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TIME VALUE OF MONEY
- 1. TIME VALUE OF MONEY
- 2. CONCEPT β’ Time value of money is the economic principle that implies money received today has greater value than the same money received in future. β’ Time value of money describes the greater benefit of receiving money now rather than later. β’ time value of money underpins the concept of interest, and can be used to compare investments, such as loans, bonds, mortgages, leases and savings.
- 3. β’ Preferring to get certain sum of money now, than receiving the same amount at some point in future. Also known as TIME PREFERENCE OF MONEY.
- 4. Not certain of cash receipts. Prefer present consumption of goods due to :- β’ Urgency of goods. β’ Risk of not being in a position to consume these goods in future.(as money is the means) Increase the total cash inflow in future by making appropriate investments. REASONS FOR TIME VALUE OF MONEY RISK PREFERENCE FOR CONSUMPTION INVESTMENT OPPORTUNITIES
- 5. ADJUSTING CASH FLOWS FOR TIME VALUE OF MONEY DISCOUNTING Process of calculating present value of cashflows. COMPOUNDING Process of calculating future value of cashflows.
- 6. COMPOUNDING ο Techniques of determining the future value of an investment made in present. ο FUTURE VALUE :- The value of money at a future date with a given interest rate is called future value. COMPOUNDING TECHNIQUES FUTURE VALUE OF SINGLE CASH FLOW. FUTURE VALUE OF AN ANNUITY SINKING FUND
- 7. π = interest rate per period π= number of years F = Future value or compound value P = Present amount invested If the present amount βPβ is invested at βiβ rate of interest for βnβ years, then the future value "π π" (viz., principal plus interest) at the end of n years will be π π = π·(π + π) π SITUATION-1:- FUTURE VALUE OF SINGLE CASH FLOW
- 8. GIVEN :- π· = 1000; π = 5%; π = 10 years
- 9. GIVEN :- β’ π = 1000 β’ π = 5% β’ π = 10 years THEN :- πΉπ = π· Γ πͺπ½π(π,π) πΉππ = π· Γ πͺπ½π(ππ,π.ππ) πΉππ = 1000 Γ 1.629 πΉππ = 1629 β« πΉπ = π· Γ πͺπ½π(π,π) πΉπ = π(π + π) π (π + π) π = ππππππππ πππππ π πππππ πππ for a given interest rate, π and the time period, π. Compound value factor of a lumpsum of βΉ 1
- 10. οANNUITY :- A fixed payment/receipt each year for a specified number of years. SITUATION-2:- FUTURE VALUE OF AN ANNUITY Suppose βΉ 1 is deposited in a saving A/c at the end of each year for 4 years at a rate of interest of 6%. How much would this annuity accumulate at the end of fourth year? Period 0 1 2 3 Deposit at the end of year (βΉ) 1 1 1 1 Yields no interest Yields interest for 1 year Yields interest for 2 years Yields interest for 3 years Value after 4 years 1.000 1.060 1.124 1.191 4.375FUTURE SUM AFTER 4 YEARS
- 11. GIVEN:- π΄ = 100 π = 10% π = 3 years
- 12. π π = π¨ (π + π) πβπ π COMPOUND VALUE FACTOR OF AN ANNUITY (CVFA) for βnβ number of years at βiβ rate of interest. βΉ π π = π¨ Γ πͺπ½ππ¨ π,π GIVEN :- β’ π΄ = 100 β’ π = 10% β’ π = 3 years THEN :- πΉπ = π¨ Γ πͺπ½ππ¨(π,π.ππ) πΉπ = 1000 Γ 3.310 πΉπ = 331.00 Compound value factor of an annuity of a lumpsum of βΉ 1
- 13. οSINKING FUND :- A fund created out of fixed payment each period to accumulate to a future sum after a specified period. SITUATION-3 :- SINKING FUND Suppose MR. X wants to accumulate βΉ10,000 at the end of fourth year. How much amount should MR. X deposit at an interest rate of 6% such that it grows to βΉ10,000 at the end of 4th year. SINKING FUND REQUIRED DEPOSITS = βΉ 10,000 At the end of FOUR years Interest rate of 6% π π π π 1st year 2nd year 3rd year 4th year
- 14. Sinking fund (annuity) = Future value Compound value factor of an annuity of Re 1 As we know, π π= π¨ Γ πͺπ½ππ¨ π,π βΉ π¨ = π π Γ π πͺπ½ππ¨(π,π) βΉ π¨ = π π Γ π (π+π) πβπ ; since,πΆππΉπ΄(π,π) = (1+π) π β1 π Also, π πͺπ½ππ¨ π,π = SINKING FUND FACTOR (SFF) β΄ π¨ = π π Γ πΊππ π,π
