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Unformatted text preview: .10 62. $1,677.27 = PV0 of Mixed Flow [Using Tables] 677. [Using $600(PVIFA10%,2) = $600(1.736) = $1,041.60 $400(PVIFA10%,2)(PVIF10%,2) = $400(1.736)(0.826) = $573.57 $100 (PVIF10%,5) = $100 (0.621) = $62.10 51 Certified Financial Controller CFC “Group-At“Group-At-A-Time” (#2) (#2 0 1 2 3 $400 $400 $400 1 2 $200 $200 1 2 4 $400 $1,268.00 268. Plus 0 PV0 equals $1677.30. 1677.30. $347.20 347. Plus 0 3 4 5 $100 $62.10 62. 52 Certified Financial Controller CFC 26 Frequency of Compounding General Formula: Formula: FVn = PV0(1 + [i/m])mn n: m: i: FVn,m: Number of Years Compounding Periods per Year Annual Interest Rate FV at the end of Year n PV0: PV of the Cash Flow today 53 Certified Financial Controller CFC Impact of Frequency Julie Miller has $1,000 to invest for 2 Miller has invest for Years at an annual interest rate of 12%. Annual FV2 = 1,000(1+ [.12/1])(1)(2) 000 = 1,254.40 Semi FV2 = 1,000(1+ [.12/2])(2)(2) 000 = 1,262.48 262. 54 Certified Financial Controller CFC 27 Impact Impact of Frequency Qrtly FV2 FV = 1,000(1+ [.12/4])(4)(2) = 1,266.77 266. Monthly FV2 = 1,000(1+ [.12/12])(12)(2) 000 = 1,269.73 269. Daily FV2 = 1,000(1+[.12/365])(365)(2) 000 = 1,271.20 271. 55 Certified Financial Controller CFC Effective Annual Interest Rate Effective Annual Interest Rate Annual Interest Rate The actual rate of interest earned (paid) after adjusting the nominal rate for factors such as the number of compounding periods per year. (1 + [ i / m ] )m - 1 56 Certified Financial Controller CFC 28 BWs Effective Annual Interest Rate Basket Wonders (BW) has a $1,000 Wonders (BW) has CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate Interest Rate (EAR)? EAR = ( 1 + .06 / 4 )4 - 1 = 1.0614 - 1 = .0614 or 6.14%! 14%! 57 Certified Financial Controller CFC Steps to Amortizing a Loan 1. Calculate the payment per period. 2. Determine the interest in Period t. (Loan Balance at t-1) x (i% / m) 3. Compute principal payment in Period t. (Payment - Interest from Step 2) 4. Determine ending balance in Period t. (Balance - principal payment from Step 3) 5. 58 Start again at Step 2 and repeat. Certified Financial Controller CFC 29 Amortizing Amortizing a Loan Example Julie Miller is borrowing $10,000 at a 10, compound annual interest rate of 12%. Amortize the loan if annual payments are made for 5 years. Step 1: Payment PV0 = R (PVIFA i%,n) $10,000 10, = R (PVIFA 12%,5) $10,000 10, = R (3.605) R = $10,000 / 3.605 = $2,774 10, 59 Certified Financial Controller CFC Amortizing a Loan Example End of Year 0 Paym ent In te re s t P rin c ip a l --- --- --- E n d in g B a la n c e $ 1 0 ,0 0 0 1 $ 2 ,7 7 4 $ 1 ,2 0 0 $ 1 ,5 7 4 8 ,4 2 6 2 2 ,7 7 4 1 ,0 1 1 1 ,7 6 3 6 ,6 6 3 3 2 ,7 7 4 800 1 ,9 7 4 4 ,6 8 9 4 2 ,7 7 4 7 563 2 ,2 1 1 2 2 ,4 7 8 4 5 2 ,7 7 5 297 2 ,4 7 8 0 $ 1 3 ,8 7 1 $ 3 ,8 7 1 $ 1 0 ,0 0 0 [Last Payment Slightly Higher Due to Rounding] 60 Certified Financial Controller CFC 30 Usefulness of Amortization 1. 2. 61 Determine Interest Expense Determine Interest Expense -Interest expenses may reduce taxable income of the firm. Calculate Debt Outstanding -The quantity of outstanding quantity of outstanding debt may be used in financing the day-to-day activities of the firm. Certified Financial Controller CFC Chapter 7 Risk and Return 62 Certified Financial Controller CF...
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