경졔성공학특론-중간고사-2012년2학기

(30p)

What value of X makes these two cash flows equivalent assuming an interest rate of 10%

• 좌측 Cash Flow의 0시점 현가는
  1. 100(P|F 10%, 1) = 90.9091
  2. 100(P|F 10%, 2) = 82.6446
  3. 150(P|F 10%, 3) = 112.697
  4. 100(P|F 10%, 4) = 68.3013
  5. 150(P|F 10%, 5) = 93.1382
• P = 447.69

• 우측 Cash Flow의 0시점 현가는
  1. 100(P|F 10%, 1) = 90.9091
  2. X (P|F 10%, 2) = 0.8264 X
  3. -X (P|F 10%, 3) = -0.7513 X
  4. -200(P|F 10%, 4) = -136.603
  5. X (P|F 10%, 5) = 0.6209 X
• P = 0.696 X - 45.6939

• 좌측 Cash Flow와 우측 Cash Flow가 같아야 하므로
  • 447.69 = 0.696 X - 45.6939
  • X = 708.885

(30p)

a) What is the future worth of an equal payment series of ＄3000 each quarter for five years if the annual interest rate is 8% and compounded quarterly?

b) If your credit card calculates interest based on 12% annually. what are your monthly interest rate and annual effective interest rate? (Hint: We assume that the credit card is compounding monthly)

c) At what rate of interest, compounded daily, will an investment double itself in 5 years? (Hint: 1 year = 365 days)

a)

• F = 3000(F|A 2.02%, 20) = 137,286

b)

• 월 이자율 = 연간 명목 이자율 / 12 = 12% / 12 = 1%
• 연간 실질 이자율 = $(1.1)^{12}-1=12.6825%$

c)

• $2x=x(F|P\ i\%, 365 \times 5)$
• $2 = (F|P\ i\%, 1825)$
• $i=0.037988%$

(30p)

Suppose you borrowed ＄10,000 at an interest rate of 12%, compounded monthly over 36 months. At the end of the first year (after 12 payments), you want to negotiate with the bank to pay off the remainder of the loan in 8 equal quarterly payments. What is the amount of the quarterly payment. if the interest rate and compounding frequency remain the same (i.e. compounded monthly)? (Hint: think about the quarterly effective interest rate)

• 36개월간 갚아 나가는 금액 $A_{1}$는
  • $A_{1} = P(A_{1}|P\ 1\%, 36)=332.143$
• 12월 까지 납입 후 12월 시점의 남은 금액
  • $P_{1}=A_{1}(P|A_{1}\ 1\%,24)=6261.7$
• 남은 기간 분기 별로 갚을 경우 금액 $A_{2}$는
  • $A_{2}=P_{1}(A_{2}|P_{1}\ 3.03\%,8)=1006.42$

(20p - Difficult Question. Solve this only after you completed all other questions)

A project requires a ＄200,000 investment today, one year from now and subsequent investments of ＄200,000 at the end of years6, 12 and 18 That is, the investments are ＄200,000 each in year 0, 1, 6, 12 and 18 The project is expected to generate a cash flow of ＄100,000 in year 2, growing by 10% for each year until including year 10. After 10, the cash flow are expected to decrease by 10% until project termination at the end of 20 years.

a) Assuming a required rate of return of 8%, what is the present worth of the project?

b) Clearly, this project requires money to get started. If the company can borrow and invest at the 8% rate, by what year does this project generate enough cash so that it no longer requires financing?

a)

• 투자비의 전체 현가
  1. -200,000
  2. -200,000 (P|F 8%, 1) = -185,185
  3. -200,000 (P|F 8%, 6) = -126,034
  4. -200,000 (P|F 8%, 12) = -79,422.8
  5. -200,000 (P|F 8%, 18) = -50,049.8
• $P_{1}=-640,692$

• 수익 중 상승 구간의 전체 현가
  • $P_{2}=A_{1}(P|A_{1}\ i\%,j\%,n_{1})(P|F\ i\%,1)=100,000(P|A_{1}\ 8\%,10\%,9)(P|F\ 8\%,1)=1,268,180$

• 수익 중 하강 구간의 전체 현가
  • $$\begin{displaymath}\begin{split} P_{3} &= A_{2}(P|A_{2}\ i\%,j\%,n_{2})(P|F\ i\%,10) &= 192,923(P|A_{2}\ 8\%,-10\%,10)(P|F\ 8\%,10) &= 416,269 \end{split}\end{displaymath}$$

• $P_{1}+P_{2}+P_{3}=1,043,757$

b)

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