Discount Rate/Cash Flows/NPER

Rate formula

r = (FV/PV)^1/t-1

You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest?

* r = (1,200/1,000)^1/5 -1
* = .03714
* = 3.71%

\

Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest?

* r = (2/1)^1/6-1
* = .122462
* = 12.25%

NPER formula

t = ln(FV/PV) / ln(1+r)

You want to purchase a new care and you are willing to pay $20,000. If you can invest at 10% per year and you currently have $15,000, **how long** will it be before you have enough money to pay cash for the car?

* t = ln(20,000/15,000) / ln(1+ .10)
* = 3.018 years

Suppose you want to buy some new furniture for your family room. You currently have $500 and the furniture you want costs $600. If you can earn 6%, **how long** will you have to wait if you don’t add any additional money?

* t = ln(600/500) / ln(1.06)
* = 3.1289 years

You think you will be able to deposit $4,000 at the **end** of each of the next three years in a bank account paying 8% interest. You currently have $7,000 in the account. **How much will you have** in three years? (FV cash flows)

* Year 0: FV = 7,000 (1.08)^3 = 8,817.98
* Year 1: FV = 4,000 (1.08)^2 = 4,665.60
* Year 2: FV = 4,000 (1.08)^1 = 4,320
* Year 3: FV = 4,000 (1.08)^0 =4,000
* Added together = $**21,803.58**

Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, **how much will you have** in two years? (FV)

* FV = 500(1.09)^2
* FV = 600 (1.09)^1
* Added together = **$1248.05**

Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, **how much will you have** in two years? (FV)

*How much will you have in 5 years if you make no further deposits?*

* FV = 500 (1.09) ^5
* FV = 600(1.09) ^4
* Added together = **$1616.26**

You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year, and $800 at the end of the fourth year. You can earn 12% on very similar investments. **What is the most you should pay for this one?** (PV cash flows)

* PV: 200 / (1.12)^1 = 178.57
* PV: 400 / (1.12)^2 = 318.88
* PV: 600 / (1.12)^3 = 427.07
* PV: 800 / (1.12)^4 = 508.41
* PV Added together = **$1432.93**

**PV** Cash flow relationship with # of years

* **PARALLEL** with order of years
* Year 1 PV: x / (y)^ ==1== =
* Year 2 PV: x/ (y)^ ==2== =
* Year 3 PV: x/ (y)^ ==3== =

**FV** Cash flow relationship with # of years

* **INVERSE** with order of years
* year 1 FV: x / (y)^ ==3== =
* year 2 FV: x/ (y)^ ==2== =
* year 3 FV: x/ (y)^ ==1== =

You are considering an investment that will pay you $1,000 in one year $2,000 in two years and $3,000 in three years. If you want to earn 10% on your money, how much would you **be willing to pay**? (PV)

* PV = 1,000 / (1.1)^1 = 909.09
* PV = 2,000 / (1.1)^2 = 1652.89
* PV = 3,000 / (1.1)^3 = 2253.94
* Added together = **$4815.93**

You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you **be willing** to invest today if you desire an interest rate of 12%? (PV)

* Year 40: PV = 25,000 / (1.12)^40 = 268.87
* Year 41: PV = 25,000 / (1.12)^41 = 239.88
* Year 42: PV = 25,000/ (1.12)^42 = 214.18
* Year 43: PV = 25,000/ (1.12)^43 = 191.23
* Year 44: PV = 25,000/ (1.12)^44 = 170.74
* Added together = **$1,084.71**

Suppose you are looking at the following cash flows:

$100 YEAR 1. $200 YEARS 2 &3. $300 YEARS 4 & 5.

Discount rate of 7%

*What is the value of the cash flows at year 5? (FV)*

* Year 1 FV: 100(1.07)^4
* Year 2 FV: 200(1.07)^3
* Year 3 FV: 200 (1.07)^2
* Year 4 FV: 300(1.07)^1
* Year 5 FV: 300(1.07)^0
* Added together = $1226.07

Suppose you are looking at the following cash flows:

$100 YEAR 1. $200 YEARS 2 &3. $300 YEARS 4 & 5.

Discount rate of 7%

*What is the value of the cash flows today? (PV)*

* Year 1 PV: 100 / (1.07)^1
* Year 2 PV: 200 / (1.07)^2
* Year 3 PV: 200 / (1.07)^3
* Year 4 PV: 300 / (1.07)^4
* Year 5 PV: 300 / (1.07)^5
* Added together = **874.17**

\