.07.

Explanation of Solution

Given information:

The R enterprise requires someone to supply the 140,000 cartons of screw machines for the year for the purpose of supporting it with the operations that are needed for the next five years. Person X has decided to make a bid on the contract. It will cost Person X $940,000 to install the necessary equipment for beginning the production. Person X depreciates on a straight-line to zero over the life of the project.

The cost of fixed production of Person X is $435,000 for a year, and the variable production cost must be $15.10 for a carton. The essential investment that is required by Person X in the net working capital is $90,000. The tax rate is assumed to be 35% and the rate of return on the investment is 12%. The price per carton is $23

Note: To calculate the bid price it is essential to set the net present value equal to zero and the essential price is found using the operating cash flow. Thus, the bid price is representing the project’s financial break-even level.

Computation of the net present value:

Year	1	2	3	4	5
Sales	3,220,000	3,220,000	3,220,000	3,220,000	3,220,000
Less: Variable costs	-2,114,000	-2,114,000	-2,114,000	-2,114,000	-2,114,000
Fixed costs	-435,000	-435,000	-435,000	-435,000	-435,000
Depreciation	-188,000	-188,000	-188,000	-188,000	-188,000
EBIT	483,000	483,000	483,000	483,000	483,000
Less: Taxes (35%)	-169,050	-169,050	-169,050	-169,050	-169,050
Net Income	313,950	313,950	313,950	313,950	313,950
Add: Depreciation	188,000	188,000	188,000	188,000	188,000
Operating cash flow	$501,950	$501,950	$501,950	$501,950	$501,950
Year	1	2	3	4	5
Operating cash flow	$501,950	$501,950	$501,950	$501,950	$501,950
Change in NWC	0	0	0	0	90,000
Capital spending	0	0	0	0	55,250
Total CF	$501,950	$501,950	$501,950	$501,950	$647,200

Computations for the above table:

Formula to calculate the sales:

$\text{Sales}=\text{Price per unit}\times \text{\$140,000}$

Computation of the sales:

$\begin{array}{c}\text{Sales}=\text{Price per unit}\times \text{\$140,000}\\ =\text{23}\times \text{\$140,000}\\ =\$3,220,000\end{array}$

Formula to calculate the cash outflow:

$\text{Cash outflow}=-\text{Capital spending}-\text{Changes in NWC}$

Computation of the cash outflow:

$\begin{array}{c}\text{Cash outflow}=-\text{Capital spending}-\text{Changes in NWC}\\ =-\$940,000-\$90,000\\ =-\$1,030,000\end{array}$

Formula to calculate the net present value:

$\text{NPV}=\text{Cash olutflow}+\text{Cash inflow}$

Computation of the net present value:

$\begin{array}{c}\text{NPV}=\text{Cash olutflow}+\text{Cash inflow}\\ =\{\begin{array}{l}-\$1,030,000+\text{Total cash flow}\left({\text{PVIFA}}_{\text{r , t}}\right)\\ +\left[\frac{\left(\text{Change in NWC}+\text{Capital spending}\right)}{{\left(1+\text{r}\right)}^{\text{t}}}\right]\end{array}\}\\ =-\$1,030,000+\$501,950\left(3.60478\right)+\left[\frac{\left(\$90,000+\$55,250\right)}{{\left(1.12\right)}^5}\right]\end{array}$

$\begin{array}{c}=-\$1,030,000+\$1,809,419.321+\$82,418.7508\\ =-\$1,030,000+\$1,891,838.0718\\ \text{= \$861,838}\text{.0718}\end{array}$

Hence, the net present value is $861,836.07.

Explanation:

The net present value of the project is positive. If the real price is above the bid price then it shows the results in zero net present value, as for the cartons sold, if the numbers of cartons sold increase, then the net present value will increase, and if the costs increase, the net present value will decline.

b)

Summary Introduction

To find: The cartons quantity that can be still supplied and still break even.

Introduction:

The price that a buyer is ready to pay for a security is the bid price.

Answer to Problem 34QP

The quantity of the cartons is 93,440.69.

Explanation of Solution

Given information:

The price per quantity is $23.

Computation of the operating cash flow using the formula of the net present value:

$\begin{array}{c}\text{NPV}=\text{0}=\{\begin{array}{l}\text{Cash outflow}+\text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)+\\ \left[\frac{\left(\text{Change in NWC}+\text{Capital spending}\right)}{{\left(1+\text{r}\right)}^{\text{t}}}\right]\end{array}\}\\ =\{\begin{array}{l}-\$1,030,000+\text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)\\ +\left[\frac{\left(\$90,000+\$55,250\right)}{{\left(1.12\right)}^5}\right]\end{array}\}\\ =-\$1,030,000+\$82,418.7508\\ \text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)=\$947,581.25\end{array}$

$\begin{array}{c}\text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)=\$947,581.25\\ \text{OCF}\left(3.60478\right)=\$947,581.25\\ =\frac{\$947,581.25}{3.60478}\\ \text{OCF}=\text{\$262,867}\text{.98}\end{array}$

Hence, the operating cash flow is $262,867.98.

