Chapter 12, Problem 55C

1.

To determine

Construct a variable-costing income statement for the proposed plant and calculate the ratio if net income to sales. Also state the Person K is right on return on sales being lower than the company average.

Explanation of Solution

Income Statement:

The statement that shows revenue and expenses incurred over a period of time (usually one year) is called an income statement. It is used for external financial reporting as it helps the outsiders and investors in evaluating the firm’s financial health.

The following table represents the income statement of Company SRM:

Company SRM
Income Statement
For the proposed plant
Particulars	Amount ($)	Amount ($)
Sales revenue1		1,575,000
Less: Variable expenses2		1,227,800
Contribution margin		347,600
Less Fixed expenses:
Salaries	135,000
Insurance	75,000
Telephone	5,000
Depreciation	56,200
Utilities	25,000	296,200
Net income		51,000

Table (1)

Therefore, the net income from the proposed project is $51,000.

Use the following formula to calculate ratio of net income to sales:

$Ratioofnetincometosales=\frac{Netincome}{Sales}$

Substitute $51,000 for net income and $1,575,000 for sales in the above formula.

$\begin{array}{c}Ratioofnetincometosales=\frac{\$51,000}{\$1,575,000}\\ =0.0324\end{array}$

Therefore, the ratio of net income to sales is 0.0324 or 3.24%.

Person K is correct as the return on sales is relatively lower than the average of the company.

Note: Depreciation excludes the erroneously reported amount of $2,000 for the land.

Working Notes:

1.

Calculation of sales revenue:

$\begin{array}{c}\text{Sales revenue}=\text{Number of units sold}\times \text{Selling price per unit}\\ =35,000\text{ units}\times \$45\\ =\$1,575,000\end{array}$

2.

Calculation of variable cost:

$\begin{array}{c}\text{Variable cost}=\text{Number of units sold}\times \text{Variable cost per unit}\\ =35,000\text{ units}\times \$35.08\\ =\$1,227,800\end{array}$

2.

To determine

Find out payback period for the proposed plant. State that the estimation of Person K about payback period being more than 4 years is correct. State that the sale of the plant on its book value will affect the answer or not.

Explanation of Solution

Payback Period:

The time taken by an investment to recover its original value is known as payback period. It is calculated by dividing the original amount of investment by annual cash flow from the investment.

Use the following formula to calculate payback period:

$Paybackperiod=\frac{Originalinvestment}{Averageannualcashflow}$

Substitute $352,000 for original investment and $107,200³ for average annual investment in the above formula.

$\begin{array}{c}Paybackperiod=\frac{\$352,000}{\$107,200}\\ =3.28years\end{array}$

Therefore, the payback period for the proposed project is 3.28 years.

Person K’s estimation about the payback period is incorrect because payback period for the proposed project is less than 4 years.

Person K’s estimation will be correct about the payback if equipment is sold for its book value. If the book value of the investment has a opportunity cost that will be added to the original investment.

Working Note:

3.

Calculation of average annual cash flow:

$\begin{array}{c}\text{Average}\text{annual}cashflow=Netincome+Depreciation\\ =\$51,000+\$56,200\\ =\$107,200\end{array}$

3.

To determine

Find out the NPV and IRR for the proposed plant. State that the sale of the plant on its book value will affect the answer or not

Explanation of Solution

Net Present Value:

The remaining balance of the present value of a project’s inflows and outflows is known as net present value (NPV). It is a discounting model of capital investment decision. A project with a positive NPV increases the wealth of a firm whereas a project with a negative NPV decreases the wealth of a firm.

Internal Rate of Return:

An interest rate at which the present value of an investment’s cash inflows is equal to the present value cost of the investment is known as internal rate of return. The value of NPV is 0 in case of an internal rate of return.

Use the following formula to calculate NPV of the investment:

$NPV=Presentvalueofcashinflow\left(P\right)-Presentvalueofcashoutflow\left(I\right)$

Substitute $658,698⁴ for P and $352,000 for I in the above formula.

$\begin{array}{c}NPV=\$658,698-\$352,000\\ =\$306,698\end{array}$

Therefore, net present value of the investment is $306,698.

Use the following formula to calculate discount factor:

$Discountfactor=\frac{Investment}{Annualcashflow}$

Substitute $352,000 for investment and $107,200 for annual cash flow in the above formula.

$\begin{array}{c}Discountfactor=\frac{\$352,000}{\$107,200}\\ =3.28358\end{array}$

Therefore, discount factor is 3.28358.

The IRR is in between 25% and 30% for 10 years and discount factor of 3.28358.

Calculate NPV and IRR if furniture and equipment are sold on their book value:

Use the following formula to calculate NPV of the investment:

$NPV=Presentvalueofcashinflow\left(P\right)-Presentvalueofcashoutflow\left(I\right)$

Substitute $658,698⁴ for P and $582,000 for I in the above formula.

$\begin{array}{c}NPV=\$658,698-\$582,000\\ =\$76,698\end{array}$

Therefore, net present value of the investment is $76,698.

Use the following formula to calculate discount factor:

$Discountfactor=\frac{Investment}{Annualcashflow}$

Substitute $582,000 for investment and $107,200 for annual cash flow in the above formula.

