...a three year cut-off period for recapturing the initial cash outflow? Assume that the cash flows are equally distributed over the year for Payback Period calculations. |Projects |A |B |C |D | |Cost |$10,000 |$25,000 |$45,000 |$100,000 | |Cash Flow Year One |$4,000 |$2,000 |$10,000 |$40,000 | |Cash Flow Year Two |$4,000 |$8,000 |$15,000 |$30,000 | |Cash Flow Year Three |$4,000 |$14,000 |$20,000 |$20,000 | |Cash Flow Year Four |$4,000 |$20,000 |$20,000 |$10,000 | |Cash Flow year Five |$4,000 |$26,000 |$15,000 |$0 | |Cash Flow Year Six |$4,000 |$32,000 |$10,000 |$0 | Solution Project A: Year One: -$10,000 + $4,000 = $6,000 left to recover Year Two: -$6,000 + $4,000 = $2,000 left to recover Year Three: -$2,000 + $4,000 = fully recovered Year Three: $2,000 / $4,000 = ½ year needed for...
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...000 invested for 11 years at 9% compounded annually b. $8,000 invested for 10 years at 8% compounded annually c. $800 invested for 12 years at 12% compounded annually d. $21,000 invested for 6 years at 5% compounded annually 5-2A. (Compound Value Solving for n) How many years will the following take? a. $550 to grow to $1,043.90 if invested at 6% compounded annually b. $40 to grow to $88.44 if invested at 12% compounded annually c. $110 to grow to $614.79 if invested at 24% compounded annually d. $60 to grow to $73.80 if invested at 3% compounded annually 5-3A. (Compound Value Solving for i) At what annual rate would the following have to be invested? a. $550 to grow to $1,898.60 in 13 years b. $275 to grow to $406.18 in 8 years c. $60 to grow to $279.66 in 20 years d. $180 to grow to $486.00 in 6 years 5-4A. (Present Value) What is the present value of the following future amounts? a. $800 to be received 10 years from now discounted back to present at 10% b. $400 to be received 6 years from now discounted back to present at 6% c. $1,000 to be received 8 years from now discounted back to present at 5% d. $900 to be received 9 years from now discounted back to present at 20% 5-5A. (Compound Annuity) What is the accumulated sum of each of the following streams of payments? a. $500 a year for 10 years compounded annually...
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...options on when to harvest next; 40, 45, 50, 55 years to see which would be the most profitable. In order to do this I will calculate the NPV of each harvest since that is the most accurate form of cost analysis (1). 40 year Harvest Revenue $39,800,250 Tractor cost 7,200,000 Road 2,700,000 Sale preparation & admin 945,000 Excavator piling 1,200,000 Broadcast burning 2,287,500 Site preparation 1,162,500 Planting costs 1,800,000 EBIT $22,505,250 Taxes 7,876,838 Net income (OCF) $14,628,413 Present Value of first harvest PV = $14,628,413/(1 + .0608)20 PV= $4,496,956 40 year interest rate 40-year project interest rate = [(1 + .0608)40] – 1 40-year project interest rate = 958.17% 40 year interest rate for Conservation fund 40-year conservation interest rate = [(1 + .0659)40] – 1 40-year conservation interest rate = 1,183.87% Present Value of thinning PV= $9,000,000/9.8517 PV= $939,286.45 Operating cash flow for 40 year harvest: $14,482,163 PV= [($14,628,413/9.5817)] / (1 + .0608)20 PV = $469,325.52 Present Value of Conservation PV = –$162,500 –$162,500/11.8387 PV= –$176.226.22 Value of Conservation today PV= –$176,226.22/(1+ .0659)20 PV = –$49,182.52 NPV for 40 year harvest NPV = $4,496,956 +...
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...$3,000,000 Taxes (40%) 1,200,000 Taxes = EBT × Tax rate NI $1,800,000 (Given) 3-4 NI = $50,000,000; R/EY/E = $810,000,000; R/EB/Y = $780,000,000; Dividends = ? R/EB/Y + NI – Div = R/EY/E $780,000,000 + $50,000,000 – Div = $810,000,000 $830,000,000 – Div = $810,000,000 $20,000,000 = Div. 3-8 Statements b and d will decrease the amount of cash on a company’s balance sheet. Statement a will increase cash through the sale of common stock. Selling stock provides cash through financing activities. On one hand, Statement c would decrease cash; however, it is also possible that Statement c would increase cash, if the firm receives a tax refund for taxes paid in a prior year. 3-9 Ending R/E = Beg. R/E Net income Dividends $278,900,000 = $212,300,000 Net income $22,500,000 $278,900,000 = $189,800,000 Net income Net income = $89,100,000. 4-1 DSO = 40 days; S = $7,300,000; AR = ? DSO = 40 = 40 = AR/$20,000 AR = $800,000. 4-2 Since the firm’s M/B ratio = 1, then its total market value of equity is equal to its book value of equity. Common equity = $14 × 5,000,000...
