Chapter 10, Problem 35QP

Calculating a Bid Price [LO3] Your company has been approached to bid on a contract to sell 4,800 voice recognition (VR) computer keyboards per year for four years. Due to technological improvements, beyond that time they will be outdated and no sales will be possible. The equipment necessary for the production will cost $2.9 million and will be depreciated on a straight-line basis to a zero salvage value. Production will require an investment in net working capital of $175,000 to be returned at the end of the project, and the equipment can be sold for $275,000 at the end of production. Fixed costs are $570,000 per year, and variable costs are $115 per unit. In addition to the contract, you feel your company can sell 11,400, 13,500, 17,900, and 10,400 additional units to companies in other countries over the next four years, respectively, at a price of $210. This price is fixed. The tax rate is 40 percent, and the required return is 10 percent. Additionally, the president of the company will undertake the project only if it has an NPV of $100,000. What bid price should you set for the contract?

Summary Introduction

To find: The bid price that must be set for the contract.

Introduction:

Bid price is the price, at which a market-maker or dealer is prepared to buy securities or shares or other assets.

Answer to Problem 35QP

The bid price is $192.71.

Explanation of Solution

Given information:

The company of Person X is been approached to bid on a contract to sell 4,800 voice recognition computer keyboards for the year for four years. As there prevail technological improvements the equipment will be outdated. The cost of the equipment that is essential for production is $2.9 million and will be depreciated on a straight line to a zero salvage value.

The production needs an investment in the net working capital of $175,000 to be returned at the project’s end and the sales of the equipment can be made for $275,000 at the end of the production. The fixed cost is $570,000 and the variable cost is $115 for a year. Additionally the company can sell 11,400, 13,500, 17,900, and 10,400 extra units to the companies in various countries for the upcoming 4 years at $210 (this is a fixed price).

The rate of tax is 40% and the required rate of return is 10%. In addition the president of the company will take over the project only if it has the net present value of $100,000.

Computation of the cash flows that are generated from the keyboard sales to other countries are as follows:

Particulars	Year 1	Year 2	Year 3	Year 4
Sales	$2,394,000	$2,835,000	$3,759,000	$2,184,000
Less: Variable costs	$1,311,000	$1,552,500	$2,058,500	$1,196,000
EBT	$1,083,000	$1,282,500	$1,700,500	$988,000
Less: Tax	$433,200	$513,000	$680,200	$395,200
Net income (and OCF)	$649,800	$769,500	$1,020,300	$592,800

Calculations for the above cash flows:

Sales:

For Year 1:

$\begin{array}{c}\text{Year 1 sale}=\text{Sales unit}\times \text{Sale price}\\ =\text{11,400}\text{units}\times \text{\$210}\\ =\text{\$2,394,000}\end{array}$

For Year 2:

$\begin{array}{c}\text{Year 2 Sale}=\text{Sales unit}\times \text{Sale price}\\ =\text{13,500units}\times \text{\$210}\\ =\text{\$2,835,000}\end{array}$

For Year 3:

$\begin{array}{c}\text{Year 3 Sale}=\text{Sales unit}\times \text{Sale price}\\ =\text{17,900units}\times \text{\$210}\\ =\text{\$3,759,000}\end{array}$

For Year 4:

$\begin{array}{c}\text{Year 4 Sale}=\text{Sales unit}\times \text{Sale price}\\ =\text{10,400units}\times \text{\$210}\\ =\text{\$2,184,000}\end{array}$

Variable cost:

For Year 1:

$\begin{array}{c}\text{Year 1 Variable costs}=\text{Sales unit}\times \text{Variable costs per unit}\\ =\text{11,400units}\times \text{\$115}\\ =\text{\$1,311,000}\end{array}$

For Year 2:

$\begin{array}{c}\text{Year 2 Variable costs}=\text{Sales unit}\times \text{Variable costs per unit}\\ =\text{13,500units}\times \text{\$115}\\ =\text{\$1,552,500}\end{array}$

For Year 3:

$\begin{array}{c}\text{Year 3 Variable costs}=\text{Sales unit}\times \text{Variable costs per unit}\\ =\text{17,900units}\times \text{\$115}\\ =\text{\$2,058,500}\end{array}$

For Year 4:

$\begin{array}{c}\text{Year 4 Variable costs}=\text{Sales unit}\times \text{Variable costs per unit}\\ =\text{10,400units}\times \text{\$115}\\ =\text{\$1,196,000}\end{array}$

Tax:

For Year 1:

$\begin{array}{c}\text{Year 1 Tax}=\text{EBT}\times \text{Tax rate}\\ =\$1,083,000\times 0.4\\ =\$433,200\end{array}$

For Year 2:

$\begin{array}{c}\text{Year 2 Tax}=\text{EBT}\times \text{Tax rate}\\ =\text{\$1,282,500}\times 0.4\\ =\$513,000\end{array}$

For Year 3:

$\begin{array}{c}\text{Year 3 Tax}=\text{EBT}\times \text{Tax rate}\\ =\text{\$1,700,500}\times 0.4\\ =\$680,200\end{array}$

For Year 4:

$\begin{array}{c}\text{Year 4 Tax}=\text{EBT}\times \text{Tax rate}\\ =\text{\$988,000}\times 0.4\\ =\$395,200\end{array}$

Formula to calculate the net present value for additional sales:

$\text{NPV}=\left[\frac{\text{Year 1 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}+\frac{\text{Year 2 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}+\frac{\text{Year 3 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}+\frac{\text{Year 4 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}\right]$

Note: Calculation of NPV of addition sale did not include the initial cash outflow, depreciation, and fixed assets.

