lecture 3 4 - time vaue of money.pptx
TRANSCRIPT
![Page 1: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/1.jpg)
How to Calculate Present Values
![Page 2: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/2.jpg)
Present Value of a single CF
• The present value of a single cash flow C expected n years from now is given by:-
• You can also use the PVIF table
𝐶(1+𝑟 )𝑛
![Page 3: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/3.jpg)
PVIF Table
![Page 4: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/4.jpg)
Future Value of a single CF
• The future value of a single cash flow C at a time n years from now is given by:-
C *
• You can also use the FVIF table
![Page 5: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/5.jpg)
FVIF Table
![Page 6: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/6.jpg)
Perpetuity
• Perpetuity is when the same cash flow C is paid every year for an infinite period
• C is the periodic cash-flow • r is the discount rate• PV is the present value of this cash flow
stream Example C=100, r=10% PV=1000
![Page 7: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/7.jpg)
Growing Perpetuity
• When the cash flows paid out every year grow at constant rate of growth g
• • C1 is the cash-flow at the end of year 1• r is the discount rate• g is the growth rate• PV is the present value of this cash flow streamExample C1=100, r=10%, g=5% PV=2000
![Page 8: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/8.jpg)
PV of Annuity
• When the same cash flow C is paid out for n years
• C is the periodic cash-flow• r is the discount rate• n is the number of periods for which the cash
flow will last• PV is the present value of this cash flow stream• If n is in months, this is the EMI (Equated
Monthly Installments) formula
![Page 9: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/9.jpg)
PVIFA Table• Alternatively, the PVIFA table can also be used
to calculate the PV of an annuity
![Page 10: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/10.jpg)
FVIFA Table• To calculate future value of an annuity, you
can use the FVIFA table
![Page 11: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/11.jpg)
2-14
• Factory costs 800,000• Produces 170,000 for 10 years• Find
– A. Its NPV if r = 14%• (86,739.66)
– B. Value of factory at the end of 5 years• (583,623.76)
![Page 12: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/12.jpg)
2-25
• If r= 8%, what amount needs to be set aside for – A perpetuity of 1 bn
• 12.5 bn– Perpetuity of 1 bn growing at 4%
• 25 bn– 1 bn for 20 yrs
• 9.82 bn– 1 bn spread evenly over the year for 20 yrs
• 10.20 bn
![Page 13: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/13.jpg)
2-34
• Couple retires in 3 yrs• Needs 15k per month, gets 9k from other
sources• Has a fund of 1,000,000• Fund grows at 3.5%• For how many years can withdrawals be
made?– 21.38 yrs
![Page 14: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/14.jpg)
2-39
• Pipeline generates 2 mn in year 1• Cash flows declining by 4% p.a. • If r= 10%, find:-
– PV of pipeline if cash flows continue forever• 14.29 mn
– PV of pipeline if cash flows last for 20 years• 13.35 mn• Can we use Value perpetuity minus TV in yr 21?
![Page 15: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/15.jpg)
Growing Annuity
• When the cash flows paid out every year grow at constant growth rate g and are paid for n years
• C1 is the cash-flow at the end of year 1• r is the discount rate• g is the growth rate• n is the number of periods for which the cash
flow will last• PV is the present value of this cash flow stream
![Page 16: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/16.jpg)
Cash flows starting at beginning of year
• All the present value formulae above assume that cash flows start at the end of year 1. If cash flows start at the beginning of year (first cash flow is at time 0), then the present values can be calculating by multiplying all the above PV formulae by an additional (1 + r) factor
• The rationale is that is cash flows start at time 0, then every cash flow is effectively being discounted for one less year than assumed in the formulae in the previous slides
![Page 17: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/17.jpg)
Calculating Future Values
• To calculate the future value of a stream of cash flows (the value of all cash flows at the end of year n instead of their value at time 0), all the present value formulae must be multiplied by the factor
![Page 18: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/18.jpg)
Compounding at higher frequencies
• To compound at higher frequencies, divide the rate by number of periods per year and multiply the time (in years) by number of periods per year
• For continuous compounding, use exp(rt) as the compounding factor
![Page 19: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/19.jpg)
Different rates of borrowing and lending
• We need to consider each cash flow individually• Example:-
– Rate of borrowing is 12%– Rate of lending is 10%– Calculate the value of the project at the end of its life
cycle
Year CF0 -551 602 803 -85
![Page 20: Lecture 3 4 - Time Vaue of Money.pptx](https://reader036.vdocuments.mx/reader036/viewer/2022062810/563db77f550346aa9a8b9e7a/html5/thumbnails/20.jpg)
Different rates of borrowing and lending
Year CFAmount Left after repayment in Yr 2
Amount invested at year 3
Amount left at the end of the project
0 -55
1 60 -1.60
2 80 78.21
3 -85 1.0288