$\begin{array}{c}Discountfactor=\frac{\$582,000}{\$107,200}\\ =5.42910\end{array}$

Therefore, discount factor is 3.28358.

The IRR is in between 12% and 14% for 10 years and discount factor of 5.42910.

Working Note:

4. Calculation of present value of future cash flow:

$\begin{array}{c}Presentvalue\text{}offuturecashflow=Futurevalue\times Discountfactor\\ =\$107,200\times 6.14457\\ =\$658,698\end{array}$

4.

To determine

Calculate the break-even cubic yards that must be sold. Calculate NPV and IRR with the help of break-even volume. State whether the investment is acceptable or not. Explain the reason of accepting an investment that promises earn only break-even.

Explanation of Solution

Break-Even Point:

The point or situation where the amount of total cost is equivalent to total revenue is known as the break-even point. It is the point where there is no loss or no profit.

Let break even volume be Z.

Use the following formula to calculate break-even volume:

$Price\times Break-evenvolume=\left(\begin{array}{l}\left(Unitvariable\cos t\times Break-evenvolume\right)\\ +\mathrm{Total}fixed\cos t\end{array}\right)$

Substitute $45 for price, Z for break-even volume, $35.08 for unit variable cost and $296,200 for total fixed cost in the above formula.

$\begin{array}{c}\$45\times Z=\left(\left(\$35.08\times Z\right)+\$296,200\right)\\ \$45Z=\$35.08Z+\$296,200\\ Z=\frac{\$296,200}{\$9.92}\\ =29,859cubicyards\end{array}$

Therefore, the break-even volume is 29,859 cubic yards.

Use the following formula to calculate NPV of the investment:

$NPV=Presentvalueofcashinflow\left(P\right)-Presentvalueofcashoutflow\left(I\right)$

Substitute $345,325⁵ for P and $352,000 for I in the above formula.

$\begin{array}{c}NPV=\$345,325-\$352,000\\ =\$\left(6,675\right)\end{array}$

Therefore, net present value of the investment is $(6,675).

Use the following formula to calculate discount factor:

$Discountfactor=\frac{Investment}{Annualcashflow}$

Substitute $352,000 for investment and $56,200 for annual cash flow in the above formula.

$\begin{array}{c}Discountfactor=\frac{\$352,000}{\$56,200}\\ =6.26335\end{array}$

Therefore, discount factor is 6.26335.

The IRR is in between 9% and 10% for 10 years and discount factor of 6.26335.

The investment should be rejected because it is not profitable. Its NPV is negative which will decrease the value of the firm.

Note: Refer to present value annuity table for discount factors which is given at the end of the chapter.

There is possibility to have a positive NPV at the break-even volume. Accounting income is defined on the basis of break-even rather than cash flow. The cash income must be understated by accounting income because noncash expenses are not subtracted from revenues. Zero cash inflows is not an outcome of no income.

Working Note:

5.

Calculation of present value of future cash flow:

$\begin{array}{c}Presentvalue\text{}offuturecashflow=Futurevalue\times Discountfactor\\ =\$56,200\times 6.14457\\ =\$345,325\end{array}$

5.

To determine

Calculate the volume of cement at which IRR equals firm’s cost of capital. Calculate the firm’s expected annual income using the calculated volume. Explain the answer.

Explanation of Solution

Let the volume be Y.

Use the following formula to calculate the volume of cement which earns an IRR equals to the cost of capital:

$\left(Price\times Volume\right)+\left(Unitvariable\cos t\times Volume\right)=\left(\begin{array}{l}Netincome\\ +\mathrm{Total}fixed\cos t\end{array}\right)$

Substitute $45 for price, Y for volume, $35.08 for unit variable cost, $1,086⁶ for net income and $296,200 for total fixed cost in the above formula.

$\begin{array}{c}\$45Y-\$35.08Y=\$1,086+\$296,200\\ \$9.92Y=\$297,286\\ Z=\frac{\$297,286}{\$9.92}\\ =29,968cubicyards\end{array}$

Therefore, the volume is 29,968 cubic yards.

The following table represents the income statement of Company SRM:

Company SRM
Income Statement
	Amount ($)
Sales revenue7	1,348,560
Less: Variable expenses8	1,051,277
Contribution margin	297,283
Less Fixed expenses:	296,200
Net income	1,083

Table (2)

Therefore, the net income from the proposed project is $1,083.

Working Note:

6.

Calculation of net income:

Calculate cash flow:

The discount factor for 10% cost of capital for 10 years is 6.14457 with reference to the present value annuity table given at the end of the chapter.

$\begin{array}{c}Cashflow=\frac{Investment}{Discountfactor}\\ =\frac{\$352,000}{6.14457}\\ =\$57,286\end{array}$

Calculate net income:

$\begin{array}{c}Netincome=Cashflow-Depreciation\\ =\$57,286-\$56,200\\ =\$1,086\end{array}$

7.

Calculation of sales revenue:

$\begin{array}{c}\text{Sales revenue}=\text{Number of units sold}\times \text{Selling price per unit}\\ =29,968\text{ units}\times \$45\\ =\$1,348,560\end{array}$

8.

Calculation of variable cost:

$\begin{array}{c}\text{Variable cost}=\text{Number of units sold}\times \text{Variable cost per unit}\\ =29,968\text{ units}\times \$35.08\\ =\$1,051,277\end{array}$