Darren Dillard, majority stockholder and president of Dillard, Inc., is working with his top managers on future plans for the company. As the company’s managerial accountant, you’ve been asked to analyze the following situations and make recommendations to the management team.

Requirements

1. Division A of Dillard, Inc. has \(5,250,000 in assets. Its yearly fixed costs are \)557,000, and the variable costs of its product line are \(1.90 per unit. The division’s volume is currently 500,000 units. Competitors offer a similar product, at the same quality, to retailers for \)4.25 each. Dillard’s management team wants to earn a 12% return on investment on the division’s assets.

a. What is Division A’s target full product cost?

b. Given the division’s current costs, will Division A be able to achieve its target profit?

c. Assume Division A has identified ways to cut its variable costs to \(1.75 per unit. What is its new target fixed cost? Will this decrease in variable costs allow the division to achieve its target profit?

d. Division A is considering an aggressive advertising campaign strategy to differentiate its product from its competitors. The division does not expect volume to be affected, but it hopes to gain more control over pricing. If Division A has to spend \)120,000 next year to advertise and its variable costs continue to be \(1.75 per unit, what will its cost-plus price be? Do you think Division A will be able to sell its product at the cost-plus price? Why or why not?

2. The division manager of Division B received the following operating income data for the past year:

DIVISION B OF DILLARD, INC. Income Statement For the Year Ended December 31, 2018
	Product Line		Total
	T205	B179
Net sales revenue	\)310,000	\(360,000	\)670,000
Cost of goods sold:
Variable	31,000	44,000	75,000
Fixed	275,000	67,000	342,000
The total cost of goods sold	306,000	111,000	417,000
Gross profit	4,000	249,000	253,000
Selling and administrative expenses:
Variable	68,000	80,000	148,000
Fixed	47,000	27,000	74,000
Total selling and administrative expenses	115,000	107,000	222,000
Operating income (loss)	\((111,000)	\)142,000	\(31,000

The manager of the division is surprised that the T205 product line is not profitable. The division accountant estimates that dropping the T205 product line will decrease fixed cost of goods sold by \)75,000 and decrease fixed selling and administrative expenses by \(10,000.

a. Prepare a differential analysis to show whether Division B should drop the T205 product line.

b. What is your recommendation to the manager of Division B?

3. Division C also produces two product lines. Because the division can sell all of the product it can produce, Dillard is expanding the plant and needs to decide which product line to emphasize. To make this decision, the division accountant assembled the following data:

	Per unit
	K707	G582
Sales price	\)84	\(50
Variable cost	24	21
Contribution margin	\)60	\(29
Contribution margin ratio	71.4%	58.0%

After expansion, the factory will have a production capacity of 4,700 machine hours per month. The plant can manufacture either 40 units of K707s or 62 units of G582s per machine hour.

a. Identify the constraining factor for Division C.

b. Prepare an analysis to show which product line to emphasize.

4. Division D is considering two possible expansion plans. Plan A would expand a current product line at a cost of \)8,600,000. Expected annual net cash inflows are \(1,525,000, with zero residual value at the end of 10 years. Under Plan B, Division D would begin producing a new product at a cost of \)8,000,000. This plan is expected to generate net cash inflows of \(1,100,000 per year for 10 years, the estimated useful life of the product line. Estimated residual value for Plan B is \)980,000. Division D uses straight-line depreciation and requires an annual return of 10%.

a. Compute the payback, the ARR, the NPV, and the profitability index for both plans.

b. Compute the estimated IRR of Plan A.

c. Use Excel to verify the NPV calculations in Requirement 4(a) and the actual IRR for the two plans. How does the IRR of each plan compare with the company’s required rate of return?

d. Division D must rank the plans and make a recommendation to Dillard’s top management team for the best plan. Which expansion plan should Division D choose? Why?

Step by step solution

01

Definition of Payback Period

A capital budgeting metric that determines the time period in which the investment will give back the cash invested or the investment/cash recovery period is known as the payback period.

02

Division A

(a) Targeted full product cost:

Particular	Amount $
Revenue	$2,125,000
Less: Desired profit	(630,000)
Targeted full product cost	$1,495,000

(b) Target profit of division:

Particular	Amount $
Total variable cost	$950,000
Add: Fixed cost	557,000
Current full product cost	1,507,000

The business entity will not be able to achieve its targeted profit because the current full product cost is higher than the target full product cost.

(c) Targeted fixed cost:

Particular	Amount $
Targeted full product cost	$1,495,000
Less: variable cost	875,000
Targeted fixed cost	$620,000

The current fixed cost is $557,000 which is lower than the targeted fixed cost of $620,000. Therefore, the business entity will be able to achieve its targeted profit.

(d) Calculation of cost-plus price:

Particular	Amount $
Variable cost	$875,000
Add: Total fixed cost	677,000
Full product cost	1,552,000
Add: Desired profit	630,000
Cost-plus price	$2,182,000
Volume in units	500,000
Cost-plus price Per unit	$4.364

The business entity will not be able to sell its product at cost plus price because the same product is offered by another retailer at a lower cost.

03

Division B

(a) Differential analysis:

Particular	Including T205	Excluding T205
Net sales revenue	$670,000	$360,000
Cost of goods sold:
Variable	75,000	44,000
Fixed	342,000	267,000
The total cost of goods sold	417,000	311,000
Gross profit	253,000	49,000
Selling and administrative expenses:
Variable	148,000	80,000
Fixed	74,000	64,000
Total selling and administrative expenses	222,000	144,000
Operating income (loss)	$31,000	($95,000)

The business entity must not drop the product line T205.

