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Unformatted text preview: CARNEGIE MELLON UNIVERSITY Tepper School of Business Finance  70391 Summer 2009 Practice Problems Topic 3 Solution  Valuing Riskless Cash Flows Note: Since many of the problems involve computations with annuities, let A T r;g denote the present value of a Tyear growing annuity payable at the end of each year when the annual interest rate is r , the annual growth rate in cash &ows is g , and the ¡rst cash &ow at t = 1 is $1 . From lecture, the present value of this cash &ow stream is A T r;g = 1 r & g " 1 & & 1 + g 1 + r ¡ T # : This simplifying notation will be used throughout this answer key. CONCEPT QUESTIONS 1. Quiz in Chapter 3 of Brealey, Myers and Allen The answer is in the back of Brealey, Myers and Allen. 2. Factory NPV First, we can compute the present value of the 10 year stream of cash in&ows at time t = 0 : PV = 170 ; 000 ¡ A T =10 r =14% ;g =0% = 170 ; 000 ¡ 5 : 216 = $886 ; 720 : Thus, NPV = & 800 ; 000 + 886 ; 720 = $86 ; 720 . At the end of ¡ve years, the factory¢s value will be the present value of the ¡ve remaining $17 ; 000 cash &ows. Discounting at time t = 5 , we have PV = 170 ; 000 ¡ A T =5 r =14% ;g =0% = 170 ; 000 ¡ 3 : 433 = $583 ; 610 : 3. Harold Filbert 1 (a) Using the growing annuity formula, the present value of future salary payments is PV = 20 ; 000 & A T =30 r =8% ;g =5% = 20 ; 000 & 19 : 01656 = $380 ; 331 : (b) The present value of 5 percent of future salary payments at time t = 30 is PV ( salary at t=30 ) & : 05 = $19 ; 016 : 56 ; so the future value of this savings at time t = 60 is FV ( t=60 ) = 19 ; 016 : 56 & (1 : 08) 30 = $191 ; 357 : (c) From the annuity formula, we have PV = C r & 1 ¡ 1 (1 + r ) T ¡ = C & A T r;g =0% ; $191 ; 357 = C & A T =20 r =8% ;g =0% = C & 9 : 8181 : Solving, C = $19 ; 490 : 4. Halcyon Lines We can break this down into several di/erent cash &ows such that the sum of the these separate cash &ows is the total cash &ow. Then, the sum of the present values of these separate cash &ows will be the present value of the entire project. All ¡gures are in millions of dollars. ¢ Ship Cost. PV = ¡ $8 ¢ Revenue and Expenses. Revenue is $5 per year; operating expenses are $4 per year. Thus, the operating cash &ow is $1 per year for 15 years. PV = $1 & A T =15 r =8% ;g =0% = $1 & 8 : 559 = $8 : 559 : ¢ Re&t. Major re¡ts cost $2 each, and will occur at times t = 5 and t = 10 . PV = ¡ $2 (1 : 08) 5 ¡ $2 (1 : 08) 10 ; = ¡ $2 : 288 : ¢ Scrap Value. Sale for scrap brings in revenues of $1 : 5 at t = 15 . PV = $1 : 5 (1 : 08) 15 = $0 : 473 : Adding up all these present values gives the value of the entire project: NPV = ¡ $8 + $8 : 559 ¡ $2 : 288 + $0 : 473 = ¡ $1 : 256 : Finance 2 Tepper 5. Breakfast Cereal Competition The value of the prizes are as follows: (a) PV = $100 ; 000 (b) PV = $180 ; 000 = 1 : 12 5 = $102 ; 137 (c) PV = $11 ; 400 =: 12 = $95 ; 000 (d) PV = $19 ; 000 & A T =10 r =12% ;g =0% = $19 ; 000 & 5 : 650 = $107 ; 350 (e) PV = $6 ; 500 = ( : 12 ¡ : 05) = $92...
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This note was uploaded on 01/20/2012 for the course INVESTMENT 101 taught by Professor Unknown during the Spring '08 term at Carnegie Mellon.
 Spring '08
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