- 15. GIVEN:- β’ πΉ3= 331 β’ π = 10% β’ π = 3 years β’ π΄ = ? Using, π¨ = π π Γ π πͺπ½ππ¨(π,π) π΄ = πΉ3 Γ π πͺπ½ππ¨(π,π.ππ) π΄ = 331 Γ 1 3.310 π΄ = 100 Compound value factor of an annuity of a lumpsum of βΉ 1
- 16. DISCOUNTING ο Techniques of determining the present value of a some of money to be received in future. ο PRESENT VALUE :- The worth of money today, that is receivable or payable in future is called the present value. ο Present value is determined by applying a discount rate to the given future value. DISCOUNTING TECHNIQUES PRESENT VALUE OF SINGLE CASH FLOW. PRESENT VALUE OF AN ANNUITY PRESENT VALUE OF UNEVEN CASHFLOWS PRESENT VALUE OF PERPETUITY
- 17. Let βIβ represent the interest rate per period, βnβ the numbe o periods, βFβ the Future Value of Cashflow and βPβ the present value of cash flow . We know, π π = π·(π + π) π SITUATION-1:- PRESENT VALUE OF SINGLE CASH FLOW π= interest rate per period π= number of years π= Future value or compound value π· = present value
- 18. Suppose:- β’ π= 9% β’ π= 20 years β’ π ππ= βΉ 50,000 β’ π· = ? βΉ π = πΉπ (1 + π) π βΉ π = πΉ20 (1 + π)20 βΉ π = 50,000 (1 + 0.09)20 βΉ π· = ππ,πππ (π.ππ)20 = 89,00 βΉ π· = π π Γ π (π + π) π π (π+π) π = discount factor or Present Value Factor
- 19. βΉ π· = π π Γ π (π + π) π Suppose:- β’ π= 10% β’ π= 10 years β’ π ππ= βΉ 50000 βΉ π· = π π Γ π·π½π(π,π) SOLUTION:- βΉ π· = π π Γ π·π½π(π,π) βΉ π· = πππππ Γ π. πππ βΉ π· = πππππ Present value factor of lumpsum of βΉ 1
- 20. Mr. X Has an investment opportunity of RECEIVING an annuity of βΉ A for n years at an interest rate of π%. The present value π can be calculate as follows:- Consider, π· = π¨ (π + π) + π¨ (π + π) π + π¨ (π + π) π +ββββββ + π¨ (π + π) π π· = π¨ π (π + π) + π (π + π) π + π (π + π) π +ββββββ + π (π + π) π π· = π¨ πβ π (π+π) π π = π¨ (π+π) πβπ π(π+π) π π· = π¨ π π β π π(π + π) π SITUATION-2 :- PRESENT VALUE OF ANNUITY
- 21. π· = π¨ π π β π π(π + π) π π π β π π(π+π) π is the Present Value Factor of an Annuity (PVFA). π· = π¨ Γ π·π½ππ¨ π,π Suppose:- β’ π = ππ% β’ π = 4 years β’ A = βΉ 5000 SOLUTION:- βΉ π = π Γ πππ π¨(π§,π’) βΉ π = ππππ Γ π. πππ βΉ π = πππππ Present value factor of an annuity of βΉ 1
- 22. SITUATION-3 :- PRESENT VALUE OF PERPETUITY β’ PERPETUITY :- Perpetuity is an annuity that occurs indefinitely. For e.g. :- In the case of irredeemable preference shares, the company is expected to pay preference dividend perpetually. π = π΄ 1 π β 1 π(1+π) π ; π = π΄ 1 π ; π = π΄ π {In perpetuity the time period is so large that time period βnβ approaches infinity, β and expression (π + π) π in the equation tends to become zero} Since, (π + π) π in the equation tends to become zero. β΄ ππππ πππ‘ π£πππ’π ππ ππππππ‘π’ππ‘π¦ = ππππππ‘π’ππ‘π¦ πΌππ‘ππππ π‘ π ππ‘π
- 23. β΄ ππππ πππ‘ π£πππ’π ππ ππππππ‘π’ππ‘π¦ = ππππππ‘π’ππ‘π¦ πΌππ‘ππππ π‘ π ππ‘π π = π΄ π EXAMPLE:- An investor expects a perpetual sum of βΉ 500 annually from his investment. What is the present value of this perpetuity if the interest rate is 10% GIVEN: π΄ = 500 ; π = 10% ; Using,π = π΄ π π = 500 0.10 = βΉ 5000
- 24. SITUATION-4 :- PRESENT VALUE OF UNEVEN CASH FLOWS Consider, π· = π¨ π (π + π) + π¨ π (π + π) π + π¨ π (π + π) π +ββββββ + π¨ π (π + π) π π· = π=π π π¨ π (π + π) π In the above equation, π indicates the number of years, extending from 1 year to π years.
- 25. π· = π¨ π π (π+π) + π¨ π π (π+π) π + π¨ π π (π+π) π +βββββββ + π¨ π π (π+π) π π· = π¨ π Γ π·π½π π,π + π¨ π Γ π·π½π π,π + π¨ π Γ π·π½π π,π + ------------+ π¨ π Γ π·π½π π,π Present value factor of lumpsum of βΉ 1
- 26. Prepared and presented by:- RIYA ARORA ROLL NO. - 501470001