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Time Value of Money -2

Time Value of Money -2. Batch 2013-16 2 nd Semester MMM/MFM SIMSR. Present Value of a Single Flow. Recall what is DISCOUNTING……….

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Time Value of Money -2

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  1. Time Value of Money -2 Batch 2013-16 2nd Semester MMM/MFM SIMSR

  2. Present Value of a Single Flow Recall what is DISCOUNTING……….. Using this approach, we can determine the present value of a future cash flow or a stream of future cash flows. The present value approach is commonly followed approach for evaluating the financial viability of projects.

  3. Example of Present Value If we invest Rs. 1,000 today at 10 % rate of interest for a period of 5 yrs, we know that we will get Rs.1,000*FVIF(10,5) = Rs.1,000*1.611 = Rs.1,611 at the end of 5 yrs. The sum of Rs. 1,611 is called the accumulation of Rs.1000 for the given values of ‘k’ and ‘n’. Conversely, the sum of Rs.1,000 invested today to get Rs.1,611 at the end of 5 yrs is called the present value of Rs.1,611 for the given values of ‘k’ and ‘n’. It therefore follows that to determine the present value of a future sum we have to divide the future sum by FVIF value corresponding to the given values.

  4. Example of Present Value The PV of Rs.1611 will be: 1611/ FVIF(10,5) = 1611/1.611 =Rs.1000/- In general the present Value(PV) of a sum (FVn) receivable after n yrs at a rate of interest (k) is given by the expression: PV = FVn / FVIF(k,n) = FVn/ (I+k)^n The inverse of FVIF(k,n) is defined as PVIF(k,n). therefore the above equation can be written as: PV = FVn * PVIF(k,n)

  5. Brain Gym The cash certificate of Andhra Bank is a term deposit scheme under reinvestment plan. Interest on deposit money earns interest as it is reinvested at quarterly rests. These deposits suit depositors from lower and middle income groups, since the small odd sums invested grow into large amts over a period of time. Given an interest rate of 12% p.a. on a certificate having a value of Rs. 100 after 1 year, calculate the issue price of the cash certificate. Ans) Rs.88.85

  6. Brain Gym Pragati cash certificate scheme of Syndicate Bank is an ideal scheme for all classes of people under different income groups. A small odd sum can be invested for a period ranging from 1 to 10 yrs. The certificates are issued in convenient denominations of Rs.25, Rs.100, Rs.1,000 and Rs.1,00,000. The rates of interest is 12% p.a. compounded quarterly.Calculate the issue price of a certificate of Rs.1,00,000 to be received after 10 yrs. Ans) Rs.30,658

  7. Present Value of Multiple Flows Suppose a project involves an initial investment of Rs.10 lakh and generates net inflows as follows: End of Yr 1 Rs.2 lakhs 2 Rs.4 lakhs 3 Rs.6 lakhs What is the present Value of the future cash inflows? (Hint: Relevant Rate of interest is given as 12%) Indulge in a bit of brain gym now……………..

  8. Present Value of Multiple Flows

  9. Present Value of Multiple Flows A project is said to be financially viable if the present value of the cash inflows exceeds the present value of the cash outflow. In this case, the project is not financially viable because the present value of the net cash inflows (Rs.9.25 lakhs) is less than the initial investment of Rs.10 lakh. The difference of –Rs75 000 is called the net present value.

  10. Present Value of an Annuity The present value of an annuity ‘A’ receivable at the end of every year for a period of n years at a rate of interest k is equal to: PVA(n) = A + A + A +…………..A (1+k) (1+k)^2 (1+k)^3 (1+k)^n Which reduces to PVA(n )= A [(1+k)^(n) –1] k(1+k)^n

  11. Present Value of an Annuity The expression [(1+k)^(n) –1] k(1+k)^n is called the PVIFA and it represents the present value of a regular annuity of Re. 1 for the given values of k and n.