(b) The manager must try to bring down the fixed cost incurred for product line T205 or try to increase the level of production. Increasing the level of production will generate a higher contribution margin that will be available to cover the fixed cost of the business entity.

04

Division C

1. The constraining factor for division C is machine hour. It can work up to 4,700 machine hours per month.
2. Product line to be emphasized:

Particular	K707	G582
Increase in production	188,000	291,400
Contribution margin per unit	$60	$29
Increase in contribution margin	$11,280,000	$8,450,600

The business entity must focus on the K707 product line because it will increase the contribution margin at a higher rate after expansion.

05

Division D

(a) Capital budgeting methods:

Calculation of payback period:

Plan	Initial investment	/	Expected net annual cash flow	=	Payback period
A	$8,600,000	/	$1,525,000	=	5.64 years
B	$8,000,000	/	$1,100,000	=	7.27 years

Calculation of ARR:

1. Plan A:

$\begin{array}{c}\mathrm{ARR}=\frac{\mathrm{Average}\mathrm{annual}\mathrm{operating}\mathrm{income}}{\mathrm{Average}\mathrm{amount}\mathrm{invested}}\times 100\\ =\frac{\mathrm{\$}1,372,000}{\frac{\mathrm{\$}8,600,000+\mathrm{\$}0}{2}}\times 100\\ =\frac{\mathrm{\$}665,000}{\mathrm{\$}4,300,000}\times 100\\ =15.46\mathrm{\%}\end{array}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	$15,250,000
Less: Total depreciation during the life of the asset $\left(\$8,600,000-\$0\right)$	8,600,000
Total operating income during the operating life	$6,650,000
Asset operating life in years	10
Average annual operating income $\left(\frac{\$6,650,000}{10}\right)$	$665,000

Server B:

$\begin{array}{c}\mathrm{ARR}=\frac{\mathrm{Average}\mathrm{annual}\mathrm{operating}\mathrm{income}}{\mathrm{Average}\mathrm{amount}\mathrm{invested}}\times 100\\ =\frac{\mathrm{\$}398,000}{\frac{\mathrm{\$}8,000,000+\mathrm{\$}980,000}{2}}\times 100\\ =\frac{\mathrm{\$}398,000}{\mathrm{\$}4,490,000}\times 100\\ =8.86\mathrm{\%}\end{array}$

Working note:

Particular	Amount $
Total net cash flows during the life of the project	$11,000,000
Less: Total depreciation during the life of the asset $\left(\$8,000,000-\$980,000\right)$	7,020,000
Total operating income during the operating life	3,980,000
Asset operating life in years	10
Average annual operating income $\left(\frac{\$3,980,000}{10}\right)$	$398,000

Calculation of net present value:

Plan A:

Time	Particular	Net cash inflow	Ordinary annuity PV factor	PV factor	Present value
1-10years	PV of annuity	$1,525,000	6.145 $\left(\frac{1-\frac{1}{{\left(1+0.10\right)}^{10}}}{0.10}\right)$	-	$9,371,125
10 years	Residual value		-		0
Total PV of net cash flow					$9,371,125
0	Initial investment				(8,600,000)
Net present value of the project					$771,125

Plan B:

Time	Particular	Net cash inflow	Ordinary annuity PV factor	PV factor	Present value
1-8years	PV of annuity	$1,100,000	6.145$\left(\frac{1-\frac{1}{{\left(1+0.10\right)}^{10}}}{0.10}\right)$	-	$6,759,500
8 years	Residual value	$980,000	-	0.3855 $\frac{1}{{\left(1+0.10\right)}^{10}}$	$377,790
Total PV of net cash flow					$7,137,290
0	Initial investment				($8,000,000)
Net present value of the project					($862,710)

Calculation of profitability index:

Plan A:

$\begin{array}{c}\mathrm{Profitability}\mathrm{index}=\frac{\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{net}\mathrm{cashflows}}{\mathrm{Initial}\mathrm{investment}}\\ =\frac{\mathrm{\$}9,371,125}{\mathrm{\$}8,600,000}\\ =1.09\end{array}$

Plan B:

$\begin{array}{c}\mathrm{Profitability}\mathrm{index}=\frac{\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{net}\mathrm{cash}\mathrm{flows}}{\mathrm{Initial}\mathrm{investment}}\\ =\frac{\mathrm{\$}7,137,290}{\mathrm{\$}8,000,000}\\ =0.89\end{array}$

b. Estimated IRR of plan A:

$\begin{array}{c}\mathrm{NPV}=\sum _{\mathrm{t}=0}^{\mathrm{T}}\frac{{\mathrm{C}}_{\mathrm{t}}}{{\left(1+\mathrm{IRR}\right)}^{\mathrm{t}}}\\ 0=\left(\begin{array}{l}\frac{-\mathrm{\$}8,600,000}{{\left(1+\mathrm{IRR}\right)}^0}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^1}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^2}+\\ \frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^3}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^4}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^5}+\\ \frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^7}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^6}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^7}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^8}+\\ \frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^9}+\frac{\mathrm{\$}1,525,000}{{\left(1+\mathrm{IRR}\right)}^{10}}\end{array}\right)\\ \mathrm{IRR}=12.047\mathrm{\%}\end{array}$

c. NPV calculation using Excel:

d. Division D should adopt plan A because it is having higher IRR and positive NPV.

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