/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 7 Present Values. Would you rather... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 7

Present Values. Would you rather receive \(\$ 1,000\) a year for 10 years or \(\$ 800\) a year for 15 years if a. the interest rate is 5 percent? b. the interest rate is 20 percent? c. Why do your answers to (a) and (b) differ?

Short Answer

Expert verified
a. 1000 dollars a year for 10 years. b. 800 dollars a year for 15 years. c. The difference is due to the impact of interest rate on discounting the future cash inflow.

Step by step solution

01

Calculating Present Value for 1,000 dollars per year for 10 years at an interest rate of 5%

Using the formula, the present value= \( \frac{1000}{(1+0.05)} + \frac{1000}{(1+0.05)^2 } + ...+ \frac{1000}{(1+0.05)^{10}}\)
02

Calculating Present Value for 800 dollars per year for 15 years at an interest rate of 5%

Using the similar formula, the present value= \( \frac{800}{(1+0.05)} + \frac{800}{(1+0.05)^2 } + ...+ \frac{800}{(1+0.05)^{15}}\)
03

Repeating step 1 and 2 for 20% interest rate

Similar steps are repeated for 20 percent interest rate.
04

Comparing the Present Values

Compare the present values calculated in steps 1 to 3 to answer the question.
05

Explaining difference in answers to (a) and (b)

The difference in answers is due to the difference in interest rates. Higher discount rates (interest) decrease the present value of future cash inflows, while lower discount rates increase them.

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 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Time Value of Money
The time value of money is a fundamental financial principle that suggests money available now is worth more than the same amount in the future. This concept is based on the idea that money can earn interest, making it worth more than its present value over time.

For example, receiving $1,000 today is more valuable than getting the same amount in a year because you could invest that money and earn a return during the year.
  • Money now can grow: Invest it and earn returns.
  • Inflation: Money could lose purchasing power in the future.
  • Risk: Future payments could be uncertain.
Understanding the time value of money helps in making informed decisions when comparing financial options that occur at different times. By calculating present values, you can assess which option is more financially beneficial.
Interest Rates
Interest rates are the percentage rates at which money can be borrowed or invested. They are crucial in evaluating the time value of money. High interest rates decrease the present value of future cash flows because you're applying a heavier discount on future earnings.

For example, if the interest rate is 5%, each $1,000 in the future is worth less today. If it's 20%, the discount is even greater, making future money significantly less valuable right now.
  • Interest is the cost of borrowing money or the reward for saving.
  • The higher the rate, the greater the opportunity to grow money.
  • Interest affects loans, investments, and savings alike.
The choice between different cash flow options often hinges on comparing their present values, which are directly influenced by the interest rate.
Discount Rate
The discount rate is the interest rate used to convert future cash flows into present value. It reflects the investor's opportunity cost, inflation expectations, and the risk of the cash flows not being realized.

In practice, the higher the discount rate, the lower the present value of future earnings since you're effectively saying future money is worth less today.
  • Discount rate considers risk and returns expectations.
  • Use it to evaluate bonds, investments, and financial decisions.
  • A critical tool in determining the attractiveness of various investments.
By applying a discount rate, investors and businesses can decide how much future income streams are worth in today's dollars, guiding decisions for accepting or rejecting projects.
Cash Flow Analysis
Cash flow analysis involves assessing the timing and amounts of cash inflows and outflows. It assists in analyzing the liquidity, viability, and profitability of a investment or business project.

The purpose is to determine how well a business or investment can generate and manage cash to meet financial obligations and opportunities.
  • Analyze when and how much cash comes in and goes out.
  • Helps in planning and budgeting.
  • Essential for financial health and decision making.
Conducting a cash flow analysis allows you to identify trends, potential issues, and future cash needs, supporting strategic planning and funding initiatives.

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

Real versus Nominal Annuitics. a. You plan to retire in 30 years and want to accumulate enough by then to provide yourself with \(\$ 30,000\) a year for 15 years. If the interest rate is 10 percent, how much must you accumulate by the time you retirc? b. How much must you save each year until retirement in order to finance your retirement consumption? c. Now you remember that the annual inflation rate is 4 percent. If a loaf of bread costs \(\$ 1.00\) today, what will it cost by the time you retire? d. You really want to consume \(\$ 30,000\) a year in real dollars during retirement and wish to save an equal real amount each year until then. What is the real amount of savings that you need to accumulate by the time you retire? c. Calculate the required preretirement real annual savings necessary to meet your consumption goals. Compare to your answer to (b). Why is there a difference? f. What is the nominal value of the amount you need to save during the first year? (Assume the savings are put aside at the end of cach year.) The thirticth year?

Annuity Valuc. The \(\$ 40\) million lottery payment that you just won actually pays \(\$ 2\) million per year for 20 years. If the discount rate is 10 percent, and the first payment comes in 1 year, what is the present value of the winnings? What if the first payment comes immediately?

Calculating Interest Rate. Lenny Loanshark charges "one point" per week (that is, 1 percent per weck) on his loans. What APR must he report to consumers? Assume exactly 52 weeks in a year. What is the effective annual rate?

Calculating Interest Rate. You borrow \(\$ 1,000\) from the bank and agree to repay the loan over the next year in 12 equal monthly payments of \(\$ 90 .\) However, the bank also charges you a loan-initiation fee of \(\$ 20,\) which is taken out of the initial proceeds of the loan. What is the effective annual interest rate on the loan taking account of the impact of the initiation fee?

Valuing Delayed Annuities. Suppose that you will receive annual payments of \(\$ 10,000\) for a period of 10 years. The first payment will be made 4 years from now. If the interest rate is 6 percent, what is the present valuc of this stream of payments?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation
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.