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...Chapter 6 Time Value of Money LEARNING OBJECTIVES After reading this chapter, students should be able to: • Convert time value of money (TVM) problems from words to time lines. • Explain the relationship between compounding and discounting, between future and present value. • Calculate the future value of some beginning amount, and find the present value of a single payment to be received in the future. • Solve for time or interest rate, given the other three variables in the TVM equation. • Find the future value of a series of equal, periodic payments (an annuity) as well as the present value of such an annuity. • Explain the difference between an ordinary annuity and an annuity due, and calculate the difference in their values. • Calculate the value of a perpetuity. • Demonstrate how to find the present and future values of an uneven series of cash flows. • Distinguish among the following interest rates: Nominal (or Quoted) rate, Periodic rate, and Effective (or Equivalent) Annual Rate; and properly choose between securities with different compounding periods. • Solve time value of money problems that involve fractional time periods. • Construct loan amortization schedules for both fully-amortized and partially-amortized loans. LECTURE SUGGESTIONS We regard Chapter 6 as the most important chapter in the book, so we spend a good bit of time on it. We approach time value in...
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...000 invested for 11 years at 9% compounded annually b. $8,000 invested for 10 years at 8% compounded annually c. $800 invested for 12 years at 12% compounded annually d. $21,000 invested for 6 years at 5% compounded annually 5-2A. (Compound Value Solving for n) How many years will the following take? a. $550 to grow to $1,043.90 if invested at 6% compounded annually b. $40 to grow to $88.44 if invested at 12% compounded annually c. $110 to grow to $614.79 if invested at 24% compounded annually d. $60 to grow to $73.80 if invested at 3% compounded annually 5-3A. (Compound Value Solving for i) At what annual rate would the following have to be invested? a. $550 to grow to $1,898.60 in 13 years b. $275 to grow to $406.18 in 8 years c. $60 to grow to $279.66 in 20 years d. $180 to grow to $486.00 in 6 years 5-4A. (Present Value) What is the present value of the following future amounts? a. $800 to be received 10 years from now discounted back to present at 10% b. $400 to be received 6 years from now discounted back to present at 6% c. $1,000 to be received 8 years from now discounted back to present at 5% d. $900 to be received 9 years from now discounted back to present at 20% 5-5A. (Compound Annuity) What is the accumulated sum of each of the following streams of payments? a. $500 a year for 10 years compounded annually...
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...CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) | | |Brief Exercises | | | |Topics |Questions | |Exercises |Problems | | 1. |Present value concepts. |1, 2, 3, 4, | | | | | | |5, 9, 17 | | | | | 2. |Use of tables. |13, 14 |8 |1 | | | 3. |Present and future value problems: | | | | | | |a. Unknown future amount. |7, 19 |1, 5, 13 |2, 3, 4, 7 | | | |b. Unknown payments. |10, 11, 12 |6, 12, |8, 16, 17 |2, 6 | | | | |15, 17 | | | | ...
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...Practice Problems FV of a lump sum i. A company’s 2005 sales were $100 million. If sales grow at 8% per year, how large will they be 10 years later, in 2015, in millions? PV of a lump sum ii. Suppose a U.S. government bond will pay $1,000 three years from now. If the going interest rate on 3‐year government bonds is 4%, how much is the bond worth today? Interest rate on a simple lump sum investment iii. The U.S. Treasury offers to sell you a bond for $613.81. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price? Number of periods iv. Addico Corp's 2005 earnings per share were $2, and its growth rate during the prior 5 years was 11.0% per year. If that growth rate were maintained, how long would it take for Addico’s EPS to double? PV of an ordinary annuity v. You have a chance to buy an annuity that pays $1,000 at the end of each year for 5 years. You could earn 6% on your money in other investments with equal risk. What is the most you should pay for the annuity? Payments on an annual annuity vi. Suppose you inherited $200,000 and invested it at 6% per year. How much could you withdraw at the end of each of the next 15 years? Payments on a monthly annuity vii. You are buying your first house for $220,000...
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...Figure 16-2: • senior secured debt, • junior secured debt, • senior debenture, • subordinated debenture, • preferred stock, • common stock. 6. Bond conversion. 7. The purpose of serial and sinking fund payments is to provide an orderly procedure for the retirement of a debt obligation. To the extent bonds are paid off over their life, there is less risk to the security holder. 8. A call provision may be exercised when interest rates on new securities are considerably lower than those on previously issued debt. The purpose of a deferred call is to insure that the bondholder will not have to surrender the security due to a call for at least the first five or ten years. 9. Bond prices on outstanding issues and interest rates move in opposite directions. If interest rates go up, bond prices will go down and vice versa. Long-term bonds are particularly...