  12. Brain Gym The Swarna Kalash Yojana at rural and semi-urban branches of SBI is a scheme open to all individuals/firms. A lump sum deposit is remitted and the principal is received with interest at the rate of 12% p.a. in 12 or 24 monthly installments. The interest is compounded at quarterly intervals. Calculate the amount of initial deposit to receive a monthly installment of Rs. 100 for 12 months

  13. Solution to Brain Gym Firstly, the effective rate of interest p.a. has to be calculated r= [1+k/m]^(m) –1 = [1+0.12/4]^(4) –1 = 12.55% Effective monthly rate=.1255/12 = 0.01046

  14. Solution to Brain Gym The initial deposit can now be calculated as below: PVA(n) =A[(1+k)^(n) –1] k(1+k)^n =100[(1+ 0.01046)^(12) –1] .01046 (1+.01046)^12 = 100[.1329/.01185] = Rs.1121.5

  15. Home Exercise The annuity deposit scheme of SBI provides for fixed monthly income for suitable periods of the depositor’s choice. An initial deposit has to be made for a minimum period of 36 months. After the first month of the deposit, the depositor receives monthly installment depending on the number of months he has chosen as annuity period. The rate of interest is 11% p.a. which is compounded at quarterly intervals. If an initial deposit of Rs.4,549 is made for an annuity period of 60 months, calculate the monthly annuity.

  16. Capital Recovery Factor(inverse of PVIFA factor) Often such questions rise in our minds….. “What should be the amount that must be paid annually to liquidate a loan over a specified period at a given rate of interest?” “ How much can be withdrawn periodically for a certain length of time, if a given amount is invested today?” The application of the capital recovery factor helps in answering such questions

  17. Capital Recovery Factor (inverse of PVIFA factor) Manipulating the relationship between PVAn, A ,k & n we get an equation: A = PVAn[k(1+k)^n] [(1+k)^(n) –1] [k(1+k)^n] / [(1+k)^(n) –1], this is called as the capital recovery fund. Which is nothing but the inverse or the reciprocal of the PVIFA factor

  18. Application of Capital Recovery Factor A loan of Rs.1,00,000 is to be repaid in five equal annual installments. If the loan carries a rate of interest of 14% p.a. the amount of each installment can be calculated as below: If R is defined as the equated annual installment, we are given that R*PVIFA(14%,5) = Rs.1,00,000

  19. Application of Capital Recovery Factor Therefore R= Rs.1,00,000 PVIFA(14%,5) = Rs.1,00,000 3,433 = Rs.29,129 In this example, the amount of Rs.29,129 represents the sum of the principal and interest components. To get an idea of the break up of each installment between the principal and interest components, the loan repayment schedule is given as:

  20. Application of Capital Recovery Factor ..\FM text\cap rec factor.xls

  21. Application of Capital Recovery Factor The interest content of each installment is obtained by multiplying interest rate with the loan outstanding at the end of the immediately preceding year. As it can be observed from this schedule the interest component declines over a period of time whereas the capital component increases. The loan outstanding at the end of the penultimate year must be equal to the capital content of the last installment but in practice there will be a marginal difference on account of rounding off errors.

  22. Present Value of Perpetuity An annuity of an infinite duration is known as perpetuity. The present value of such perpetuity can be expressed as follows: P = A*PVIFA(k, ) Where P = present value of a perpetuity A = Constant annual payment PVIFA(k, ) = Present value interest factor for a perpetuity

  23. Present Value of Perpetuity Therefore the value of PVIFA(k, ) is   1 = 1 t=1 (1+k)^t k Hence , we can say that PV interest factor of a perpetuity is simply one divided by interest rate expressed in decimal form. Hence PV of a perpetuity is simply equal to the constant annual payment divided by the interest rate.

  24. Brain Gym • Modern Textiles Ltd., has to redeem debentures worth Rs. 1 crore by paying Rs. 30 lakh at the end of 8th year, Rs.30 lakh at the end of 9th year and Rs. 40lakh at the end of 10th year from now. How much amount should the firm deposit in a sinking fund account at the end of every year for 7 years in order to meet the aforementioned payments? (Assume that the interest rate on the deposit account is 8% per annum)

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