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Using the time value of money Helen wants to take the next four years off work to travel around the world. She estimates her annual cash needs at $31,000 (if she needs more, she will work odd jobs). Helen believes she can invest her savings at 10% until she depletes her funds. Requirements

  1. How much money does Helen need now to fund her travels?
  2. After speaking with a number of banks, Helen learns she will only be able to invest her funds at 6%. How much does she need now to fund her travels?

Short Answer

Expert verified
  1. Present value of Amount Withdrawn = $98,265.66
  2. Present value of Amount Withdrawn = $107,418.48

Step by step solution

01

Meaning of Capital Investment

A sum of money utilized to help an enterprise accomplish its objectives or acquire long-term assets is alluded to as a capital investment.

02

Calculating money does Helen need now to fund her travels

The present value of the amount withdrawn in future years, assuming a 10% return on investment, is calculated as follows:

Statement showing present value @10%

Year

Withdrawal

PV @10%

Present value

1

$31,000

0.90909

$28,181.79

2

$31,000

0.82645

$25,619.95

3

$31,000

0.75131

$23,290.61

4

$31,000

0.68301

$21,173.31

Present value of Amount Withdrawn$98,265.66

The above calculations show that putting $98,265.66 into savings at a rate of 10% will cover Helen's annual cash outlay of $31,000 for four years of travel around the world.

03

Money needed by Helen to fund her travel.

The present value of the amount withdrawn in future years, assuming a 6% return on investment, is calculated as follows:

Statement showing present value @6%

Year

Withdrawal

PV @6%

Present value

1

$31,000

0.94340

$29,245.4

2

$31,000

0.89000

$27,590

3

$31,000

0.83962

$26,028.22

4

$31,000

0.79206

$24,553.86

Present value of Amount Withdrawn$107,417.48

The amount invested today that will withdraw in the future is calculated by computing the present values of the amount to be withdrawn in future years discounted at the savings rate of interest.

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Most popular questions from this chapter

Describe the capital budgeting process.

Using the payback method to make capital investment decisions

Refer to the Hunter Valley Snow Park Lodge expansion project in Short Exercise S26-4. Compute the payback for the expansion project. Round to one decimal place.

Darren Dillard, majority stockholder and president of Dillard, Inc., is working with his top managers on future plans for the company. As the companyโ€™s managerial accountant, youโ€™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 \(1.90 per unit. The divisionโ€™s volume is currently 500,000 units. Competitors offer a similar product, at the same quality, to retailers for \)4.25 each. Dillardโ€™s management team wants to earn a 12% return on investment on the divisionโ€™s assets.

a. What is Division Aโ€™s target full product cost?

b. Given the divisionโ€™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 LineTotal

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 companyโ€™s required rate of return?

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

What is the decision rule for IRR?

S26-6 Using the ARR method to make capital investment decisions Refer to the Hunter Valley Snow Park Lodge expansion project in Short Exercise S26-4. Calculate the ARR. Round to two decimal places.

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