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03 time value of money part 2 - lecture problems solutions

# 03 time value of money part 2 - lecture problems solutions...

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Solutions to lecture problems – time value of money part 2 How much is a building worth that is expected to produce cash flows of \$200,000 in 1 year and \$500,000 in 2 years if the cost of capital is 10 percent? Time 0 1 2 Expected cash flow 0 \$200,000 \$500,000 Present value ? PV = C 0 + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] C 0 = 0 C 1 = 200,000 C 2 = 500,000 r = .10 PV = C 0 + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] = 0 + [200,000/(1.10)] + [500,000/(1.10) 2 ] = 0 + 181,818.18 + 413,223.14 = 595,041.32 Answer: \$595,041.32 1

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Solutions to lecture problems – time value of money part 2 How much cash flow is a building expected to produce in 2 years if it is currently worth \$500,000, expected to produce cash flows of \$200,000 in 1 year, and has a cost of capital of 10 percent? Time 0 1 2 Expected cash flow 0 \$200,000 ? Present value \$500,000 PV = C 0 + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] PV = 500,000 C 0 = 0 C 1 = 200,000 C 2 = ? r = .10 PV = C 0 + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] 500,000 = 0 + [200,000/(1.10)] + [C 2 /(1.10) 2 ] 500,000 = 0 + 181,818.18 + [C 2 /(1.10) 2 ] So 500,000 – 181,818.18 = [C 2 /(1.10) 2 ] So 318,181.82 = [C 2 /(1.10) 2 ] The present value of the cash flow expected in year 2 is \$318,181.82 The value of the cash flow expected in year 2 is C 2 where 318,181.82 = [C 2 /(1.10) 2 ] So C 2 = [318,181.82 × (1.10) 2 ] = \$385,000 Confirm: PV = C 0 + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] PV = 0 + [200,000/(1.10) 1 ] + [385,000/(1.10) 2 ] = 0 + 181,818.18 + 318,181.82 = 500,000 2
Solutions to lecture problems – time value of money part 2 You own a building that is expected to make annual cash flows forever. What is the value of the building if the cost of capital is 8.0% and annual cash flows of \$500,000 are expected with the first one in 1 year? Time 0 1 2 3 4 Cash flow \$0 \$500,000 \$500,000 \$500,000 \$500,000 Present value ? The cash flows reflect a fixed perpetuity PV = C / r C = \$500,000 r = .080 PV = \$500,000 / .080 = \$6,250,000 3

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Solutions to lecture problems – time value of money part 2 You own a building that is expected to make annual cash flows forever. What is the value of the building if the cost of capital is 8.3% and annual cash flows are expected to grow by 2.3% per year forever with the first one expected to be \$500,000 in 1 year? Time 0 1 2 3 4 Cash flow \$0 \$500,000 \$500,000 × 1.023 \$500,000 × 1.023 2 \$500,000 × 1.023 3 Cash flow \$0 \$500,000 \$511,500 \$523,265 \$535,300 Present value ? The cash flows reflect a growing perpetuity PV = C 1 / (r – g) C 1 = \$500,000 r = .083 g = .023 PV = \$500,000 / (.083 – .023) = \$500,000 / .060 = \$8,333,333.33 4
Solutions to lecture problems – time value of money part 2 You own a building that is expected to make annual cash flows forever. If the building is worth \$2,300,000, the cost of capital is 5%, and annual fixed cash flows are expected with the first one due in one year, then what is the amount of the annual cash flows produced by the building expected to be? Time 0 1 2 3 4 Cash flow \$0 ? ? ? ? Present value \$2,300,000 The cash flows reflect a fixed perpetuity PV = C / r PV = \$2,300,000 r = .05 \$2,300,000 = C / .05 C = \$2,300,000 × .05 = \$115,000 5

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Solutions to lecture problems – time value of money part 2 You own a building that is expected to make annual cash flows forever. If the building is worth \$2,300,000, the cost of capital is 5%, and annual cash flows are expected with the first one due in one year and all subsequent ones growing annually by 2.2%, then what is the amount of the cash flow produced by the building in 1 year expected to be?
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