1. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -1  Example: You deposit $1,200 in your bank account today; $1,400 one year later; and $1,000 two years from today. If your bank offers you an 8% interest rate on your account, how much money will you have in the account three years from today? LO3

2. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -2  Future value example 0 1 2 $1,000 8% $1,200 8% $1,400 3 8% ? ?? ??? LO3

3. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -3 0 1 2 $1,000 8% $1,200 8% $1,400 3 8% $1,000x(1+0.08) 1 =$1,080.00 $1,400x(1+0.08) 2 =$1,632.96 $1,200x(1+0.08) 3 =$1,511.65 FV = $4,224.61 LO3

4. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -4  Example: Your auto dealer gives you the choice to pay $15,500 cash now, or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money is 8%, which do you prefer? Option 1: $15,500 today Option 2: $8,000 today; $4,000 at the end of one year; and $4,000 at the end of two years. We can only compare these two options if both of them are converted for the same time period. Today will be an ideal one to do that. LO3

5. © 2012 McGrawHill Ryerson Ltd.Chapter 5-5 0 1 $4,000 8% 2 $4,000/(1+0.08) 1 =$3,703.70 $4,000 $4,000/(1+0.08) 2 =$3,429.36 PV = $15,133.06 $8,000 LO3  Present value of option # 2:

6. © 2012 McGrawHill Ryerson Ltd.Chapter 5-6  Compare the present value of the two options at present: ◦ Option 1: $15,500 ◦ Option 2: $15,133  Thus option 2 is a better choice for the buyer. That means, option 1 is a better payment for the seller. LO3

7. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -7  Annuities: Cash flows of equal amount every period for a limited number of periods ◦ Example: Loan payments for automobile, periodic earnings from lottery wins, etc.  Perpetuities: Cash flows of equal amount every period for an unlimited number of periods ◦ Example: Property tax payments, preferred stocks, etc. LO3

8. © 2012 McGrawHill Ryerson Ltd.Chapter 5-8  The PV of a perpetuity is calculated by dividing the level cash flow by the interest rate. PV of a perpetuity = C r 0 1 3 2……. ∞ CCCCC Note: This formula gives you the present value of a perpetuity starting one period from now PV LO3

9. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -9  Example: In order to create an endowment, which pays $100,000 per year, forever, how much money must be set aside today if the rate of interest is 10%? PV of perpetuity = $100,000 0.10 0 1 … 2……. ∞ $100,000 PV $100,000 = $1,000,000 LO3

10. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -10  Example contd.: If the first perpetuity payment will not be received until four years from today, how much money needs to be set aside today? PV at end of Year 3 = $100,000 0.10 1 2 4 3 5 ∞ 10% $100,000 PV $100,000 = $1,000,000 …. … PV today = $1,000,000 (1.10) 3 = $751,315 0 LO3

11. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -11  Present Value: The PV of a t period annuity with cash flow of C and discount rate r is given by: PV of t-period annuity = 0 1 3 2……. t CCCCCPV Note: This formula gives you the present value of an annuity starting one period from now. This is called a regular annuity. LO3

12. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -12  Present Value Interest Factor of Annuity:  In the present value formula for an annuity the term in the parentheses is called the Present Value Interest Factor of an annuity (PVIFA).  There is a table that can be used to find present values of $1 annuities for different rates and time periods, as shown in the next slide LO3

13. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -13 LO3

14. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -14  Example: You are purchasing a car. You are scheduled to make 3 annual installments of $4,000 per year, with the first payment one year from now. Given a rate of interest of 10%, what is the price you are paying for the car? 0 1 2 $4,000 10% $4,000 10% $4,000 3 10% PV of 3-period annuity Or, from the PVIFA table = $4,000 x 2.487 = $9,947.41 LO3

15. © 2012 McGrawHill Ryerson Ltd.Chapter 5-15  Future Value: The FV of a t period annuity with cash flow of C and discount rate r is given by: 0 1 3 2……. t FVCCCC FV of t-period annuity = C x [(1 + r) t – 1] r Note: This formula gives you the present value of an annuity starting one period from now. This is called a regular annuity. LO3

16. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -16  Future Value Interest Factor of Annuity: ◦ In the present value formula for an annuity, the term [(1 + r)t – 1] r is called the Future Value Interest Factor of an annuity (FVIFA). ◦ There is a table that can be used to find future values of $1 annuities for different rates and time periods, as shown in the next slide. LO3

17. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -17 LO3

18. © 2012 McGrawHill Ryerson Ltd.Chapter 5-18  Annuities Due: A level stream of payments starting immediately, is known as an annuity due. The difference between an annuity due and a regular annuity is shown in the following example. LO3

19. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -19 LO3

20. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -20  A growing perpetuity with a constant growth rate of ‘g’ has a PV that can be shown as: 0 1 3 2……. ∞ C(1+g) 3 C(1+g) 2 C(1+g)CPV PV of a growing perpetuity = C r - g LO3

21. © 2012 McGrawHill Ryerson Ltd.Chapter 5 -21  A growing annuity with a growth rate of ‘g’ has a PV that can be shown as: 0 1 3 2……. t C(1+g) 3 C(1+g) 2 C(1+g)CPV LO3