Future value the value of a cash flow that is moved

  • No School
  • AA 1
  • 66

This preview shows page 21 - 33 out of 66 pages.

Future Value The value of a cash flow that is moved forward in time is known as its future value When interest rate is 10% then, $1210 is the future value of $1000 two years from today $1100 is the future value of $1000 one year from today
Image of page 21

Subscribe to view the full document.

Future Value If we were interested in the future value of $1000 three years from today we would simply multiply one more period Future Value of a Cash Flow “ $C” “n” years from today, given interest “r” The future value is increasing in the interest rate “ r” and the number of periods “n” . FV 3 = $1000 ´ (1.10) ´ (1.10) ´ (1.10) FV n = $ C ´ (1 + r ) n
Image of page 22
Image of page 23

Subscribe to view the full document.

Discounting Cash Flows Suppose we anticipate having $1,000 in one year and we want to compute the value today of this payment. If the annual risk-free interest rate is 10% then we can calculate: ($1000 in one year )/(1.10) = $909.09 today Suppose we need the money now…does our preference for money today matter for this decision between $909.09 today or $1000 tomorrow? Suppose you anticipate receiving $1000 in two years. Given that the annual risk-free rate for two years is also 10% then we can calculate: PV = $1000 1.10 2 = 826.45
Image of page 24
Present Value If we were interested in the present value of $1000 received three years from today we would simply multiply one more period Present Value of a Cash Flow “ $C” Received “n” years from today, given interest “r” The present value is decreasing in the interest rate “r” and the number of periods “n” PV = $1000 1.10 3 = 751.31 PV = $ C (1 + r ) n
Image of page 25

Subscribe to view the full document.

Image of page 26
Savings problem If the interest rate on your savings account is 10%, then how much money will you have in your account three years from now? Suppose you plan to save $1000 annually in the next three years starting from today. Time line of deposits:
Image of page 27

Subscribe to view the full document.

Savings problem We are asked to find the future value of the stream of cash flows. The future value at time 3 of the payment of $1000 received at time 0: The future value at time 3 of the payment of $1000 received at time 1: The future value at time 3 of the payment of $1000 received at time 2: The future value of the stream of cash flows:
Image of page 28
Savings problem An alternative way to find the future value of the stream of cash flows is to follow the balance on our saving account. At time 0 we have …………. in our bank account. At time 1 we have ………… in our bank account. At time 2 we have …………. in our bank account. At time 3 we have accumulated …………….
Image of page 29

Subscribe to view the full document.

Savings problem Now suppose that you wish to invest all the money now instead of $1000 each year. What size investment is required in order to obtain the exact same amount of accumulated funds three years from now? You are asked to find the present value of the stream of cash flows. The present value of the stream of cash flows is ……………. 0 0 ( ) (1 ) = = = = + N N n n n n n C PV PV C r
Image of page 30
Stream of Cash Flows Valuation
Image of page 31

Subscribe to view the full document.

Present Value of Stream of Cash Flows The present value of a stream of “n” cash flows of arbitrary amounts is the sum of the present value of all cash flows. 0 0
Image of page 32
Image of page 33
  • Fall '19

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes