Note 2-2. Discounted Cash Flow Valuation 1 1. 연금 (Annuity) 연금 : 일정기간동안일정액이매회규칙적으로지급되는투자상품 우리주변에는 연금 이라는명칭으로알려져있는투자상품외에도수없이많은금융상품이연금의형태를띄고있다. 2 1
Korea s Evolving Pension Programs By Tom Coyner (03-07-2007) More than ever, Korea s employers are facing a wider variety of opportunities and challenges when it comes to creating retirement schemes to attract, retain and reward their employees. Given all of this, changes are taking place. In the past when employees terminate, very few use the lump sum from the severance program to purchase an annuity program. Much to the Government s concern, many former employees basically blow their sudden, temporary wealth on real estate, vacations, cars or small businesses only to find themselves in great financial difficulty a few years later. To offset this, there are now special tax advantages to encourage the purchase of annuity programs. 3 Lump-Sum or Annuity? Suppose you will soon retire and have an option to choose between a lump-sum payment or annuity payments for your retirement benefits. Which are you going to choose? Dear Powerball Winner 4 2
연금의미래가치 ex) 5 년동안연리 10% 에매년 $2,000 불씩지급받는투자가있다. 이투자의 5 년후가치를계산하면? today yr. 1 yr. 2 yr. 3 yr. 4 yr. 5 + + + + $2K $2K $2K $2K $2K 5 년후시점의가치? 5 ex) 연 10% 할인율을적용할경우,5 년동안매년 $2,000 을지급하는투자상품의미래가치 FV = 2000(1.1) 4 + 2000(1.1) 3 + 2000(1.1) 2 + 2000(1.1) =12,210.20 6 3
Future Value of Annuity (Formula) [ Variable C is the periodic cash flow from the annuity] Formula: Future Value Annuity Factor: 7 Example 철수는 5 년뒤에자동차를사려고한다. 철수가사기로한자동차모델의 5 년뒤가격은 5,000 만원으로예상되며, 철수는앞으로 5 년동안매년연말에 800 만원씩 7% 이자율에저축을할계획이며, 5 년뒤시점에서금액이모자랄경우, 자동차를담보로하여은행으로부터대출을받아부족분을충당할계획이다. 5 년뒤부족분은얼마일까? 8 4
The new Pennsylvania Lottery Powerball jackpot has crossed above the $200-M mark. For the winner/winners of the $203-M is concerned, this sum comes to a value through time as an estimated annuity value of $203-M. It comes about $115.5-M in the cash value for a lump sum, which is still Kingmaker money for the bulk of the population. 9 연금의현재가치 ex) 당신은일정금액을은행에유치해놓은후앞으로 5 년동안매년말에 $1,000 씩인출을하고자한다. 은행에서제공하는이율이연 6% 일경우, 지출계획에차질이없도록하기위해지금얼마를은행에예치해야할까? today yr. 1 yr. 2 yr. 3 yr. 4 yr. 5? = + + + + $1K $1K $1K $1K $1K 10 5
ex) 연 6% 할인율을적용할경우, 앞으로 5 년동안매년 $1,000 을지급하는투자상품의현재가치 0 1 2 3 4 5 $1,000 $1,000 $1,000 $1,000 $1,000 Time $ 943.40 x 1/1.06 x 1/1.06 2 (years) 890.00 839.62 792.09 747.26 x 1/1.06 3 x 1/1.06 4 x 1/1.06 5 $4,212.37 Total present value r = 6% 1000/(1.06)+1000/(1.06) 2 +1000/(1.06) 3 +1000/(1.06) 4 +1000/(1.06) 5 =4,212.37 11 12 6
13 Once upon a time WIN $1,000,000 INSTANTLY * 14 7
Game open to individual legal residents of the Grand prize paid as 20 year annuity. See offici details. Void where prohibited. Game ends 1 Nutrition Facts: Serv. size: 1 pack Amount for Fat Cal. 120, Total Fat 14g (22% DV), S Total Carb. 26g (9% DV), Protein 5g, Ingredients: Milk Chocholate (Sugar, C Lactose, Peanuts, Soy Lecithin, Salt Distributed by DIVISION OF 15 PV = $50,000 A 20.10= $50,000 x 8.5136 = $425,680 16 8
Time Value of Money Exercise Problem 친구가 4 년전 $2,000 을꾸더니갚지않고사라져버렸다. 바로어제이친구가다시나타나꾼돈을갚겠노라전했다. 친구는꾼돈을복리로이자까지계산하여향후 5 년간연말에매년같은액수를지불하겠다고하였다. 10% 의이자율을전체기간에적용할경우, 친구가매년갚아야할액수는? 17 Solution -4-3 -2-1 0 1 2 3.. 4 5-2K C C C.. C C 10% 10% 18 9
19 Annuity Scheme If you were born in 1966, you need to make 300 monthly payments (25 years*12 months) 154,000 * 300/mo. = 46,200,000 Value at maturity = 82,000,000 + 2,000,000 annually for the next 10 years. If you estimate the return applied in the investment (interest rate) by using the annuity future value formula : 20 10
美 20 대교민매주 1 만弗 ` 대박 ` [ 헤럴드경제 ] 2006 년 09 월 05 일 ( 화 ) 사망때까지지급복권당첨 미국뉴욕퀸즈에거주하는 20 대한국교민이매주 1 만달러씩죽을때까지주는즉석복권에당첨돼화제가되고있다. 한국인남성평균수명이 77.5 세임을감안하고이때까지만당첨금을받는다고가정하면, 이 20 대남성은총 2,600 만달러 ( 한화약 249 억 6000 만원 ) 을얻게된다. 미주한국일보보도에따르면행운의주인공인강대성 (27) 씨는뉴욕주복권국발행즉석복권인 Win for Life Spectacular 1 등에당첨돼사망시점까지매주 1 만달러씩받게됐다. 강씨가 1 등에당첨된복권은확률이 325 만 8000 분의 1 에불과한것으로당첨금규모는뉴욕로터리즉석복권역사상가장많은금액이다. 강씨에게대박을안긴복권은그가직접구입한게아니라아버지로부터선물받은것. 이부자 ( 父子 ) 는일주일에 50 달러상당의복권을사는복권마니아로지금까지가장큰당첨액은 5000 달러였다. 21 Is he really that rich? 명목가치 $10,000 52 weeks/year 50.5 years = $26,260,000 실제가치 (PV; Annuity) Assume an interest rate of 7% per year PV = $10,000 [1-1/(1 + 0.07/52) 52*50.5 ]/(0.07/52) = $7,211,447.99 22 11
PV of Annuity: Question (Revisited) Your friend, who has borrowed from you $5,000 a year at 10% interest at the beginning of each year for the past four years and disappeared, suddenly came back to town yesterday. He gave you an apology and promised that he would work hard to pay off the debt in ten equal annual payments. Now, because you don t trust your friend any more, you think the appropriate rate for the payments should be higher this time at 20%. How much does your friend have to pay you each year? 23-4 -3-2 -1 0 1 2 3.. 9 10-5K -5K -5K -5K C C C.. C C 10% 20% 24 12
Application: Annuity Due ( 선급연금, 선연금 ) 보통연금의경우와비슷하나금액의지불이연말이아닌연초에이루어진다. today yr. 1 yr. 2 yr. 3 yr. 4 yr. 5? = + + + + $1K $1K $1K $1K $1K $0 PV formula for an annuity due 25 ex) 당신의가장친한친구가 18 억원짜리복권에당첨되었다. 당첨금지급조항에의하면당첨금은 20 회로나뉘어지불되며, 오늘부터시작하여매년 9,000 만원씩받게된다. 당신친구는복권당첨소식을들은후당첨금총액을일시불로받은후이민을갈계획을세웠다. 친구가복권지불담당부서에가 18 억원을현금으로당장지불해달라고하자, 담당관은연 10% 의이자율을적용해야하며, 그렇게되면, 수령액수가 18 억원보다상당히적을수있다고한다. 친구는담당자와언쟁을벌인후, 사기당한기분으로당신에게와서하소연한다. 누가옳은가? 담당관이옳다면, 당첨금의정확한가치는? 26 13
Perpetuity 영속연금 (perpetuity) 는매기간일정액을무한히지급하는연금이다. 27 Perpetuity Question 당신은방금어마어마한복권에당첨되었다. 상금지급조건은매년연말에 $1,000 씩영원히지급하는것인데, 일시불로 $20,000 을지급받는옵션을선택할수도있다. 만약이자율이 5% 라가정할때, 당신의선택은? 28 14
Perpetuity Valuation 29 Solution Option 1: $1,000/year forever Option 2: $20,000 in cash now Option 1( 영속지급 ) 의가치 : PV = $1,000/0.05 = $20,000 두옵션의가치는동일! 30 15
Perpetuity: Example U.K. Consols (war bond, 1752년발행, 3% coupon) 두산인프라코어 2012년 10월 5일, $5억규모의영구채발행싱가포르증시에상장. Coupon Rate: T-Note 5년물수익률 + 2.65% 31 HSBC Re-Opens Market for Perpetual Bonds With $3.4 Billion Sale June 18, 2010 (Bloomberg) -- HSBC Holdings Plc, Europe s largest bank, sold $3.4 billion of undated bonds in the biggest issue of its kind for almost two years, re-opening a market that s been shut since December. HSBC s bonds, which have no maturity date and are callable after 5 1/2 years, will pay a coupon of 8 percent, according to a person with knowledge of the transaction, who declined to be identified because the details are private. That s at the lower end of the marketing range of 8 percent to 8.125 percent. The deal is the biggest U.S. dollar-denominated perpetual note since Credit Suisse Group AG issued $3.5 billion of 11 percent securities in October 2008, according to data compiled by Bloomberg. The last bank to sell perpetual bonds was Paris-based lender BNP Paribas SA in December 2009. 32 16
Perpetuity Question You are considering the purchase of an investment for your retirement. If you pay lump-sum cash of $50,000 now, in return you will be paid $50,000 a year forever, with the first payment made in twenty years from now. You believe that the appropriate discount rate is 12% per year. Is this a good deal? 33 Solution 0 1 2 19 20 21 22 23 0 0 0 0 50K 50K 50K 50K FV 19? 34 17
Solution FV 19 (perpetuity) = $50,000/0.12 = $416,667 PV = FV 19 /(1.12) 19 = $416,667/(1.12) 19 = $48,378 The value of the investment is lower than $50,000. So it is not a good deal. 35 18