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**Description**

ACCOUNTING & FINANCE I- module A for JAIIB

**Type**: ppt

**BASICS OF BUSINESS MATHEMATICS : **BASICS OF BUSINESS MATHEMATICS C S PASRICHA

**Slide 2 : **Time Value of Money

**Objectives : **Objectives What do we mean by Time value of money Present Value, Discounted Value, Annuity

**Time Value approach : **Time Value approach Time value of money is the concept of measuring the value of money over time. Why do we consider? Because value of money changes with time and it’s crucial to analyse our investment to be able to measure and solve for those changes.

**Time Value approach : **Time Value approach People prefer present consumption to future consumption – demand more in future to give up present consumption Inflation effect – Greater inflation and erosion of value Uncertainty of receiving cash flow in future – Greater the risk, greater the erosion in value Process by which future cash flows are adjusted to reflect these factors is called discounting and magnitude of these factors is called discount rate

**Discount Rate : **Discount Rate Rate at which present and future cash flows are traded off. It incorporates The preference for current consumption (greater preference ____ Higher discount rate). Expected inflation (higher inflation ____ higher discount rate). The uncertainty in the future cash flows (higher risk ____ higher discount rate). A higher discount rate will lead to a lower present value for future cash flows

**Rate of Interest : **Rate of Interest Nominal or market rate of interest rate = Real rate of interest + Expected rate of Inflation + Risk of premiums to compensate uncertainty

**Compounding concepts : **Compounding concepts Compounding effect increases with both rate and compounding period As length of holding period increases, small differences in rate can lead to large differences in future values Common rule of 72 – Doubling the value

**Time Value of Money : **Time Value of Money What is Time Value of Money? Future Value Present Value Future Value: Compounding: How would you do Compounding?

**Compounding : **Compounding Compounding Formula What if compounding is done on monthly basis?

**Effective Interest Rate : **Effective Interest Rate True rate of interest – Takes into account compounding effects of more frequent interest payments Effective Interest Rate = (1+Stated Annual Interest Rate/N) n -1 As compounding becomes frequent, effective rate increases and present value of future cash flow decreases

**Charting of Cashflow : **Charting of Cashflow For any financial proposition prepare a chart of cashflow: e.g. Timeline 01.01.08 Invested in Bonds (1,000) 30.06.08 Interest Received +50 31.12.08 Interest Received + 50 New Bond Purchased (1,020) Net ( 970) 30.06.08 Interest Received + 100 Sold Bond +2,050 Total +2,150

**Discount Rate : **Discount Rate Rate at which present and future cash flows are traded off Higher discount rate – lower the present value for future cash flows

**Discounting : **Discounting Present Value You have an option to receive Rs. 1,000/- either today or after one year. Which option you will select? Why? Decision will depend upon the present value of money; which can be calculated by a process called Discounting (opposite of Compounding) Interest Rate and Time of Receipt of money decide Present Value What is the present value of Rs. 1,000/- today and a year later? Let us find out Present Value?

**Discounting contd… : **Discounting contd … Formula to find Present Value of Future Cash Receipt Where PV = Present Value, P = Principal, i = Rate of Interest, n = Number of Years after which money is received Assuming Rate of Interest is 10%, value of Rs. 1,000/- to be received after 1 year will be, Whereas the value of money to be received today will be Rs. 1,000/- What if you were to choose between: Receive Rs. 1,000/- every year for 3 years, OR Receive Rs. 2,500/- today? (assume 10% annual interest rate)

**Discounting of a Series… : **Discounting of a Series … How discounting is done for a series of cashflow? e.g. Receive Rs. 1,000/- at the end of every year for 3 years OR Receive Rs. 2,500/- today Assume Rate of Interest @10% If cashflow was to occur every 6 months instead of 1 year, what impact it will have on Present Value?

**Periodic Discounting : **Periodic Discounting What if the receipts are over six months ’ interval ? Find Present Value of the money receipts Periodic Discounting Formula Receive Rs. 1,000/- at the end of every 6 months for 1-1/2 years OR Receive Rs. 2,600/- today Assume Rate of interest @10% Where, P = Principal, i = Rate of Interest, t = Times Payments made in a Year, n = n th Period (in this case it is half year)

**Periodic Discounting Formula : **Periodic Discounting Formula Expressed mathematically, the equation will look like: Generically expressed, the formula is: Here, N = 3

**Types of Cash flows : **Types of Cash flows Simple Cash flow Annuities Growing Annuities Perpetuities Growing Perpetuities

**Simple Cash flow : **Simple Cash flow Single Cash flow in a specified future time period Discounting: process by which a cash flow is expected to occur in the future is brought to its present value Compounding: Is the process by which a cash flow today is converted to its expected future value

**Annuities : **Annuities Constant cash flow occurring at regular intervals of time An annuity can occur at the end of each period, as in this time line, or at the beginning of each period.

**example : **example Outright Buy V/s Deferred Payment Choice of Rs. 4,00,000 upfront or pay 90000 for five years PV for 90,000 using earlier formula – 3,24,430 Therefore choice…. When the present values of your instalment payments exceed the cash down price it is better to pay cash down and acquire the asset.

**Perpetuity and Annuity : **Perpetuity and Annuity Perpetuity Present Value t => PVIF(r, ) = 1/r => APV = C/r Annuity Future Value

**Slide 24 : **Annuity present value interest factors Number of periods Interest rate 5% 10% 15% 20% 1 0.9524 0.9091 0.8696 0.8333 2 1.8594 1.7355 1.6257 1.5278 3 2.7232 2.4869 2.2832 2.1065 4 3.5460 3.1699 2.8550 2.5887 5 4.3295 3.7908 3.3522 2.9906

**Examples: Annuity Present Value : **Examples: Annuity Present Value Annuity Present Value Suppose you need 20,000 each year for the next three years to make your fees payments. Assume you need the first 20,000 in exactly one year. Suppose you can place your money in a savings account yielding 8% compounded annually. How much do you need to have in the account today ?

**Examples: Annuity Present Value (continued) : **Examples: Annuity Present Value (continued) Annuity Present Value - Solution Here we know the periodic cash flows are 20,000 each. Using the most basic approach: PV = 20,000/1.08 + 20,000/1.08 2 + 20,000/1.08 3 = 18,518.52 + 17,146.77 + 15,876.65 = 51,541.94 Here’s a shortcut method for solving the problem using the annuity present value factor : PV = 20,000 [____________]/__________ = 20,000 x 2.577097 = ________________

**Examples: Annuity Present Value (continued) : **Examples: Annuity Present Value (continued) Annuity Present Value - Solution Here we know the periodic cash flows are 20,000 each. Using the most basic approach: PV = 20,000/1.08 + 20,000/1.08 2 + 20,000/1.08 3 * = 18,518.52 + 17,146.77 + 15,876.65 = 51,541.94 Here’s a shortcut method for solving the problem using the annuity present value factor : PV = 20,000 [ 1 - 1/(1.08) 3 ]/ .08 = 20,000 2.577097 = 51,541.94

**Another problem : **Another problem Suppose we expect to receive 1000 at the end of each of the next 5 years. Our opportunity rate is 6%. What is the value today of this set of cash flows? PV = 1000 {1 - 1/(1.06) 5 }/.06 = 1000 {1 - .74726}/.06 = 1000 4.212364 = 4212.36 Now suppose the cash flow is 1000 per year forever . This is called a perpetuity . And the PV is easy to calculate: PV = C / r = 1000/.06 = 16,666.66… So, payments in years 6 thru have a total PV of 12,454.30!

**Finding C : **Finding C Example: Finding C Q. You want to buy a motorcycle. It costs 25,000. With a 10% down payment, the bank will loan you the rest at 12% per year (1% per month) for 60 months. What will your monthly payment be? A. You will borrow .90 25,000 = 22,500 . This is the amount today, so it’s the present value . The rate is 1% , and there are 60 periods: 22,500 = C { 1 - (1/(1.01) }/.01 = C {1 - .55045}/.01 = C 44.955 C = 22,500 /44.955 C = 500.50 per month

**Finding t : **Finding t Q. Suppose you owe 2000 on a Visa card, and the interest rate is 2% per month. If you make the minimum monthly payments of 50, how long will it take you to pay off the debt? (Assume you quit charging immediately!)

**Slide 31 : **A. A long time: 2000 = 50 {1 - 1/(1.02) t }/.02 .80 = 1 - 1/1.02 t 1.02 t = 5.0 t ln(1.02) = 5.0 t = ln(5.0)/ln(1.02) t = 81.3 months, or about 6.78 years

**Slide 32 : **Annuity future value interest factors Number of periods Interest rate 5% 10% 15% 20% 1 1.0000 1.0000 1.0000 1.0000 2 2.0500 2.1000 2.1500 2.2000 3 3.1525 3.3100 3.4725 3.6400 4 4.3101 4.6410 4.9934 5.3680 5 5.5256 6.1051 6.7424 7.4416

**Examples for future value of annuities : **Examples for future value of annuities Q. Suppose you deposit 2000 each year for the next three years into an account that pays 8%. How much will you have in 3 years? Important: You make the first deposit in exactly one year. A. Using the most basic formula for FV: FV = 2000 * 1.08__ + 2000 * 1.08__ + 2000 = 2332,80 + 2160 + 2000 = 6,492,80 Using the shortcut formula at the top of the page: FV = 2000 * {___________} / 0.08 = 2000 * 3.2464 = 6492,80

**Example contd… : **Example contd… Q. Suppose you deposit 2000 each year for the next three years into an account that pays 8%. How much will you have in 3 years? Important: You make the first deposit in exactly one year. A. Using the most basic formula for FV: FV = 2000 * 1.08__ + 2000 * 1.08__ + 2000 = 2332,80 + 2160 + 2000 = 6,492,80 Using the shortcut formula at the top of the page: FV = 2000 * {___________} / 0.08 = 2000 * 3.2464 = 6492,80

**Slide 35 : **Q. Suppose you deposit 2000 each year for the next three years into an account that pays 8%. How much will you have in 3 years? Important: You make the first deposit in exactly one year. A. Using the most basic formula for FV: FV = 2000 * 1.08 2 + 2000 * 1.08 1 + 2000 = 2332,80 + 2160 + 2000 = 6,492,80 Using the shortcut formula at the top of the page: FV = 2000 * { (1 + 0.08) 3 - 1 } / 0.08 = 2000 * 3.2464 = 6492,80

**Perpetuity : **Perpetuity A perpetuity is a constant cash flow paid (or received) at regular time intervals forever. Thus a lifetime pension can be considered as a perpetuity or rentals received from exploitation of land which is passed on from generation to generation. The present value of a perpetuity can be written as C/r

**Console Bond : **Console Bond A is a bond that has no maturity and pays a fixed coupon (rate of interest). Assume that you have a 6 per cent coupon console bond. The original face value = Rs 1000. The current value of this bond if the interest rate is 9 per cent is as follows. Current value of Console Bond = Rs 60/0.09 = Rs 667 The value of a Console bond will be equal to its face value only if the coupon rate is equal to the interest rate. In this case Rs 1000, i.e. 60/0.06

**Growing Annuity : **Growing Annuity A growing Annuity is a cash flow that is expected to grow at a constant rate forever PV = C [1/( r-g ) - (1/( r-g ))*((1+ g )/(1+ r )) t ], Although a growing annuity and a growing perpetuity share several features, the fact that a growing perpetuity lasts forever puts constraints on the growth rate. It has to be less than the discount rate for the formula to work.

**Slide 39 : **Suppose you have just won the first prize in a lottery. The lottery offers you two possibilities for receiving your prize. The first possibility is to receive a payment of 10,000 at the end of the year, and then, for the next 15 years this payment will be repeated, but it will grow at a rate of 5%. The interest rate is 12% during the entire period. The second possibility is to receive 1,00,000 right now. Which of the two possibilities would you take?

**Slide 40 : **C = 10,000 r = 0.12 g = 0.05 t = 16 PV = 10,000 [(1/0.07) - (1/0.07)*(1.05/1.12)16] = $91,989.41 < $100,000, therefore, you would prefer to be paid out right now.

**Slide 41 : **Assume the same situation as in Example I, but with the difference that you can now make a choice between receiving a payment of 10,000 at the end of year 1, which will then grow at 5% per year, and be paid out to you for the next 15 years. Or, you can receive 85,000 right now. What would you do?

**Slide 42 : **We know from Example I that the present value of the growing annuity is equal to 91,989.41. However, the annuity starts only at the end of year 1, and hence, we need to bring this value back one additional period before we can compare it to the 85,000 to received right now. Thus: PV = 91,989.41 / (1.12) = 82,133.40 < 85,000, so we still prefer to be paid out immediately.

**Growing Perpetuity : **Growing Perpetuity A growing perpetuity is the same as a regular perpetuity (C/r),but the cash flow is growing (or declining) each year. A perpetuity has no limit to the number of cash flows, it will go indefinitely. The growing perpetuity is in that way just the same as a growing annuity with an extremely large t.

**Slide 44 : **PV = C / ( r-g ), What would you be willing to pay (given that you could live forever, and hence could receive cash flows for a share in the ABC Co., that promises you to pay a cash dividend to you at the end of the year of 25, which will increase every year by 1%, forever. The interest rate is fixed at 4.75%.

**Slide 45 : **PV = 25 / (0.0475 - 0.01) = 666.67

**Capital Budgeting : **Capital Budgeting Every business has four basic decisions to make: Which projects to take? (Investment decisions) How to finance these projects? (Financing decisions) How much to return to investors? (Dividend decisions) How to manage working capital and its components? (Liquidity decisions)

**Net Present Value : **Net Present Value Net Present Value means the difference between the PV of Cash Inflows & Cash Outflows How do you compute NPV? Prepare Cashflow Chart Net off Inflow & Outflow for each period separately If Inflow > Outflow, positive cash If Inflow < Outflow, negative cash Find present values of Inflows & Outflows by applying Discount Factor (or Present Value Factor) NPV = (PV of Inflows) LESS (PV of Outflows); Result can be +ve OR -ve Continuing with our example of Bond Investment:

**NPV contd… : **NPV contd … If Cashflows are discounted at say 10%, the sum of PV is 25.05, a positive number What is IRR? Description Date Amount In / Out PV Outflow PV Inflow Invested in 10% Bonds 01-Jan-08 (1,000) Outflow (1,000.00) Interest received 30-Jun-08 50 Inflow 47.62 Interest received 31-Dec-08 50 Inflow 45.35 New Bond Purchased from Open Market 31-Dec-08 (1,020) Outflow (925.17) Interest received 30-Jun-08 100 Inflow 86.38 Sold Bond in Open Market 30-Jun-08 2,050 Inflow 1,770.87 Sum (1,925.17) 1,950.22 Net Present Value 25.05 How these values are arrived at?

**NPV : **NPV If... It means... Then... NPV > 0 the investment would add value to the firm the project may be accepted NPV < 0 the investment would subtract value from the firm the project should be rejected NPV = 0 the investment would neither gain nor lose value for the firm We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria, e.g.IRR etc.

**Internal Rate of Return (IRR) : **Internal Rate of Return (IRR) Definition: The Rate at which the NPV is Zero. It can also be termed as “ Effective Rate ” If we want to find out IRR of the bond investment cashflow:

**IRR Contd… : **IRR Contd … To prove that at IRR of 11.38% the NPV of Investment Cashflow is zero, see the formula & table:

**IRR contd… : **IRR contd… As an investment decision tool, the calculated IRR should not be used to rate mutually exclusive projects, but only to decide whether a single project is worth investing in. Since IRR does not consider cost of capital, it should not be used to compare projects of different duration

**BOND VALUATION : **BOND VALUATION

**Objectives : **Objectives Distinguish bonds coupon rate, current yield, yield to maturity Find the market price of a bond given its yield to maturity, find a bond’s yield given its price, and demonstrate why prices and yields may vary inversely Why bonds Interest rate risk Bond ratings and investors demand for appropriate interest rates

**Bond characteristics : **Bond characteristics Bond - evidence of debt issued by a body corporate or Govt. In India, Govt predominantly A bond represents a loan made by investors to the issuer. In return for his/her money, the investor receives a legaI claim on future cash flows of the borrower. The issuer promises to: Make regular coupon payments every period until the bond matures, and Pay the face/par/maturity value of the bond when it matures

**Elements of Bond : **Elements of Bond Bonds require coupon or interest payments determined as part of the contract Coupon payments represent interest on the bond Final interest payment and principal are paid at specific date of maturity face (par) value: amount paid to bondholder at maturity coupon payments: interest paid maturity (or term): the end of life time of a bond

**Bond Concepts : **Bond Concepts Issuer: company, state or country Coupon: fixed interest rate that issuer pays to lender (investor) Maturity date: date when borrower will pay the lenders (investor) principal back Bid price: price that someone is willing to pay the lenders Yield: indicates annual returnuntil the bond matures

**How do bonds work? : **How do bonds work? If a bond has five years to maturity, an Rs.80 annual coupon, and a Rs.1000 face value, its cash flows would look like this: Time 0 1 2 3 4 5 Coupons Rs.80 Rs.80 Rs.80 Rs.80 Rs.80 Face Value 1000 Market Price Rs.____ How much is this bond worth? It depends on the level of current market interest rates. If the going rate on bonds like this one is 10%, then this bond has a market value of Rs.924.18 . Why?

**Slide 59 : **Coupon payments Face value Maturity Annuity component Lump sum component

**Bond prices and Interest Rates : **Bond prices and Interest Rates Interest rate same as coupon rate Bond sells for face value Interest rate higher than coupon rate Bond sells at a discount Interest rate lower than coupon rate Bond sells at a premium

**Bond terminology : **Bond terminology Yield to Maturity Discount rate that makes present value of bond’s payments equal to its price Current Yield Annual coupon divided by the current market price of the bond Current yield = 80 / 924.18 = 8.66%

**Rate of return : **Rate of return Rate of return = Coupon income + price change ---------------------------------------- Investment e.g. you buy 6 % bond at 1010.77 and sell next year at 1020 Rate of return = 60+9.33/1010.77 = 6.86%

**Risks in Bonds : **Risks in Bonds Interest rate risk Short term v/s long term Default risk Default premium

**Variations in Corporate Bonds : **Variations in Corporate Bonds Zero coupon bonds Floating Rate bonds Convertible bonds Callable bonds

**Bond pricing : **Bond pricing The following statements about bond pricing are always true. Bond prices and market interest rates move in opposite directions. When a bond’s coupon rate is ( >=< ) the market’s required return, the bond’s market value will be ( >=< ) its par value. Given two bonds identical but for maturity, the price of the longer-term bond will change more (in percentage terms) than that of the shorter-term bond, for a given change in market interest rates. Given two bonds identical but for coupon, the price of the lower-coupon bond will change more (in percentage terms) than that of the higher-coupon bond, for a given change in market interest rates.

**Depreciation Accounting : **Depreciation Accounting Depreciation is a method of allocating the cost of a tangible asset over its useful life. Businesses depreciate long-term assets for both tax and accounting purposes. It is a decrease in an asset's value caused by unfavorable market conditions. a decrease in an asset's value, may be caused by a number of other factors as well such as unfavorable market conditions, etc. Machinery, equipment, currency are some examples of assets that are likely to depreciate over a specific period of time.

**Depreciation – Different Methods : **Depreciation – Different Methods Straight line method;(cost-residual value)/ estimated useful life Written Down Value method or declining balance method : %age is fixed. Accelerated Depreciation Sum of years’ digits method; Example, if an asset is to be depreciated over five years, add digits 5,4,3,2,1 .The total is 15.For the 1st year depreciation is 5/15,for 2nd year,4/15 , and so on

**Need for depreciation : **Need for depreciation To know correct profit Show correct financial position Make provision for replacement of assets

**Factors of depreciation : **Factors of depreciation Cost of asset Residual value Life of an asset AS-6 deals with Depreciation Accounting

**Quick Quiz : **Quick Quiz 1. Under what conditions will the coupon rate, current yield, and yield to maturity be the same? A bond’s coupon rate, current yield, and yield-to-maturity be the same if and only if the bond is selling at par. 2. What does it mean when someone says a bond is selling “at par”? At “a discount”? At “a premium”? A par bond is selling for its face value (typically 1000 for corporate bonds); the price of a discount bond is less than par, and the price of a premium bond is greater than par.

