Time Value of Money (TVM). The TVM concepts you will learn this week will be app

Question

Time Value of Money (TVM). The TVM concepts you will learn this week will be applied to most all future course concepts and analysis. For example, we will use the approaches below for security valuation – valuing stocks, bonds and options, capital budget analysis and business valuation – valuing uneven cash flows, and the concept of corporate valuation. 1) Present value of a single future sum How much will you pay today to receive a lump sum in the future? How much must I have saved today to cover a future expense (college, wedding, trip)? 2) Present value of an annuity How much will you pay today to receive an annuity in the future (retirement income, business income, sell a business for an annuity stream)? 3) Future value of a single deposit made today How much will this deposit be worth in x years? 4) Future value of an annuity If I save x amount each year, how much will I have accumulated in y years? 5) Uneven cash flow streams What is the value of the following stream of cash flows resulting from my investment? Please discuss each of the above concepts for TVM and illustrate your points with examples. If you are using financial calculators, tell us which buttons do you need to press to get the answers.

Explanation / Answer

1) Present value of a single future sum is today's value of a cash flow that is to be recived at some point of time in future .

It is the amount of money that must be invested today, at a given rate of return over a given period of time,this process is also known as discounting .

          Formula = Fv/(1+I/Y)^N

Example : the discount rate is 9% we need to calculate the pv of the future cash flow $100,000 that will be recived in 10 years ?

Solution) Input the given data is fv=$100,000 pmt=0 i/y =9% pv=? N= 10

                  Using financial calculator we put fv =$100,000 pmt =0 i/y =9% pv =? N = 10

                               Then press CPT at top of the calculator then pv button in tvm line

                           So pv = -$42241.0807 ignoring (–)sign pv is 42241.0807

2) Present value of an annuity is the collective pv of a stream of equal cash flow recived at the end of each coumpunding period over a stated no. of years .

Example pv of an annuity that pays $2,000 per year at the end of each of the next 13 years, where discount rate is 8% ?

sol) using financial calculator putting N= 13 I/Y =8 PMT =-$2,000 FV =0 PV=?

then press CPT then pv, so pv = $15,807.55

Note: before solving this don't forget to do clear tvm by pressing 2nd button and fv button so that no earlier record is retained .

and here you will $15,807.55 today to recive future annuties $ 2000 for the next upcoming years .

3)  Future value of a single deposit is the current deposit will grow over time it is also called compund value .

Formula = pv(1+I/Y)^N

using financial calculator

Example: calculate future value of a $3,000 investment at end of 10years it earns an annually coumponded rate of return of 8%

Sol) N=10 PV=$3,000 I/Y = 8% PMT=0 FV=?

Putting these values in financial calculator then pess CPT then FV

so the $3,000investment made today to recive future value of a single deposit is $6476.78 in 10years.

note : please put pv as (-) to caluclate positive fv otherwise calculator will show negative fv

4) Future value of an annuity is the fv of a stream of equal perodic cash flows. FVof annutiy measures how much you would have in future given a specified rate of return ,

Example : what is the FV of an annuity that pays $1,500 per year at the end of each of the next 15 years , given the investment is expected to earn 7% rate of return ?

Sol) N=15 I/Y =7% PMT= -$1500 PV =0 FV=?

Putting these value in financial calculator then press CPT button then FV

so the FV is $37,693.53

if i save $1,500 amount each year then i will accumalate $37,693.53 . in 15 years .

5) Uneven cash flow streams is that in which cash flows are different each year there can be one year with 0 cash flow and 2 years with negative cash flow the series of of uneven cash flow is nothing more than a stream of annual single sum cash flows. thus , to find to find the PV FV of this cash flow stream we need to sum the PV & FV of invdividual cash flows .

Example : uneven cash flows 1st yerar -1000, 2nd year-500, 3rd year 0, 4th year 4,000, 5thyear 3,500, 6thyear2,000

i) calculating FVs of uneven cash flow

FV1: PV=-1000;I/Y=10;N=5; CPT FV = FV1=-16,10.51

FV2: PV=-500;I/Y=10;N=4; CPT FV = FV2=-732.05

FV3: PV=0;I/Y=10;N=3; CPT FV = FV3=0.00

FV4: PV=4,000;I/Y=10;N=2; CPT FV = FV4=4,840.00

FV5: PV=3,500;I/Y=10;N=1; CPT FV = FV5=3,850.00

FV6: PV=2,000;I/Y=10;N=0; CPT FV = FV6=2,000.00

FV of cash flow stream = 8,347.44

ii) compute PV of cash flow stream described above

PV1: FV=-1,000;I/Y=10;N=1; CPT PV = PV1=-909.09

PV2: FV=-500;I/Y=10;N=2; CPT PV = PV2=-413.22

PV3: FV=0;I/Y=10;N=3; CPT PV = PV3=0

PV4: FV=4,000;I/Y=10;N=4; CPT PV = PV4=2,732.05

PV5: FV=3,500;I/Y=10;N=5; CPT PV = PV5=2173.22

PV6: FV=2000;I/Y=10;N=6; CPT PV = PV6=1,128.95

PV of cash flow stream = $4,711.91

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