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...simple interest, you earn 4% of $1,000 or $40 each year. There is no interest on interest. After 10 years, you earn total interest of $400, and your account accumulates to $1,400. With compound interest, your account grows to: $1,000 × (1.04)10 = $1480.24 Therefore $80.24 is interest on interest. PV = $700/(1.05)5 = $548.47 5. 4-1 6. Present Value a. $400 Years 11 Future Value $684 Interest Rate ⎡ 684 ⎤ ⎢ 400 ⎥ ⎣ ⎦ ⎡ 249 ⎤ ⎢ 183 ⎥ ⎦ ⎣ (1 / 11) − 1 = 5.00% (1 / 4 ) b. $183 4 $249 − 1 = 8.00% (1 / 7 ) c. $300 7 $300 ⎡ 300 ⎤ ⎢ 300 ⎥ ⎣ ⎦ − 1 = 0% To find the interest rate, we rearrange the basic future value equation as follows: ⎡ FV ⎤ FV = PV × (1 + r) ⇒ r = ⎢ ⎣ PV ⎥ ⎦ t (1 / t ) −1 7. You should compare the present values of the two annuities. a. ⎡ 1 ⎤ 1 − PV = $1,000 × ⎢ = $7,721.73 10 ⎥ ⎣ 0.05 0.05 × (1.05) ⎦ ⎡ 1 ⎤ 1 − PV = $800 × ⎢ = $8,303.73 15 ⎥ ⎣ 0.05 0.05 × (1.05) ⎦ b. ⎡ 1 ⎤ 1 − = $4,192.47 PV = $1,000 × ⎢ 10 ⎥ ⎣ 0.20 0.20 × (1.20) ⎦ ⎡ 1 ⎤ 1 − PV = $800 × ⎢ = $3,740.38 15 ⎥ ⎣ 0.20 0.20 × (1.20) ⎦ c. When the interest rate is low, as in part (a), the longer (i.e., 15-year) but smaller annuity is more valuable because the impact of discounting on the present value of future payments is less significant. 8. $100 × (1 + r)3 = $115.76 ⇒ r = 5.00% $200 × (1 + r)4 = $262.16 ⇒ r = 7.00% $100 × (1 + r)5 = $110.41 ⇒ r = 2.00% 4-2 9. PV = ($200/1.06) + ($400/1.062) + ($300/1.063) = $188...
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...tomorrow » But how much more?.. 2 1 1 Topic Overview Compounding & Future Value Discounting & Present Value Multiple Cash Flows “Special” Streams of Cash Flows » Perpetuities » Annuities Interest Rates » APR versus EAR 3 Lottery Example You just won a lottery which gives you two options: (1) Receive $100 today (2) Receive $120 in one year $100 $120 0 Money Time 1 Which option should one take? 4 2 2 Lottery Example: Future Value If you take money now, you can put them in the bank at the current interest rate “r” of 5%, and have the following amount in one year: V0=$100 0 Money Time V1=$105 1 The amount in one year – future value (FV) – is calculated as FV = Principal + r × Principal = $100 + 0.05 × $100 = $105 Which option should we take now? 5 Lottery Example: Present Value Alternatively, we can compare the value at time 0: V0=$114.3 0 Money Time V1=$120 1 The amount in a given year – Present Value (PV) – is: $120 = PV+ r × PV = PV+ 0.05 × PV → PV = $114.3 Which option should we take? 6 3 3 Basic Terminology Timeline: a linear representation of the timing of potential cash flows. Two types of cash flows: 1. Inflows (i.e., money we get) are represented by positive numbers 2. Outflows (i.e., money we give) are represented by negative numbers Example: » Assume that you are lending $10,000 today...
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...Chapter 5 A1. (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond? Calculating PV factor: i= required return = 9% = 0.09 n= 10 years Using Cash Flow of $1000 to calculate present value, Cash flow= $1000 PV factor = 1/(1+i)^n = 0.42241 PV = $1000*0.42241= 422.41 Using Coupon Rate to calculate present value of Annuity Cash flow= $1000 * 7.4/100 = $74 PV factor = (1/i)*(1- 1/(1+i)^n) = 6.4176 So, PV = $74*6.4176 = 474.90| So the fair value of bond = 474.90+422.41 = $897.31 A10. (Dividend discount model) Assume RHM is expected to pay a total cash dividend of $5.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the required return on RHM common stock is 10%? Current market value = D1/(Required return – growth rate) = 5.60/(10%-6%) = $140 A12. (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividends is now growing. What is the required return on James River preferred stock? Required Return = Dividend/Market Price Dividend = $3.38 Market Price = $45.25 Required Return = $3.38 / $45.25 Required Return = 7.47% A14...
