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Slides for BAII+ Calculator Training Videos 1 Slides for Lesson 1 There are no corresponding slides for Lesson 1, “Introduction to the Calculator” 2 Slides for Lesson 2 The following three (3) slides are used in Lesson 2, “Introduction to Time Value of Money” and are referred to in the video as the slides from Ch. 3, 6-8 3 Example: Investment Evaluation (referred to as slide 6) • Propose to buy an asset costing $350 million. Assume the asset will sell for $520 million at the end of 4 years. • You could invest your money elsewhere for 10%, where risk is similar to the risk of proposed asset. • Should you buy the asset? Why or why not? It is helpful to draw a timeline IMPORTANT FINANCE PRINCIPLE 0 1 2 3 4 Assets with similar risk should have -350* similar return. Thus the appropriate rate to use here is the 10% benchmark. 520 * By convention, cash OUTFLOWS are listed as negatives, while cash INFLOWS are listed as positives. 4 Example Solution (referred to as slide 7) 1. Calculate Present Value of the $520 520 PV . 4 35517 (1.10) 2. Calculate Future Value of the $350 FV 350 (110 . ) 512.44 4 3. Calculate Rate of Return on Asset 1/ t FV r 1 PV 520 r 350 1/4 Should Buy intrinsic value ($355.17) greater than cost ($350) Should Buy Future expected value of not buying ($512.44) less than value of buying ($520) Should Buy expected return of buying (10.4%) Greater than investing elsewhere (10%) 1 = 0.1040 = 10.40% 5 Example Solution – Calculator (referred to as slide 8) Clear TVM registers Set P/Y=1 Calculate Present Value N I/Y PV PMT FV 4 10 -355.17 0 520 Calculate Future Value N I/Y PV PMT FV 4 10 -350 0 512.435 Calculate Interest Rate N I/Y PV PMT FV 4 10.403 -350 0 520 6 Slides for Lesson 3 The following six (6) slides are used in Lesson 3, “TVM – Annuities and Periods other than Annual” and are referred to in the video as the slides from Ch. 3, 1719, 21, and 36 7 Example: Present Value of an Annuity (referred to as slide 17) • You need $25,000 a year for business school. – 1st $25,000 at the end of 12 months – 2nd $25,000 at the end of 24 months • You can earn 8% per year in an investment account. • How much money do you need today? 8 Example Solution – Annuity Formula (referred to as slide 18) 0 $? 1 $ 25,000 PMT PV ( Annuity ) r 2 $ 25,000 1 1 (1 r )t 25, 000 1 PV 1 44,581.62 2 0.08 (1.08) 9 Example Solution – Calculator and Excel (referred to as slide 19) On the calculator, input N, I/Y, PMT, and FV N 2 I/Y 8 PV -44581.62 PMT 25000 FV 0 In Excel, Use the PV Function 10 Example: Future Value of an Annuity (referred to as slide 21) • Suppose you plan to retire ten years from today. You plan to invest $2,000 a year at the end of each of the next ten years. You can earn 8% per year (compounded annually) on your money. How much will your investment be worth at the end of the tenth year? PMT t (1+r) - 1 FV(Annuity) = r 2,000 10 FV(Annuity ) = (1.08) - 1 28,973.13 0.08 11 Example Solution – Calculator and Excel (referred to as slide 21, continued) On calculator, set P/Y=1, set payments to END, input N, I/Y, PV, PMT and compute FV N I/Y PV 10 8 0 PMT FV -2,000 28,973.13 In Excel, use the FV function The zero indicates that the cash flows occur at the END of the year. If they were at the beginning, we would enter a 1 here. 12 Present Value Example (referred to as slide 36) • Suppose you need $400 to buy textbooks in 2 quarters. Current interest rates are 12% per year (compounded quarterly). How much money do you need to deposit today? (Remember that t and 4* 1 4 r must match) 0.12 EPR 1 1 0.03 – Can use quarters 4 FV 400 PV 377.04 t 2 (1 r ) (1.03) – Is there another way? What if we use 6-month periods? APR EPR = 1 + m my -1 0.12 EPR 1 4 4* 1 2 1 0.0609 FV 400 PV 377.04 t 1 (1 r ) (1.0609) 13 Slides for Lesson 4 The following six (6) slides are used in Lesson 4, “TVM – Amortizing Loans” and are referred to in the video as the slides from Ch. 3, 39-44. 14 Amortizing Loans – Example (referred to as slide 39) • You have decided to buy a new SUV and finance the purchase with a five year loan. The car costs $36,000 and you are going to put $2,500 down. Interest starts accruing when the loan is taken. The first loan payment is one month after the interest starts accruing. The interest rate on the loan is 8.4% (APR) per year for the five year period. 15 Amortizing Loans – Example (referred to as slide 40) – You know you will be paying an equal amount each month for the next 60 months. What type of security is this? It is an annuity with t=60 – What is the present value of the loan? What is the present value of the annuity? 36,000 – 2,500 = 33,500 – What is the effective monthly rate that you are paying for your car? What is the EAR? 12* 1 0.084 12 EAR 1 + - 1 0.007 12 – How can you determine your monthly payment? 16 Determining Your Payment (referred to as slide 41) • Recall you are borrowing $33,500 at 8.4% APR for 60 months. Also recall: C 1 PV(Annuity ) = 1 t r (1 + r) • We know the present value, r, and t. Thus, we can solve for C which is the payment 33,500 0.007 PV r C $685.69 1 1 1 - (1 + r) t 1 60 (1 + 0.007) 17 Determining Your Payment – Calculator (referred to as slide 42) • Recall you are borrowing $33,500 at 8.4% APR for 60 months. • On BA II+ – Clear TVM – Set payments per year to 12 (<2nd><I/Y>12<ENTER>) N I/Y PV PMT FV 60 8.4 33,500 -685.69 0 18 Amortization Table (referred to as slide 43) $33,500 car loan at 8.4% APR for 60 months Month Payment Interest Principal Balance 1 0.007 x 33,500 685.69 234.50 685.69 – 234.50 33,500 – 451.19 451.19 0.007 x 33,048.81 685.69 – 231.34 33,048.81 33,048.81 – 454.35 2 685.69 231.34 454.35 32,594.46 3 685.69 228.16 457.53 32,136.93 685.69 1 Balance after 3 payments PV 1 57 32,136.92 0.007 (1007 . ) 685.69 1 PV 1 . 19 Balance after 48 payments 12 7,86581 0.007 (1007 . ) What if ? (referred to as slide 44) • What if you wanted to know the balance remaining after 2 years of payments? • What if you wanted to know the total amount you paid in principal during the first 2 years? • What if you wanted to know the total amount paid in interest during the first 2 years? • What if you wanted to know the total amount of interest paid during the third year? 20 Slides for Lesson 5 The following six (6) slides are used in Lesson 4, “Bonds” and are referred to in the video as the slides from Ch. 5, 11-15. 21 Bond Pricing, Example (Referred to as slide 11) • Suppose IPC Co. Issues $1,000 bonds with 5 years to maturity. The semi-annual coupon is $50. Suppose the market quoted yield-to-maturity for similar bonds is 10% (APR, compounded semiannually). What is the present value (i.e. current market price) of the bond? What if the YTM was 8%? What if the YTM was 12%? IMPORTANT FINANCE PRINCIPLE REMEMBER: Assets with similar risk should have similar return. Thus the appropriate rate to use here is 10% • Steps to calculate bond price – Calculate the present value of the Face amount – Calculate the present value of the coupon payments – Add the two components to get the price 22 IPC Example (Referred to as slide 13) Face Value C 1 Price = + 1 t YTM (1 + YTM) (1 + YTM) t 1. Price if similar bonds have a 10% yield-to-maturity: Remember that payment, time, and rate ALL must match. Since we have a semiannual payment we NEED a semiannual rate. What is the effective semiannual rate? 2 1 2 my APR EPR 1 m 0.10 1 EPR 1 2 1 0.05 Notice that 5 years means 10 semiannual periods. 50 1 1,000 Price = + 1 10 0.05 (1 + 0.05) (1 + .05)10 = 386.09 613.91 1,000 23 IPC Example (Referred to as slide 13 and slide 14) Face Value C 1 Price = + 1 t YTM (1 + YTM) (1 + YTM) t 2. Price if similar bonds have an 8% yield-to-maturity: 50 1 1,000 Price = + 1 10 0.04 (1 + 0.04) (1 + .04)10 = 405.55 675.56 1,081.11 3. Price if similar bonds have a 12% yield-to-maturity: 50 1 1,000 Price = + 1 10 0.06 (1 + 0.06) (1 + .06)10 Notice the impact of Change in YTM on Price = 368.00 558.39 926.39 24 Easy Bond Pricing on your Calculator (Referred to as slide 15) Clear TVM registers Set P/Y=2 (2 payments per year) Price if YTM = 10% N 10 I/Y 10 PV -1,000 PMT 50 FV 1,000 Price if YTM = 8% N 10 I/Y 8 PV -1,081.11 PMT 50 FV 1,000 What is YTM if Price=$1,200? N 10 I/Y 5.384 PV -1,200 PMT 50 FV 1,000 25 Par, Discount, and Premium Bonds Recall IPC Bond Example YTM = 10%, Price = $1000 • Par Bonds – Price = Face Value – YTM = Coupon Rate – Current yield = Coupon rate • Discount Bonds – Price < Face Value – YTM > Coupon Rate – Current yield > Coupon rate • Premium Bonds – Price > Face Value – YTM < Coupon Rate – Current yield < Coupon rate Coupon Rate Current Yield 100 10% 1000 100 10% 1000 YTM = 12%, Price = $926.39 100 10% 1000 100 Current Yield 10.80% 926.39 Coupon Rate YTM = 8%, Price = $1081.11 100 10% 1000 100 Current Yield 9.25% 26 1081.11 Coupon Rate Slides for Lesson 6 The following six (6) slides are used in Lesson 6, “Cash Flow Worksheet – NPV and IRR” and are referred to in the video as the slides from Ch. 6, and Ch 5, slides 12-15. 27 NPV Example (referred to as slide 6) • Decide whether to open a new production plant. The initial cost of the plant is $600 million. Over the next four years, the plant is expected to generate cash flows from assets of $200 mm, $220 mm, $225 mm, and $210 mm. The risk of the cashflows requires that the appropriate discount rate is 20%. • How do you compute cash flows from assets? • Should we proceed with the project? 28 NPV Example 0 1 -600 200 2 3 220 225 4 210 Required Rate of return on project is 20% T CFt NPV Cost t ( 1 r ) t 1 200 220 225 210 NPV 600 2 3 4 (1.20) (1.20) (1.20) (1.20) NPV = -600 + 166.67 + 152.78 + 130.21 + 101.27 = -49.07 29 Internal Rate of Return (IRR) • Thus, for our example: T CFt 0 = t t = 0 (1 + IRR) 200 220 0= - 600 1 2 (1 IRR) (1 IRR) 225 210 3 4 (1 IRR) (1 IRR) The rate that makes this equation true is 15.67%. Thus, IRR = 15.67% 30 Bond Pricing, Example (Referred to as slide 12 in Ch. 5) • Suppose IPC Co. Issues $1,000 bonds with 5 years to maturity. The semi-annual coupon is $50. Suppose the market quoted yield-to-maturity for similar bonds is 10% (APR, compounded semiannually). What is the present value (i.e. current market price) of the bond? What if the YTM was 8%? What if the YTM was 12%? IMPORTANT FINANCE PRINCIPLE REMEMBER: Assets with similar risk should have similar return. Thus the appropriate rate to use here is 10% • Steps to calculate bond price – Calculate the present value of the Face amount – Calculate the present value of the coupon payments – Add the two components to get the price 31 IPC Example (Referred to as slide 13 in Ch. 5) Face Value C 1 Price = + 1 t YTM (1 + YTM) (1 + YTM) t 1. Price if similar bonds have a 10% yield-to-maturity: Remember that payment, time, and rate ALL must match. Since we have a semiannual payment we NEED a semiannual rate. What is the effective semiannual rate? 2 1 2 my APR EPR 1 m 0.10 1 EPR 1 2 1 0.05 Notice that 5 years means 10 semiannual periods. 50 1 1,000 Price = + 1 10 0.05 (1 + 0.05) (1 + .05)10 = 386.09 613.91 1,000 32 IPC Example (Referred to as slide 13 and slide 14, in Ch. 5) Face Value C 1 Price = + 1 t YTM (1 + YTM) (1 + YTM) t 2. Price if similar bonds have an 8% yield-to-maturity: 50 1 1,000 Price = + 1 10 0.04 (1 + 0.04) (1 + .04)10 = 405.55 675.56 1,081.11 3. Price if similar bonds have a 12% yield-to-maturity: 50 1 1,000 Price = + 1 10 0.06 (1 + 0.06) (1 + .06)10 Notice the impact of Change in YTM on Price = 368.00 558.39 926.39 33 Easy Bond Pricing on your Calculator (Referred to as slide 15, in Ch. 5) Clear TVM registers Set P/Y=2 (2 payments per year) Price if YTM = 10% N 10 I/Y 10 PV -1,000 PMT 50 FV 1,000 Price if YTM = 8% N 10 I/Y 8 PV -1,081.11 PMT 50 FV 1,000 What is YTM if Price=$1,200? N 10 I/Y 5.384 PV -1,200 PMT 50 FV 1,000 34