Problems on Time value of money January 22, 2015

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1 Investment Planning Problems on Time value of money January 22, 2015 Vandana Srivastava SENSEX closing value on Tuesday: closing value on Wednesday: opening value on Thursday: Top news of any financial newspaper: 1

2 Problems on Present Value (cash flow is same) -1 A firm has given a person, about to retire, the option of retiring with a lump sum amount of Rs. 50,000 or an annuity of Rs. 8,000 for 10 years. Which is worth more now, if the discount rate is (a) 8% and (b) 18%? EXCEL function: PV = PV(rate, nper, pmt) where: rateis in decimal, nperis number of periods and pmt is the cash flow per period (entered as negative value because we are discounting money every period) Cash flow per year (A) 8, , time (in years) (t) discount rate ( 8% 18% PV (annuity) 53, , PV C C C = + + L L (1 C + r ) n Problems on Present Value -2 A player signs a contract of Rs. 1,00,00,000 with a sports equipment company. The contract requires the payment should be given 20 lakhsper year for 5 years. Discount rate is 6%. PV of the contract = ( /.06) *(1-1/(1.06)^5) = 84,24, Cash flow per year (A) 20,00,000 20,00,000 20,00,000 20,00,000 20,00,000 20,00,000 time (in years) (t) discount rate ( 3% 4% 5% 6% 7% 8% PV (annuity) 91,59, ,03, ,58, ,24, ,00, ,85,

3 Problems on Present Value -3 Sticker price of a car is $15,000. The dealer offers two deals: a) Borrow $15,000 at an annual percentage of 3% for 6 months. b) Reduce the sticker price by $1,000 and borrow $14,000 at the financing rate 12% per annum for 36 months. Which is the better deal? solution: a) monthly rate = 3%/12 =.25% monthly payment = 15000*(.0025/(1-(1/(1.0025^36))) = $ a) monthly rate = 12%/12 = 1% monthly payment = 14000*(.01/(1-(1/(1.01^36))) = $ option 1 is better Problems on Present Value -4 You can deposit $4000 per year into an account that pays 12% interest. If you deposit such amounts for 15 years and start drawing money out of the account in equal annual instalments, how much could you draw out each year for 20 years? A = $4000, r =.12, n = 15 for the duration of deposit FV of annual deposits for 15 years = 4000*(1.12^15 1) /.12 = 1,49, This value becomes PV for the annuity to continue for 20 years. Now we have to find the cash flow of this annuity. A = *.12 / (1 1/ (1.12^20)) = 19,

4 Problems on Present Value -5 You are planning to retire in twenty years. You'll live ten years after retirement. You want to be able to draw out of your savings at the rate of $10,000 per year. How much would you have to pay in equal annual deposits until retirement to meet your objectives? Assume interest remains at 9%. A = $10000, r =.09, n = 10 for the duration of withdrawl PV of annual withdrawlfor 10 years = 10000*(1-1/(1.09^10)) /.09 = 64, This value becomes PV for the annuity that starts after retirement (20 years afte PV of this money = 64, / (1.09^20) = 11, value of annual deposits for 20 years will be: A = 11,451.08*0.09/(1-1/(1.09^20)) = 1, Problems on Perpetuity - 6 What is the value of a $100 perpetuity if interest is 7%? PV = 100/(.07) = $

5 Present Value of Uneven Cash Flow PV C1 C2 C3 = + + LL Cn n interest rate = 12% Period cash flow present value PV of all the cash flows 1, In this case, the PV of all the cash flows is calculated separately and then added in the end. Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows: NPV = PV of cash inflows PV of cash outflows (cash outflow is considered as negative cashflowand cash inflow is considered positive cashflow) used in capital budgeting to analyze the profitability of an investment or project if NPV >0, accept the project if NPV <0, reject the project Advantage: more reliable than other investment appraisal techniques which do not discount future cash flows Disadvantage: based on estimated future cash flows of the project and estimates may be far from actual results 5

6 Calculating NPV: Problem 1 An initial investment on plant and machinery of $8,320 thousand is expected to generate cash inflows of $3,411 thousand, $4,070 thousand, $5,824 thousand and $2,065 thousand at the end of first, second, third and fourth year respectively. At the end of the fourth year, the machinery will be sold for $900 thousand. Calculate the present value of the investment if the discount rate is 18%. initial investment = 8,320 interest rate = 18% Period cash flow present value 0-8, , , , , PV of the investment is $2568 PV of all the cash flows 2,568 NPV with Varying Discount rates: Problem 2 Analyze a four year project that requires investing Rs. 1 billion in software development today. The project will generate cash flows of Rs. 300 million in year1, 400 million in year2, 500 million in year3 and 600 million in year4. The discount rate for year1 is 10%, 11% in year2, 12% in year3 and 13% in year4. NPV of the project is Rs million. 6

7 Internal Rate of Return (IRR) discount rate that makes the NPV = 0 OR interest rate that makes the cash outflows spent on an investment equal the cash inflows that come into the company as a result of the investment can be thought as the rate of growth a project is expected to generate. in the previous example, IRR = 25% EXCEL function for calculating IRR: =irr(values,...) where valuesis the series of cash flows higher IRR is desirable for a project to be accepted NPV states the value of the project in monetary terms (like $, Rs. etc) but IRR states the worth of project in %. can be very useful to make a choice between different projects, a company is planning to undertake 7

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