Illustration 1
Four equal annual payments of 5,000 are made into a deposit account that pays 8 per cent interest per year. What is the future value of this annuity at the end of 4 years?
Illustration 2
If the interest rate is 10%, what are the doubling periods of an investment at this rate?
Illustration 3
Find the present value of 50,000 to be received at the end of four years at 12 per cent interest compounded quarterly.
Illustration 4
A bank promises to give you 10,000 after 3 years at the rate of 10% interest. How much should you deposit today?
Illustration 5
Find the present value of 10,000 receivable 6 years hence if the rate of interest is 10 per cent? Will your answer differ if number of years is 3 years?
Illustration 6
Calculate the present value of annuity of 5,000 received annually for four years, when discounting factor is 10%.
Illustration 7
Mr. Parekh has invested 50,000 on Xerox Machine on 1^{st} Jan 2012. He estimates net cash income from Xerox Machine in next 5 years as under.
Year | Estimated Inflows |
2012
2013 2014 2015 2016 |
12,000 15,000 18,000 25,000 30,000 |
At the end of fifth year, machine will be sold at scrap value of 5,000. In addition to investment, working capital is 10,000. Advice him whether his project is viable, considering interest rate of 10% p.a.
Illustration 8
An investment of 40,000 made on 01/04/10 provides inflows as follows:
Date | Alternative I | Alternative II |
01/04/11
01/04/12 01/04/13 01/04/14 |
20,000 10,000 10,000 10,000 |
10,000 20,000 10,000 10,000 |
Which alternative would you prefer if the investor’s expected return is 10% give reason(s) for your preference?
Illustration 9
The share of Ridhi Ltd. ( 10) was quoting at 102 on 01.04.2002 and the price rose to 132 on 01/04/2005. Dividends were received at 10% on 30^{th} March each year. Cost of funds was 10%. Is it a worthwhile investment considering the time value of money? (Present value factor at 10% were 0.909, 0.826 and 0.751).
Illustration 10
XYZ & Co. is considering investing in a project requiring a capital outlay of 2,00,000. Forecast for annual income after tax is as follows:
Year |
1 |
2 |
3 |
4 |
5 |
Profit after Tax () |
1,00,000 |
1,00,000 |
80,000 |
80,000 |
40,000 |
Depreciation is 20% on straight line basis |
Evaluate the project on the basis of Net Present Value taking 14% discounting factor and advise whether XYZ & Co. should invest in the project or not? The present value of Re. 1 at 14% discounting rate are 0.8772, 0.7695, 0.6750, 0.5921 and 0.5194.
Illustration 11
Miss Sonali is considering an investment opportunity which will give her cash inflows of 1,000, 1,500, 1,200, 1,100 and 400 respectively at the end of each of the next 5 years. The initial investment is 4,000. If the time preference rate is 10%, state whether the investment is profitable or not (present value factor at 10% are 0.9091, 0.8264, 0.7513, 0.6830 and 0.6209).
Illustration 12
A finance company has offered a scheme of investment where a person investing 40,000, presently is entitled to returns of 8,000, 9,000, 10,000, 11,000 and 12,000 in the next five years. The indicated rate of interest is 10% p.a. Advise whether the investment is profitable. (PVIF 10%, 1 = 0.9091, PVIF 10%, 2 = 0.8264, PVIF 10%, 3 = 0.7513, PVIF 10%, 4 = 0.6830 and PVIF 10%, 5 = 0.6209).
Illustration 13
Mukesh has invested 10,000 in bank certificate of deposit for 2 years at 8%. How much will he receive at maturity?
Illustration 14
Shashikant deposits 10,000 with the bank which pays 10% interest compounded annually for a period of 3 years. How much amount he will get on maturity?
Illustration 15
Assume that you have given a choice between incurring an immediate outlay of 10,000 and having to 2,310 a year for 5 years the discount rate 11%. What would be your choice? Will our answer change if 2,310 is to be paid at the beginning of each year for 5 years.
Illustration 16
Mr. Yogesh is planning to retire this year. His company can pay him a lump sum retirement payment of 2,00,000 or 25,000 lifetime annuity whichever he chooses. Mr. Yogesh is in good health and estimates to live for at least 20 years. If the interest rate is 12%, which alternative should he choose?
Illustration 17
Mittal enterprises purchases a machinery for 1,00,000 on 1^{st} January 2002. The profit expected from the machinery are as follows:
2002 – 7000
2003 – 9000
2004 – 19000
2005 – 23,000
2006 – 35,000
The depreciation on machinery is to be provided @10% p.a. WDV. At end of 2006, the machinery is sold at loss of 7,500. The rate of interest being 9%. Comment on Decision.
Illustration 18
Four equal annual payments of 5,000 are to be made into a deposit account that pays 8% per year. What is future value of this annuity at end of 4 years (FVIFA @ 8% for 4 years 4.5061)?
Illustration 19
A bank advertises that it will pay a lump sum of 45,750 at end of 8 years to the investor who is depositing annually 4,000 for 8 years. What is the interest rate bank is paying?
Illustration 20
A bank offered to lend you 1,00,000 if you sign a note to repay 1,61,050 at end of 5 years. What would be rate of interest?
Illustration 21
Krishnamurthy has inherited 1,000 a year for next 20 years. First payment being made in one years time. However he is need of money immediately and would like to sell his income to any buyer who would pay him the right price. Assume that the current market rate of interest is 10%.
(a) What should be the right price he should accept?
(b) How much of his income should he sell if he wants only 2,500 at present.
(c) If you are interested in buying the income but if you had only 5,000 to invest, what would be your proposal.
Illustration 22
Doubling period
If the interest rate is 10% what are the doubling periods of an investment at this rate?
Illustration 23
Umesh can save 2,00,000 a year for 5 years and 3,000 a year for 10 years. Find Future Value (FVIFA @10% for 5 years = 6.1051 and FVIFA @10% for 10 years =15.937).
Illustration 24
A is due to receive 10,000 at end of 5 years. Since A is need of money immediately, he wants to sell his interest to B. B wants return of 10% p.a. on his investment. How much he should pay to A?
Illustration 25:
If you invest 5,000 today at a compound interest of 9 per cent, what will be its future value after 75 years?
Illustration 26
If the interest rate is 12 per cent, what are the doubling periods as per the rule of 72 and the rule of 69 respectively?
Illustration 27
A borrower offers 16 per cent nominal rate of interest with quarterly compounding. What is the effective rate of interest?
Illustration 28
Fifteen annual payments of 5,000 are made into a deposit account that pays 14 per cent interest per year. What is the future value of this annuity at the end of 15 years?
Illustration 29
A finance company advertises that it will pay a lump sum of 44,650 at the end of five years to investors who deposit annually 6,000 for 5 years. What is the interest rate implicit in this offer?
Illustration 30:
What is the present value of 1,000,000 receivable 60 years from now, if the discount rate is 10 per cent?
Illustration 31
A 12 year payment annuity of 10,000 will begin 8 years hence. (The first payment occurs at the end of 8 years). What is the present value of this annuity if the discount rate is 14 per cent?Illustration 32
What is the present value of the following cash flow stream if the discount rate is 14 per cent?
Year 0 1 2 3 4 |
Cash flow 5,000 6,000 8,000 9,000 8,000 |
Illustration 33
Mahesh deposits 2,00,000 in a bank account which pays 10 per cent interest. How much can he withdraw annually for a period of 15 years?
Illustration 34:
You want to take a world tour which costs 10,00,000 – the cost is expected to remain unchanged in nominal terms. You are willing to save annually 80,000 to fulfill your desire. How long will you have to wait, if your savings earn a return of 14 per cent per annum?
Illustration 35
Shyam borrows 80,000 for a musical system at a monthly interest of 1.25 per cent. The loan is to be repaid in 12 equal monthly installments, payable at the end of each month. What is the monthly installment? Prepare the loan amortisation schedule.
Illustration 36
Find the present value of the following cash flow and also state whether the investment is worthwhile if the amount of cash outflow presently is 60,000.
Year |
Cash Flow |
Discounted Factor |
1 |
20,000 |
0.9091 |
2 |
16,000 |
0.8264 |
3 |
20,000 |
0.7513 |
4 |
30,000 |
0.6830 |
5 |
10,000 |
0.6209 |
Illustration 37
You are negotiating with the government the right to mine 1,00,000 tons of iron ore per year for 15 years. The current price per ton is 3,000 and it is expected to increase at the rate of 6 percent per year. What is the present value of the iron ore that you can mine if the discount rate is 16 percent?
Illustration 38
As a winner of a competition, you can choose one of the following prizes:
- 5,00,000 now
- 10,00,000 at the end of 6 years
- 60,000 a year forever
- 1,00,000 per year for 10 years
- 35,000 next year and rising thereafter by 5 percent per year forever.
If the interest rate is 10 percent, which prize has the highest present value.
Illustration 39
Kuber Investors has introduced a scheme of investment called as “SHRI LAMXMI”. As per the scheme you have to invest 50,000/- as the start of five year investment period and your returns at the end of each year for next five years will be 10,000/-, 11,000/-, 12,000/-, 13,000/- and 15,000/-. The indicated rate of interest is 10% and Present Value @ 10% for first five years are: 0.9091, 0.8264, 0.7513, 0.6830 and 0.6209 respectively.
You are required to compute present value of investment and advise regarding the profitability of the investment. (MU, BMS, Apr. 2011)
Illustration 40
XYZ Ltd. is planning to purchase a machinery Costing 2,80,000/- and Installation charges at 50,000/-. It expects to generate the yearly cash flow for first five years at 90,000/-, 85,000/-, 70,000/-, 60,000/- and 50,000/- respectively. If the cost of capital is 12% and discount factor @ 12% for first five years is at 0.8929, 0.7972, 0.7118, 0.6355 and 0.5674.
You are required to calculate the present value of the cash inflows and advice is it worth buying the machine? (MU, BMS, Oct. 2011)
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