Question

Time Value of Money

Overview: In corporate finance, students need to be able to calculate present and future values of investments.

Purpose: The purpose for this project is to demonstrate an understanding of how to calculate present and future values.

Requirements: Review the examples then answer all of the questions below.

Example 1: What is the present value of the $800 to be received 10 years from now discounted back to the present at 10%.

Use your financial calculator to find the present value of -$308.43. Be sure that you have cleared all on your calculator and have it set up correctly. Please see the HB10B Calculator Podcast under Start Here in Content if you need to make sure you have done this. Then press the following keys where N is the time frame, I/YR is your interest rate, PV is your present value, PMT is your payment and FV is your future value.

N         =          10

I/YR          =       10

PV             =       –308.43

PMT          =       0

FV             =       800

Example 2: What is the accumulated sum of $500 a year for 10 years compounded annually at 5%?

Use your financial calculator to find the sum of $6,289.

            N              =       10

I/YR          =       5

PV             =       0

PMT          =       –500

FV             =       6,289

Example 3: What is the present value of a $2,500 a year annuity for 10 years discounted back to the present at 7%?

Use your financial calculator to find the present value of -$17,559.

             N              =       10

I/YR          =       7

PV             =       -17,559

PMT          =       2,500

FV             =       0

1. What is the present value of the following future amounts? Show your work for your financial calculator as shown in Example 1.

1. $300 to be received 5 years from now discounted back to the present at 5%.
2. $1,000 to be received 8 years from now discounted back to the present at 3%.
3. $1,000 to be received 8 years from now discounted back to the present at 20%.

2. What is the accumulated sum of each of the following streams of payments? Show your work for your financial calculator as shown in Example 2.

1. $100 a year for 5 years compounded annually at 10%.
2. $35 a year for 7 years compounded annually at 7%.
3. $25 a year for 3 years compounded annually at 2%.

3. What is the present value of the following annuities? Show your work for your financial calculator as shown in Example 3.

1. $70 a year for 3 years discounted back to the present at 3%.
2. $280 a year for 7 years discounted back to the present at 6%.
3. $500 a year for 10 years discounted back to the present at 10%.

Answer 1

1

a

Future value = present value*(1+ rate)^time

300 = Present value*(1+0.05)^5

Present value = 235.06

Using Calculator: press buttons "2ND"+"FV" then assign

FV =-300

I/Y =5

N =5

PMT = 0

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(0.05,5,,300,)

b

Future value = present value*(1+ rate)^time

1000 = Present value*(1+0.03)^8

Present value = 789.41

Using Calculator: press buttons "2ND"+"FV" then assign

FV =-1000

I/Y =3

N =8

PMT = 0

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(0.03,8,,1000,)

c

Future value = present value*(1+ rate)^time

1000 = Present value*(1+0.2)^8

Present value = 232.57

Using Calculator: press buttons "2ND"+"FV" then assign

FV =-1000

I/Y =20

N =8

PMT = 0

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(0.2,8,,1000,)

2a

FVOrdinary Annuity = C*(((1 + i/100)^n -1)/(i/100))

C = Cash flow per period

i = interest rate

n = number of payments

FV= 100*(((1+ 10/100)^5-1)/(10/100))

FV = 610.51

Using Calculator: press buttons "2ND"+"FV" then assign

PMT =-100

I/Y =10

N =5

PV = 0

CPT FV

Using Excel

=FV(rate,nper,pmt,pv,type)

=FV(10/(100),5,-100,,)

Please ask remaining parts seperately