Loading in 5 sec....

Compounding and Discounting -A Presentation to DVC Field TripPowerPoint Presentation

Compounding and Discounting -A Presentation to DVC Field Trip

- 97 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Compounding and Discounting -A Presentation to DVC Field Trip' - preston-raymond

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Compounding and Discounting are used to calculate:

- How much is one dollar now worth at t years later?
- How much is one dollar at t years later worth now?

Interest

- The time value of money
- In your bank account, $1 now (the present value) becomes $1.06 one year later (the future value)
- The interest is $0.06
- The interest rate is $0.06/$1 = 6% per year

- When do you pay interests?
- Student loans, Credit Cards, Mortgage

- When do you receive interests?
- Saving accounts

Compound Interest

- Present Value, V0
- Interest rate, r per year, calculate the interest once per year
- One year later
- V1=V0 (1+r)

- Two years later
- V2=V1 (1+r) = V0 (1+r)^2

- N years later
- VN = V0 (1+r)^N

Compounding at Various Intervals

- Present Value, V0; Nominal rate, r per year
- One and two years later
- If compounding quarterly
- V1 = V0 [ 1 + (r/4) ]^4
- V2 = V0 [ 1 + (r/4) ]^8

- If compounding monthly
- V1 = V0 [ 1 + (r/12) ]^12
- V2 = V0 [ 1 + (r/12) ]^24

- If compounding daily
- V1 = V0 [ 1 + (r/365) ]^365
- V2 = V0 [ 1 + (r/365) ]^730

- If compounding quarterly

Effective interest rate Example, the Credit Card APR (annual percentage rate) is a nominal rate and compounds monthly

- Nominal rate, r per year
- Compounding m times per year
- Effective rate, r’ per year
- 1 + r’ = [ 1 + (r / m) ] ^ m

- If the APR is 15%
- Then the effective APR is
- 1 + r’ = [ 1 + (15% / 12) ] ^ 12
- r’ = 16.1%

Continuous Compounding

- Nominal rate, r per year
- Compounding at infinite small time intervals
- Effective rate, r’ per year

Continuous Compounding

- Present Value, V0
- Nominal rate, r per year
- One year later
- V1 = V0 exp (r)

- Two year later
- V2 = V1 exp (r) = V0 exp (2r)

- t year later (t is a real number)
- Vt = V0 exp (rt)

Discounting Continuous Compounding

- How much is Vt dollar at t years later worth now?
- Nominal rate, r per year
- Discount factor, Dt, is the factor by which the value at t years later must be multiplied to obtain an equivalent present value
- Compounding m periods per year
- V0 = Vt [ 1 + (r / m) ] ^ (- m t) = Dt Vt
- Dt = [ 1 + (r / m) ] ^ (- m t)

- V0 = Vt exp (- r t) = Dt Vt
- Dt = exp (- r t)

Compounding and Discounting with variable interest rate

- Present Value, V0
- Variable interest rate, r(u) at time u
- Continuous compounding
- Value at time t, Vt

- Discount Factor

Application of Discounting

- Present Value of a future cash flow
- At time t, t=1,2, … N; Payment Vt; Discount factor Dt; then the PV is
- Could be used to compare two projects

Unit PV and levelization calculation

- At time t, t=1,2, … N; Payment Vt per unit; Volume at t, Ut unit; Discount factor Dt;
- The Unit PV is
- The levelized PV is

Either PV is validated, implicating different views of the value of project in the future

- A Project receives $1 million 1 year later, D1=0.75, and $3 million 2 years later, D2 = 0.5
- If we use the unit PV method, then V0U=(1X0.75+3X0.5)/2=1.125 million
- It means that the average unit present value is 1.125 million

- If we use the levelized PV method, then V0L=(1X0.75+3X0.5)/(0.75+0.5) = 1.8 million
- It is equivalent to receive a flat future cash flow
- V1 = 1.8 million
- V2 = 1.8 million

- If we use the unit PV method, then V0U=(1X0.75+3X0.5)/2=1.125 million

Download Presentation

Connecting to Server..