**Slide 71 : **If A invests Rs. 24 at 7 % interest rate for 5 years, total value at end of five years is 31.66 33.66 36.66 39.66

**Slide 72 : **If A invests Rs. 24 at 7 % interest rate for 5 years, total value at end of five years is 31.66 33.66 36.66 39.66

**Slide 73 : **What is the effective annual rate of 12% compounded semiannually? A) 11.24% B) 12.00% C) 12.36% D) 12.54%

**Slide 74 : **What is the effective annual rate of 12% compounded semiannually? A) 11.24% B) 12.00% C) 12.36% * D) 12.54%

**Slide 75 : **What is the effective annual rate of 12% compounded continuously? A) 11.27% B) 12.00% C) 12.68% D) 12.75%

**Slide 76 : **What is the effective annual rate of 12% compounded continuously? A) 11.27% B) 12.00% C) 12.68% D) 12.75% *

**Slide 77 : **In 3 years you are to receive 50,000. If the interest rate were to suddenly increase, the present value of that future amount to you would fall. rise. remain unchanged. cannot be determined without more information.

**Slide 78 : **In 3 years you are to receive 50,000. If the interest rate were to suddenly increase, the present value of that future amount to you would fall. rise.* remain unchanged. cannot be determined without more information.

**Slide 79 : **You are considering investing in a zero-coupon bond that sells for 2,500. At maturity in 16 years it will be redeemed for 10,000. What approximate annual rate of growth does this represent? 8 percent. 9 percent. 12 percent. 25 percent.

**Slide 80 : **You are considering investing in a zero-coupon bond that sells for 2,500. At maturity in 16 years it will be redeemed for 10,000. What approximate annual rate of growth does this represent? 8 percent. 9 percent.* 12 percent. 25 percent.

**Slide 81 : **For 1,000 you can purchase a 5-year ordinary annuity that will pay you a yearly payment of 263.80 for 5 years. The compound annual interest rate implied by this arrangement is closest to 8 percent. 9 percent. 10 percent. 11 percent.

**Slide 82 : **For 1,000 you can purchase a 5-year ordinary annuity that will pay you a yearly payment of 263.80 for 5 years. The compound annual interest rate implied by this arrangement is closest to 8 percent. 9 percent. 10 percent.* 11 percent. 1000 = 263.80 (PVIFA, x%, 5)

**Slide 83 : **The value of a 4 year 12 per cent bond with face value of Rs. 100 is coupon payments are made every half year anda prevailing interest rate is 10% is 96.46 106.46 116.46 86.46

**Slide 84 : **The value of a 4 year 12 per cent bond with face value of Rs. 100 is coupon payments are made every half year anda prevailing interest rate is 10% is 96.46 106.46* 116.46 86.46

**Slide 85 : **If the prevailing interest rate is greater than coupon rate of a bond then the Bond is traded at a premium Bond is traded at a discount Bond is available at zero premium Bond price does not matter

**Slide 86 : **If the prevailing interest rate is greater than coupon rate of a bond then the Bond is traded at a premium Bond is traded at a discount* Bond is available at zero premium Bond price does not matter

**Slide 87 : **Value of a bond depends on its yield. Following is appropriate when price of a bond goes up: Yield goes up Yield goes down Yield remains unchanged Yield and bond price go hand in hand

**Slide 88 : **Value of a bond depends on its yield. Following is appropriate when price of a bond goes up: Yield goes up Yield goes down* Yield remains unchanged Yield and bond price go hand in hand

**Slide 89 : **Consider a bond maturing in 3 years with face value of Rs. 100 and coupon rate 6 per cent. The price prevailing today at prevailing interest rate of 8 per cent is Rs. 96.43 Rs. 94.85 Rs. 98.15 Rs. 100.00

**Slide 90 : **Consider a bond maturing in 3 years with face value of Rs. 100 and coupon rate 6 per cent. The price prevailing today at prevailing interest rate of 8 per cent is Rs. 96.43 Rs. 94.85* Rs. 98.15 Rs. 100.00

**Thank You : **Thank You

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