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...GLOBAL MARKET OUTLOOK For Photovoltaics 2014-2018 Supported by: GLOBAL MARKET OUTLOOK For Photovoltaics 2014-2018 Principal authors and analysts: Gaëtan Masson (iCARES Consulting), Sinead Orlandi, Manoël Rekinger Publication coordination: Benjamin Fontaine, Sinead Orlandi External contributors: AECEA, APERe, APESF, APISOLAR, APREN, assoRinnovabili, Australian PV Association, BPVA, BSWSolar, CANSIA, CREIA, CRES, CZEPHO, Danish PV Association, EDORA, ENERPLAN, Fronius, GENSED, GIFI, Goldbeck, HELAPCO, Holland Solar, HUPIA, IEA-PVPS, JPEA, KOPIA, Martifer, PV AUSTRIA, PV Russia, PV Poland, PV Vlaanderen, Renewable Association of Israel, RPIA, RTS Corporation, SAPI, SAPVIA, SASIA, SEIA, SEMI Taiwan, SolarMax, SolarTrade Association, SunEdison, Swissolar, TOTAL, UNEF, Wacker, ZSFI Editor: Tom Rowe Design: Onehemisphere, Sweden Images: iStock.com/CaiaImage (cover), REC – Renewable Energy Corporation ASA (page 8), Sharp (page 10), ENEL (page 12), First Solar (page 14), First Solar (page 16), Kyocera Fineceramics, Stromaufwart Photovoltaik GmbH (page 26), Sharp (page 48), JA Solar (page 54). Supported by: Intersolar Europe Solar irradiation world map has been derived from the SolarGIS database: http://solargis.info (© 2014 GeoModel Solar) Disclaimer: Please note that all historical figures provided in this brochure are valid at the time of publication and will be revised when new and proven figures are available. All forecast figures are based on...
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... Compounding Translating today’s $1 into its equivalent FV FVn = PV ( 1 + i )n FV1= 100(1+.10)1=110 Discounting Translating tomorrow's $1 into its equivalent PV PVn = FV÷( 1 + i )n PV1= 110÷ (1+.10)1=100 4-3 Compounding and Discounting When making investment decisions, managers usually calculate PV. 4-4 2 FVIFi,n (FVIF Table) FVn = PV ( 1 + i )n 4-5 FV– Single Sum If you deposit $100 in an account earning 6%, how much would you have after 1 year? PV = 100 FV = 0 106 1 Tabular and Mathematical Solution: FV = PV (FVIF i, n ) (use FVIF table) FV = 100 (FVIF .06, 1 ) = 100 (1.06)= $106 FV = PV (1 + i)n = 100 (1.06)1 = $106 4-6 3 FV– Single Sum If you deposit $100 in an account earning 6%, how much would you have after 5 years? PV = 100 FV = 0 133.82 5 Tabular and Mathematical Solution: FV = PV (FVIF i, n ) (use FVIF table) FV = 100 (FVIF .06, 5 ) = 100 (1.3382)= $133.82 FV = PV (1 + i)n = 100 (1.06)5 = $133.82 4-7 FV– Single Sum If you deposit $100 in an account earning 6% with quarterly compounding, how much would you have after 5 years? PV = 100 0 FV = 134.68 5 Tabular and Mathematical Solution: FV = PV (FVIF i, n ) (use FVIF table) FV = 100 (FVIF .015, 20 ) (can’t use FVIF table) FV = PV (1 + i/m)n×m = 100 (1.015)20 = $134.68 4-8 4 FV– Single Sum If you deposit $100 in an account earning 6% with monthly compounding, how much would you have after 5 years? PV = 100 FV...
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...values of money to get the present value of $100 using different periods of time and interest rates. Time Value of Money In the world of business, it is essential to know what TVM represents and how it helps make better choices in how we spend our money. TVM is also known as Time Value of money which is a given amount of interest earned in a period of time (Wikipedia, 2011). Each member in group “C” will use 100 as our present value and we will choose an interest rate and period. Time value of money concept is used to determine present and future values of money. “The time value of money refers to the relationship between time, money, and the rate of interest.” (Letsche, 2011). The formula consist of four components FV = Future Value, PV = Present Value, i = the interestrate per period and n= the number of compounding periods (TeachMeFinance.com). In business, TVM is used to evaluate expected returns on investments and monitoring the company’s cash flow. “However, understanding the time value of money is also very important for you as an self-employed business person to make sure you are able to realize your spending, purchasing and retirement goals.” (Loughran, 2011). On a personal level, individuals can use TVM to calculate interest that will be paid on mortgages, car payments and individual loans. Knowing how your money can work for you is important to personal financial success. When one considers the time value of money it is important to understand that “a dollar...
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