Computation of the net present value for additional sales:

$\text{NPV}=\left[\frac{\text{Year 1 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}+\frac{\text{Year 2 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}+\frac{\text{Year 3 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}+\frac{\text{Year 4 OCF}}{{\left(1+\text{r}\right)}^{\text{t}}}\right]$

$\begin{array}{c}\text{NPV}=\left[\frac{\$649,800}{{\left(1+0.1\right)}^1}+\frac{\$769,500}{{\left(1+0.1\right)}^2}+\frac{\$1,020,300}{{\left(1+0.1\right)}^3}+\frac{\$592,800}{{\left(1+0.1\right)}^{\text{4}}}\right]\\ =\left[\$590,727.273+\$635,950.413+\$766,566.491+\$404,890.376\right]\\ =\text{\$2,398,134}\text{.55}\end{array}$

Hence, the net present value is $2,398,134.55.

Formula to calculate the after tax salvage value:

$\text{After tax salvage value}=\text{Salvage value}\left(1-\text{Tax rate}\right)$

Computation of the after tax salvage value:

$\begin{array}{c}\text{After tax salvage value}=\text{Salvage value}\left(1-\text{Tax rate}\right)\\ =\text{\$275,000}\left(1-\text{0}\text{.40}\right)\\ =\$165,000\end{array}$

Hence, the after tax salvage value is $165,000.

Formula to calculate the operating cash flow of the project with the net present value:

$\text{NPV}=\left[\begin{array}{l}-\text{Cost of equipment}-\text{NWC}+\text{NPV of additional sales}\\ \text{+OCF}\left({\text{PVIFA}}_{10\%,4}\right)+\left[\frac{\left(\text{after tax salvage value}+\text{NWC}\right)}{{\left(1+\text{r}\right)}^{\text{t}}}\right]\end{array}\right]$

Note:

• NPV for entire project is taken as $100,000.
• PVIFA represents Present Value Interest of Future Annuity.
• NWC represents Net Working Capital.

Computation of the operating cash flow of the project:

$\text{NPV}=\left[\begin{array}{l}-\text{Cost of equipment}-\text{NWC}+\text{NPV of additional sales}\\ \text{+OCF}\left({\text{PVIFA}}_{10\%,4}\right)+\left[\frac{\left(\text{after tax salvage value}+\text{NWC}\right)}{{\left(1+\text{r}\right)}^{\text{t}}}\right]\end{array}\right]$

$\begin{array}{c}\text{\$100,000}=\left[\begin{array}{l}-\text{\$2,900,000}-\text{\$175,000}+\text{\$2,398,134}\text{.55}\\ +\text{OCF}\left({\text{PVIFA}}_{10\%,4}\right)+\left[\frac{\left(\text{\$165,000}+\text{\$175,000}\right)}{{\left(1+0.1\right)}^4}\right]\end{array}\right]\\ \text{\$100,000}=-\text{\$676,865}\text{.45}+\text{OCF}\left({\text{PVIFA}}_{10\%,4}\right)+\$232,224.575\\ \text{OCF}\left(3.169865\right)=\$544,640.87\\ \text{OCF}=\frac{\$544,640.87}{3.169865}\end{array}$

$\text{OCF}=\$171,818.32$

Hence, the operating cash flow is $171,818.32.

Formula to calculate the bid price:

$\text{OCF}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\left(1-\text{T}\right)+\text{T}\times \text{Depreciation}$

Computation of the bid price:

$\begin{array}{c}\text{OCF}=\left[\left(\text{P}-\text{v}\right)\text{Q}-\text{FC}\right]\left(1-\text{T}\right)+\text{T}\times \text{Depreciation}\\ \text{\$171,818}\text{.31}=\left[\left(\text{P}-\text{\$115}\right)\text{4,800}-\text{\$570,000}\right]\left(1-\text{0}\text{.40}\right)+\text{0}\text{.40}\times \frac{\$2,900,000}{4\text{years}}\\ =\left[\text{4,800P}-\text{\$552,000}-\text{\$570,000}\right]\left(0.60\right)+\$290,000\\ =\left[\text{4,800P}-\text{\$}1,122,000\right]\left(0.60\right)+\$290,000\end{array}$

$\begin{array}{c}\text{\$171,818}\text{.31}=\text{2,880P}-\text{\$673,200}+\$290,000\\ =\text{2,880P}-\text{\$}383,200\\ \text{P}=\frac{\$555,018.31}{2,880}\\ =\text{\$192}\text{.71}\end{array}$

Hence, bid price is $192.71.