[管理學(xué)]財(cái)務(wù)管理第三章-資料下載頁(yè)
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【正文】 e of Money Problems Julie Miller will receive the set of cash flows below. What is the Present Value at a discount rate of 10%. 0 1 2 3 4 5 $600 $600 $400 $400 $100 PV0 10% Mixed Flows Example 0 1 2 3 4 5 $600 $600 $400 $400 $100 10% $ $ $ $ $ $ = PV0 of the Mixed Flow 0 1 2 3 4 5 $600 $600 $400 $400 $100 10% $1, $ $ $1, = PV0 of Mixed Flow [Using Tables] $600(PVIFA10%,2) = $600() = $1, $400(PVIFA10%,2)(PVIF10%,2) = $400()() = $ $100 (PVIF10%,5) = $100 () = $ General Formula: FVn = PV0(1 + [i/m])mn n: Number of Years m: Compounding Periods per Year i: Annual Interest Rate FVn,m: FV at the end of Year n PV0: PV of the Cash Flow today Frequency of Compounding Julie Miller has $1,000 to invest for 2 Years at an annual interest rate of 12%. Annual FV2 = 1,000(1 + [])(1)(2) = 1, Semi FV2 = 1,000(1 + [])(2)(2) = 1, Impact of Frequency Qrtly FV2 = 1,000(1 + [])(4)(2) = 1, Monthly FV2 = 1,000(1 + [])(12)(2) = 1, Daily FV2 = 1,000(1 + [])(365)(2) = 1, Impact of Frequency Effective Annual Interest Rate The actual rate of interest earned (paid) after adjusting the nominal rate for factors such as the number of pounding periods per year. (1 + [ i / m ] )m – 1 Effective Annual Interest Rate Basket Wonders (BW) has a $1,000 CD at the bank. The interest rate is 6% pounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAR)? EAR = ( 1 + / 4 )4 – 1 = 1 = or %! BWs Effective Annual Interest Rate 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. Start again at Step 2 and repeat. Steps to Amortizing a Loan Julie Miller is borrowing $10,000 at a pound 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 = R (PVIFA 12%,5) $10,000 = R () R = $10,000 / = $2,774 Amortizing a Loan Example End of Year Payment Interest Principal Ending Balance 0 — — — $10,000 1 $2,774 $1,200 $1,574 8,426 2 2,774 1,011 1,763 6,663 3 2,774 800 1,974 4,689 4 2,774 563 2,211 2,478 5 2,775 297 2,478 0 $13,871 $3,871 $10,000 [Last Payment Slightly Higher Due to Rounding] Amortizing a Loan Example 2. Calculate Debt Outstanding – The quantity of outstanding debt may be used in financing the daytoday activities of the firm. 1. Determine Interest Expense – Interest expenses may reduce taxable ine of the firm. Usefulness of Amortizatio
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