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Financing Corporations Oct 8, 2013

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Four Types of Cash Flows 1. Lump Sum Type Time 2. Annuity Type Time 3. Bond Type Time 4. Irregular Payment Type Time

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Four Types of Cash Flows 1. Lump Sum Type Time

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Lump Sums – Single payment in the future Question 1 What is the value of $150,000 today if it is paid seven years from now and you want to make 10%? Answer = 150,000/(1.1 7 ) = 76,973.71

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Four Types of Cash Flows 1. Lump Sum Type Time 2. Annuity Type Time

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Question 2 Annuity Payments What is the value of a series of equal payments of $10, 000 per year for 5 years at 7% Answer 1 10,000.00 2 3 4 5 0.93458 0.87344 0.81630 0.76290 0.71299 9,345.79 8,734.39 8,162.98 7,628.95 7,129.86 4.10020 41,001.97 TOTAL Factor from Annuity Table 1/(1+r) n

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Four Types of Cash Flows 1. Lump Sum Type Time 2. Annuity Type Time 3. Bond Type Time

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Question 3 – Bond type Payments What is the value of a bond issued for $250,000 with coupons paying 5% in a market paying 8%. The bond expires in 7 years Answer 1. First, we calculate the coupons – 250,000 X 5% = 12,500 2.Next, we calculate the value of the coupons as though they are an annuity at market rate (7 years @ 8%) – 12,500 X 5.206 = 65,075 3.Then we treat the final payment of $250,000 as a lump sum payment 7 years from now at 8% 250,000/(1.08 7 ) = 145,872.60 4.Add the two numbers together, and that is the present value (PV) of the bond 65,075 + 145,872.60 = 210,947.60

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The figures representing the amount you would pay today are called the Present Value or PV. These tell you how much the investment is worth.

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Four Types of Cash Flows 1. Lump Sum Type Time 2. Annuity Type Time 3. Bond Type Time 4. Irregular Payment Type Time

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The PV minus the amount paid out is called the Net Present Value. If the Net Present Value of an investment at a given rate of return is zero, then we know that the return on that investment is exactly that rate of return. In the last case, the NPV was negative, so the return was less than 10% Net Present Value

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Question 4 – Irregular Payment Types The following investment has been proposed to you. And you want a return of at least 10% on the investment. What is the Present Value?

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Note – each payment must be handled as a lump sum payment, then the PVs must all be totalled

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Question 5 What is the Net Present Value of this investment? Answer 10,115.56 – 10,000 = 115.56. We can see that the return is greater than 10%, but by how much?

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Question 6 What is the IRR (Internal Rate of Return) of this investment? IRR is somewhere here

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What is duration??? The amount of time it takes to recuperate an “average” Dollar, Crown, Pound, Euro, etc. from a bond. It is helpful because two investments may have identical PV’s, but may turn out to have higher time risk.

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Question 7 – Duration Which is a preferable investment, all other things being equal: a)A ten year bond for $10,000 which pays nominally 10% or b)An investment of $11,342.02 which will pay $ 24,486.56 after 10 years when the market rate is 8%

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a) Let’s start with the cash flows Then we need the present values of the cash flows @ 8% Total the values Multiply the present values by the year of payment Take the sum and divide by the present value This is the duration DURATION

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We can conclude from this that even though these two investments may be sold to you at the same price, and will give the same return (8%), you will not get your money back as quickly with the second one, and the first one is therefore a more attractive investment, all other things being equal.

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