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lab%202011.02.11%20solutions

lab%202011.02.11%20solutions - FNAN 301 Solutions to lab...

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FNAN 301 Solutions to lab problems – 2/11/2011 Group lab problem You own a bowling alley that is expected to make annual cash flows forever. The cost of capital is 12.5%. The next annual cash flow is expected in one year from today and all subsequent cash flows are expected to grow annually by 2.5%. What is the value of the bowling alley if you know that the cash flow in 5 years from today is expected to be $100,000? Time 0 1 2 3 4 5 Cash flow 0 C 1 C 1 × (1.025) C 1 × (1.025) 2 C 1 × (1.025) 3 C 1 × (1.025) 4 Cash flow 0 C 1 C 1 × (1.025) C 1 × (1.025) 2 C 1 × (1.025) 3 $100,000 Present value ? Approach: 1) find the expected cash flow in 1 year 2) use the expected cash flow in 1 year to find the value today 1) find the expected cash flow in 1 year The cash flows reflect a growing perpetuity We know that C 5 = C 1 × (1+g) 4 C 5 = 100,000 g = .025 100,000 = C 1 × (1.025) 4 So C 1 = 100,000 / (1.025) 4 = $90,595.06 2) use the expected cash flow in 1 year to find the value today The cash flows reflect a growing perpetuity We know that PV = C 1 / (r – g) C 1 = $90,595.06 r = .125 g = .025 PV = 90,595.06 / (.125 – .025) = 90,595.06 / .100 = $905,950 1
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FNAN 301 Solutions to lab problems – 2/11/2011 Group lab problem What is the value of a night club that is expected to generate fixed cash flows of $170,000 with the first cash flow in 4 years and the last cash flow in 9 years if the appropriate discount rate is 13.5 percent? The value can be found in 2 steps. 1) Find the value of the night club as of one year before the first payment is made 2) Find the present value (as of today) of the night club Time 0 1 2 3 4 5 6 7 8 9 Pmt # 1 2 3 4 5 6 CF 0 0 0 0 170k 170k 170k 170k 170k 170k 1) The first of a series of 6 fixed payments occurs in 4 years, so we can find the value of the night club as of 3 years from now as an ordinary annuity. The 6 fixed payments occur in 4, 5, 6, 7, 8, and 9 years from now. END Mode Enter 6 13.5 170,000 0 N I% PV PMT FV Solve for -670,226 The night club is expected to be worth $670,226 in 3 years 2) The value today of something worth 670,226 in 3 years can be found as PV 0 = PV 3 / (1+r) 3 PV 3 = 670,226 r = .135 PV 0 = 670,226 / (1.135) 3 = $458,388 Mode is not relevant, since PMT = 0 Enter 3 13.5 0 670,226 N I% PV PMT FV Solve for -458,388 Today, the value of the night club is $458,388 Note: the following 3 cash flow patterns have the same present value when r = 13.5% Time 0 1 2 3 4 5 6 7 8 9 CF 0 0 0 0 170k 170k 170k 170k 170k 170k CF 0 0 0 670,22 6 0 0 0 0 0 0 CF 458,38 8 0 0 0 0 0 0 0 0 0 2
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FNAN 301 Solutions to lab problems – 2/11/2011 Group lab problem Cheryl wants to buy a computer.
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