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 Present value of Amount Withdrawn = $98,265.66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 Present value of Amount Withdrawn = $107,418.48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The present value of the amount withdrawn in future years, assuming a 10% return on investment, is calculated as follows: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Present value of Amount Withdrawn$98,265.66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The present value of the amount withdrawn in future years, assuming a 6% return on investment, is calculated as follows: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Present value of Amount Withdrawn$107,417.48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invested today that will withdraw in the future is calculated by computing the present values of the amount to be withdrawn in future years discounted at the savings rate of interest.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

How can spreadsheet software, such as Excel, help with sensitivity analysis?

Why are net present value and internal rate of return considered discounted cash flow methods?

What is the decision rule for payback?

You are planning for a very early retirement. You would like to retire at age 40 and have enough money saved to be able to withdraw \(215,000 per year for the next 40 years (based on family history, you think you will live to age 80). You plan to save by making 10 equal annual installments (from age 30 to age 40) into a fairly risky investment fund that you expect will earn 10% per year. You will leave the money in this fund until it is completely depleted when you are 80 years old.

Requirements

1. How much money must you accumulate by retirement to make your plan work? (Hint:Find the present value of the \)215,000 withdrawals.)

2. How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different?

Splash Nation is considering purchasing a water park in Atlanta, Georgia, for \(1,910,000. The new facility will generate annual net cash inflows of \)483,000 foreight years. Engineers estimate that the facility will remain useful for eight years andhave no residual value. The company uses straight-line depreciation, and its stockholdersdemand an annual return of 10% on investments of this nature.

Requirements

1. Compute the payback, the ARR, the NPV, the IRR, and the profitability index ofthis investment.

2. Recommend whether the company should invest in this project.

See all solutions

Recommended explanations on Business Studies Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free