Formula to calculate the tax shield approach:

$\text{OCF = }\{\begin{array}{c}\left[\left(\text{P – v}\right)\text{Q – FC}\right]\left(\text{1 –Tax rate}\right)\\ \text{+Tax rate}\times \text{Depreciation}\end{array}\}$

Computation of the quantity using the formula of the operating cash flow:

$\begin{array}{c}\text{OCF =\$262,867}\text{.98 }\{\begin{array}{c}\left[\left(\text{P – v}\right)\text{Q – FC}\right]\left(\text{1 –Tax rate}\right)\\ \text{+Tax rate}\times \text{Depreciation}\end{array}\}\\ \$\text{262,867}\text{.98 = }\{\begin{array}{c}\left[\left(\text{23 – 15}\text{.10}\right)\text{Q– \$435,000}\right]\\ \left(\text{1 – }\text{.35}\right)\text{ + }\text{.35}\left(\frac{\text{\$940,000}}{\text{5}}\right)\end{array}\}\\ \text{\$262,867}\text{.98}=\{\left[\text{7}\text{.9Q}\text{– \$435,000}\right]\times \text{0}\text{.65 + }\text{.35}\left(\frac{\text{\$940,000}}{\text{5}}\right)\}\\ =\text{5}\text{.135Q – \$282750}+\$65,800\end{array}$

$\begin{array}{c}=\text{5}\text{.135Q}\\ \text{Q}=\frac{\$479,817.98}{\text{5}\text{.135}}\\ \text{Q}=\text{93,440}\text{.69}\end{array}$

Hence, the quantity of the carton is 93,440.69.

c)

Summary Introduction

To find: The highest level of the fixed cost that can be afforded and still breaks even.

Introduction:

The price that a buyer is ready to pay for a security is the bid price.

Answer to Problem 34QP

The highest fixed cost is $802,818.49.

Explanation of Solution

Given information:

The price per quantity is $23, and the number of cartons is 140,000. The fixed price must be more than $435,000.

Computation of the operating cash flow using the formula of the net present value:

$\begin{array}{c}\text{NPV}=\text{0}=\{\begin{array}{l}\text{Cash outflow}+\text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)+\\ \left[\frac{\left(\text{Change in NWC +Capital spending}\right)}{{\left(1+\text{r}\right)}^{\text{t}}}\right]\end{array}\}\\ =\{\begin{array}{l}-\$1,030,000+\text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)\\ +\left[\frac{\left(\$90,000+\$55,250\right)}{{\left(1.12\right)}^5}\right]\end{array}\}\\ =-\$1,030,000+\$82,418.7508\\ \text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)=\$947,581.25\end{array}$

$\begin{array}{c}\text{OCF}\left({\text{PVIFA}}_{\text{12\%,5}}\right)=\$947,581.25\\ \text{OCF}\left(3.60478\right)=\$947,581.25\\ =\frac{\$947,581.25}{3.60478}\\ \text{OCF}=\text{\$262,867}\text{.98}\end{array}$

Hence, the operating cash flow is $262,867.98.

Formula to calculate the tax shield approach:

$\text{OCF = }\{\begin{array}{c}\left[\left(\text{P – v}\right)\text{Q – FC}\right]\left(\text{1 –Tax rate}\right)\\ \text{+Tax rate}\times \text{Depreciation}\end{array}\}$

Computation of the fixed cost using the tax shield approach:

$\begin{array}{c}\begin{array}{l}\text{ OCF }=\{\begin{array}{c}\left[\left(\text{P – v}\right)\text{Q – FC}\right]\left(\text{1 –Tax rate}\right)\\ +\text{Tax rate}\times \text{Depreciation}\end{array}\}\hfill \\ \text{\$262,867}\text{.98}=\{\begin{array}{c}\left[\left(\text{23 – 15}\text{.10}\right)\text{140,000}\text{– FC}\right]\\ \left(\text{1 – }\text{.35}\right)+\text{.35}\left(\frac{\text{\$940,000}}{\text{5}}\right)\end{array}\}\hfill \\ \hfill \end{array}\\ \text{\$262,867}\text{.98}=\{\left[\$1,106,000-\text{FC}\right]\times \text{0}\text{.65 + }\text{.35}\left(\frac{\text{\$940,000}}{\text{5}}\right)\}\\ =\$718,900-\text{.65FC}+\$65,800\end{array}$

$\begin{array}{c}=.65\text{FC}\\ \text{FC =}\frac{\$521,832.02}{\text{0}\text{.65}}\\ \text{= \$802,818}\text{.49}\end{array}$

Hence, the highest level of fixed cost is $802,818.49.