FIN 323-6 Discounted Cash Flow Valuation

How do you find the interest rate if you write a check for $115 in the future and take $100 now using the FV formula?

$115 = $100 + (1 + r)^1 1.15 = (1 + r) 0.15=r or 15%

The formula for the PV of an annuity due is?

( 1 + r ) x PV of an ordinary annuity

What is the formula for EAR?

(1 + quoted rate/m)^m -1 where m is the number of times compounded (usually noted as the number of payments per year).

What is the annuity present value factor?

(1 - present value factor) / r

9% APR is what percent interest each month?

.09/12=0.0075 or 0.75% monthly interest.

What is the present value factor?

1 / (1 + r) ^ t

PVIFA=

= (1 - PVIF ) / r or = (1 - ( 1 + r ) ^-n ) // r

PVIF=

= 1 / ( 1 + r)^t

You have decided to fund an account that will pay your descendants the inflation-adjusted equivalent of $100 per year forever. You assume inflation will equal 3% per year, and you expect the account to earn 7% per year. How much do you need to put in the account today to ensure your gift will continue forever?

= C / (r-g) = 100 / (.07 - .03) = 100/ .04 = $2,500

What is the formula for Growing Annuity PV?

=C x [ 1 - { ( 1 + g) ^t / (1 + r) } ] // ( r - g )

How do you calculate the PV of an ordinary annuity of $100 per year for 10 years at 10% interest per year in excel?

=PV(.10, 10, -100, 0)

A British consol is an example of what?

A perpetuity.

How do you find the APR for a pay day loan if you write a check for $115 dated 14 days in the future and take $100 now? The interest rate is 15%.

APR= .15 x 365/14 APR=3.9107 or 391.07%

You agree to pay back $1,100 in 4 weeks for a $1,000 payday loan. What is your annual percentage rate (APR) rounded to 2 decimal places with weekly compounding with 52 weeks in a year?

APR= 0.1 x 52/4 = 1.3 or 130%

What are you doing if you pay the interest each period plus some fixed amount of the principal of a loan OR if you pay principal and interest every period in a fixed payment.

Amortizing a loan

An annuity due is a series of payments that are made when?

At the beginning of each period.

What is the formula for Growing Perpetuity PV?

C / ( r - g )

What are some ways you can calculate future value for multiple cash flows besides the equations?

Compound the accumulated balance forward one year at a time or calculate the future value of each cash flow first and then add them up.

If an interest rate is 10% per week, what is the EAR? *Note that this is not an APR, it is a weekly rate (quoted rate/m). **There are 52 weeks in a year.

EAR= (1 + .1)^52 -1 =1.1^52 -1 = 142.0429 - 1 = 141.0429 or 14,104.29%

What is the formula for a future value of an annuity?

FV = C x [ ( 1 + r ) ^t - 1 /r ]

How do you find the future value of an annuity?

FV= C x { (1 + r )^t - 1 // r }

Find the FV of an annuity of $100 per year for 10 years at 10% per year.

FV= C x { (1 + r )^t - 1 // r } FV= 100 x { (1 + .1 )^10 - 1 // .1 } FV = 100 x 1.5937 / 0.1 FV = 100 x 15.937 FV = $1,593.74

What is the difference in the future value of $100 at 7% interest for 5 years if the interest is compounded semiannually rather than annually? What steps do you take to solve this problem?

First, find the amount if it is compounded annually. PV= 100; N=5; I/Y=7; CPT FV of $140.255. Then compute for semi annually: PV=100; N=5 x 2 = 10; I/Y= 7 / 2 = 3.5 CPT FV of $141.059 $141.059 - 140.255 = $0.804 or $0.80

A traditional (non-growing) annuity consists of a _____ stream of cash flows for a fixed period of time.

Level

What are some common real world examples of annuities?

Mortgages and pensions.

How do you use your financial calculator to find the present value of an ordinary annuity that pays $100 per year for 3 years if the interest rate is 10% per year?

PMT= 100 N=3 I/Y=10 CPT PV

Using a financial calculator, compute the PV of $100 per year for 30 years if the discount rate is 5%.

PMT= 100 N=30 I/Y=5 CPT PV which is $1,537.25

How do you use your financial calculator to find the future value of an annuity of $400 per year for 10 years at 5%?

PMT= 400 N=10 I/Y= 5 CPT FV which is $5,031.16

The present value interest factor for an annuity with an interest rate of 8% per year over 20 years is:

PVIF= 1 / ( 1 + r)^t 1 / ( 1 + .08)^20= 0.21458207 PVIFA= (1 - PVIF ) / r (1 - 0.2145) / .08 = 9.81815

When using the spreadsheet (Excel) function for finding the PV of an annuity, it's a good idea to enter the _____ as a negative value.

Payment

What is indicated by the phrase "an annuity of such amount per year?"

That this is a payment, not a FV or PV.

APR

The interest per period multiplied by the number of periods in the year.

What is the APR equal to?

The interest rate per period multiplied by the number of periods in a year.

How should the following items be valued? -Cash flows from a product whose sales are expected to remain constant forever. -Preferred Stock -A consol (bond that pays interest only and does not mature).

Using a perpetuity formula

You invest the following money at the end of each year at 4.5% interest for the next 5 years. What are the N values for every year if calculate the PV at the end of the 5 years? Year 1: $500 Year 2: $1,200 Year 3: $1,000 Year 4: $2,400 Year 5: $2,200

Year 1: N=4 Year 2: N=3 Year 3: N=2 Year 4: N=1 Year 5: N=0

A growing annuity has...

a finite number of growing cash flows.

