MT solution - MGCR 341: Finance 1 Summer 2010 Vadim di...

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MGCR 341: Finance 1 Summer 2010 Vadim di Pietro Midterm: Solutions 1) (5 points, 5 mins) Would you rather invest your money for one year at an APR of 8% with monthly compounding, or in a 1-yr zero coupon bond that has a YTM of 8.4% ? (Assume both investments are risk free.) (1+0.08/12) 12 -1 = 0.083 < 0.084, thus you prefer to invest in the zero coupon bond. 2) (10 points, 15 mins) Today is year t = 0 . You are planning for your retirement. Assume that your first purchase in retirement will be made at t = 31 and your last purchase will be made at t = 70 . At t = 31 , you want to purchase the same amount of goods that $30,000 can buy today. Each year after that, you would like to be able to purchase 1% more, in real terms , than you did in the previous year. The annual inflation rate is 2% . The risk free rate is 10% . What is the Present Value of the cash flows you plan to spend in retirement? (You may solve this question using either the nominal approach or the real approach.) The cash flows are a forward starting growing annuity with a total of 40 cash flows. Nominal Approach: The first nominal cash flow at t = 31 is 30,000 (1.02) 31 = 55,427.66 If the real growth rate is 1%, and the inflation rate is 2%, then nominal cash flows have to grow at a rate of (1.01)(1.02)-1 = 0.0302 Thus PV = gguG±²U³³ ´Uµ´ – ´U´¶´± ·µ ¸ ¹ µU´¶´± µUµ´ º » ¹ µ µUµ´ ¶´ º = 42,202.74 The ¹ µ µUµ´ ¶´ º is included in this expression because we have to discount the value of the forward starting growing annuity back to t = 0. Recall that the standard formula for a growing annuity gives you the value of the cash flows one period before the first cash flow. Real Approach: The first real cash flow is 30,000, and the real growth rate is 1%. The real interest rate is 1.10/1.02 – 1 = 0.0784 Thus PV = ¶´u´´´ ´U´²¼G½´U´µ ·µ ¸ ¹ µU´µ µU´²¼G º »¹ µ µU´²¼G ¶´ º = 42,202.74
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3) (10 points, 15 mins) You are considering building a power plant. Today is t = 0 . Building the power plant will require a $4bn investment at t = 0 , and another $500M investment at t = 2 . Starting at t = 3 , there will be a maintenance cost each year. The maintenance cost at t = 3 is expected to be $60M , and is expected to grow by 3% each year thereafter. The project is expected to generate $300M in revenues at t = 6 , and revenues are expected to grow at a rate of X each year thereafter, forever. Assume the appropriate discount rate for a project with this type of risk is 10% . Based on the NPV rule, what is the minimum value of the growth rate
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MT solution - MGCR 341: Finance 1 Summer 2010 Vadim di...

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