Chapter 5 & 6 Financial Calculator and Examples

Chapter 5 & 6

Financial Calculator

and Examples

Konan Chan

Financial Management, Spring 2016

Five Factors in TVM



Present value: PV



Future value: FV



Discount rate: r



Payment: PMT



Number of periods: N

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Time Value of Money



N: number of compounding periods



I/Y: periodic rate (I/Y = APR/m)



PV: present value



PMT: periodic payment



FV: future value



N = m*n (m: number of interests paid per year; n: number of years)



It’s always to determine one of the five variables



If you can’t figure out one of the four variables, it must be the case that this one is zero

Annual &Non-annual Compound

Annual Non-annual

m =

1

4 (quarterly); 12 (monthly)

N =

n

4 * n ; 12 * n

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Texas Instruments BA-II Plus

N

= number of periods

I/Y = period interest rate (r)

PV = present value

PMT = payment

FV = future value

N

I/Y PV PMT

FV

Tips of Financial Calculator



Convert between Annuity and Annuity due

 END on the screen is for annuity, BGN is for annuity due  2nd,PMTcheck current mode (suppose current is END)  2nd,ENTERset BGN mode

 Press again2nd,ENTERwill covert back to END mode



Time value of Money (TVM)

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Tips of Financial Calculator



Set up # of digits after the decimal point

 Press 2nd,• (Format) the screen shows DEC=  If you want to have 4 digits, press4, ENTER



Clean the screen

 2nd, CPT (QUIT)



To avoid confusion, set P/Y=1 and don’t

change later

 2nd,I/Y (P/Y)  Press 1, ENTER

Example 1



You are willing to pay $15,625 to purchase a

perpetuity which will pay you $1,250 each

year, forever. If your required rate of return

does not change, how much would you be

willing to pay if this were a 20-year, annual

payment, ordinary annuity instead of a

perpetuity?

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Example 1 Solution



Find the interest rate first

 PV (perpetuity) = PMT / r  r = 8%



Find the PV of the annuity

 N = 20  I/Y = 8  PMT = 1,250  FV = 0  CPT PV = -12,273

Example 2



Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep you money in a bank time deposit that pays a nominal annual rate of 5 percent,

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Example 2 Solution



First clear all inputs:

2nd, FV(CLR TVM)



Find the PV of the annuity on the monthly

interest basis



For $500 option: (at the time of right now)

 N = 12 , I/Y = 5/12 = 0.4167, PMT = 500, FV = 0  CPT PV = -5,840.61



For $700 option: (at the end of 3rd month)

 N = 9, I/Y = 5/12 = 0.4167, PMT = 700, FV = 0  CPT PV = -6,170.73



Discount the value back to present (time 0)



N = 3, I/Y = 0.4167, PMT = 0, FV = 6,170.73



CPT PV = -6,094.23

( or PV = 6,170.73 / (1.004167)

3

_{= 6,094.23)}



Net worth change

= 5,840.61 - 6,094.23 = -253.62

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Example 3



You have just taken out a 30-year, $120,000

mortgage on your new home. This mortgage

is to be repaid in 360 equal end-of-month

installments. If each of the monthly

installment is $1,500, what is the effective

annual interest rate on this mortgage?

Example 3 Solution



Find the rate of return (APR)

 N = 360, PV = 120,000, PMT = -1,500, FV = 0  CPT I/Y = 1.235 (periodic rate)

 Nominal rate (APR) = periodic rate*12 = 14.82



Find EAR

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Example 4



You just graduated, and you plan to work for 10 years and then to leave for the Australian “Outback” bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when you start, into an

account which pays 8 percent compounding annually, what will your financial “stake” be when you leave for Australian 10 years from now?

Example 4 Solution



Find PV of uneven cash flows

 Enter cash flow worksheet:CF  CF0 = 5,000 Enter  (INS)

 C01 = 1,000; F01 = 5;  C02 = 2,000;  F02 = 5;  Go to NPV worksheet:NPV

 let I = 8, CPT NPV = 14,427



Find the FV of a single cash flow

 Discount the value back to present (time 0)  N = 10; I/Y = 8 ; PV = 14,427; PMT = 0

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

Suppose you borrow $4,500 at 6% and you

are going to make annual payments of

$806.1076. How long before you pay off the

loan?

 I/Y= , PV= , PMT= , FV=  CPT N =

Example 5

Example 6



Suppose you borrow $15,600 from your

parents to buy a smart phone. You agree to

pay $716.9842 per month for 24 months.

What is the monthly interest rate?

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Excel Functions



FV(Rate,Nper,Pmt,PV,

0/1

)



PV(Rate,Nper,Pmt,FV,

0/1

)



RATE(Nper,Pmt,PV,FV,

0/1

)



NPER(Rate,Pmt,PV,FV,

0/1

)



PMT(Rate,Nper,PV,FV,

0/1

)

 Inside parens: (RATE,NPER,PMT,PV,FV,0/1)

 “0/1”Ordinary annuity = 0 (default; no entry needed) Annuity Due = 1 (must be entered)

Konan Chan Financial Management