A single cash flow is also known as what?

a lump sum

Payday loans allow you to...

borrow now and repay later.

The effective annual rate (EAR) takes into account the _______ of interest that occurs within a year.

compounding

If the interest rate is greater than zero, the value of an annuity due is always _____ than an ordinary annuity.

greater

For a positive stated annual interest & multiple compounding periods per year, the EAR is always _____ than the APR.

larger than

Most investments involve

multiple cash flows

Amortization is the process of paying off loans by regularly reducing the...

principal

The original loan amount is called the...

principal

What is true about a partial amortization loan?

-The monthly payments do not fully pay off the loan by the end of the loan period. -The borrower makes a large balloon payment at the end of the loan period. -The amortization period is longer than the loan period. -The monthly payment is based on a longer amortization period than the maturity of the loan.

What is the formula for the present value interest factor of an annuity?

1 - ( 1 / ( 1 + r ) ^t )) /r *1/x key on calc*

What is the monthly interest of an APR of 12% with monthly payments?

1%

You borrow $100 and agree to pay back your payday loan in 2 weeks for 10% interest over that 2-week period. What is your APR?

APR= 0.10 x 52/2 = 2.6 = 260% or =0.10 x 365/14 = 2.6071 = 260.71%

Another common term for the effective annual rate (EAR) is the ....?

APY

How do you find the Annuity Present Value?

C x Annuity Present Value Factor where C is the dollars per period.

When calculating the future value of multiple cash flows using a spreadsheet, you must...

Calculate the future value of each cash flow then add the compounded values together.

How do you find the EAR from the APR?

EAR = ( 1 + APR/m)^m -1 OR EAR= (1 + monthly interest)^m -1

How do you find the EAR for a pay day loan if you write a check for $115 dated 14 days in the future and take $100 now? The interest rate is 15%.

EAR = (1 + quoted rate/m)^m -1 EAR = (1 + .15)^ 365/14 -1 EAR = (1 + .15)^26.071 -1 EAR = 37.2366 or 3,723.66%

An APR of 9% with continuous compounding gives an EAR of what?

EAR = e^q -1 0.09 2nd e^x (ln) - 1

You agree to repay $1,200 in 2 weeks for a $1,000 payday loan. What is your EAR assuming that there are 52 weeks in a year?

EAR= ( 1 + q)^m -1 q= 200/1000 = .2 EAR= ( 1 + .2)^52/2 -1 = 113.4755 or 11,347.55%

FV=

PV + (1 + r)^n

If C=$100, g=10%, r=15%, and t=2 years, then what is the PV of this growing annuity?

PV = 100 x [1 - (1.1/1.15)^2 ] // .15 - .1 = 100 x 1.701323 = $170.13

What is the present value formula for a perpetuity?

PV = C / r where C is the constant and regularly timed cash flow and r is the interest rate.

What is the excel spreadsheet function for PV of an ordinary annuity?

PV( interest, time, payment,

What is the spreadsheet formula for calculating the present value of $100 at the end of each year for 2 years at 10% per year?

PV(0.1, 2, -100, 0).

You buy a CD for $1,352 and you receive $1,500 in 2 years. How do you use a financial calculator to find the interest rate?

PV= -1352 FV= 1500 N= 2 CPT I/Y which is 5.33%

If $100 earns a stated 10% rate compounded quarterly, how do you use a financial calculator to find the value of the $100 after one year?

PV= 100 I/Y= 10/4 N= 4 CPT FV= $110.38

How do you use a financial calculator to find the payment to principal and interest each month of a mortgage of $100,000 at 4.5% interest with monthly payments for 30 years?

PV= 100,000 I/Y = 4.5/12 = 0.375 N= 30 x 12 = 360 CPT PMT which is $506.69

$100 at the end of each year forever at 10% interest per year is worth how much today?

PV= 100/ 0.1 = $1000

You have $1,000 in an account that pays 10% per year. You want to give this money to charity by making 3 equal donations at the end of the next 3 years. How do you calculate each donation using a financial calculator?

PV= 1000 I/Y=10 N=3 CPT PMT which is $402.11

What is the present value of an annuity that makes payments of $100 per year for 10 years if the first payment is made immediately and the discount rate is 10% per year?

PV= C x { 1 - ( 1 + r )^-n } // r x ( 1 + r ) PV= 100 x { 1 - (1 + .1)^-10 } // .1 x (1 + .1) = 100 x { 1 - 1.1^-10 } / .1 x (1.1) = 100 x 6.7590238 = $675.90

You owe $1,200 on your credit card which charges, 1.5% per month. You pay $50/month starting at the end of this month. How do you use a financial calculator to find how many months will it take to pay it off?

PV=1200 PMT= -50 *if you forget the negative, your answer will be wrong I/Y= 1.5 CPT N which is almost 30 months.

To find the present value of an annuity of $100 per year for 5 years at 10% per year using the tables, look up the present value interest factor which is _____ and multiply that by _______.

PVIFA = (1 - ( 1 + r )^-n ) // r = (1 - (1 + .1 )^-5 ) // .1 = 3.7908 Multiply this by the $100 yearly annuity payments.

EAR

The interest stated as though it were compounded once per year.