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**Unformatted text preview: **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? Step 1: cash flow is $200,000 in 1 year and $500,000 in 2 years Step 2A: cash flows can be expressed as taking place in 1 year and in 2 years, and since 1 and 2 are whole numbers, a year is the largest period from this step Step 2B: no compounding period is given Step 2C: the discount rate has no associated time period, so we assume it’s annual Step 2D: the shortest of the periods identified in steps 2A, 2B, and 2C is a year and is the length that each period on the timeline should reflect Step 3: the discount rate is given as 10 percent Time 1 2 Expected cash flow $200,000 $500,000 Present value ? PV = C + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] C = 0 C 1 = 200,000 C 2 = 500,000 r = .10 PV = C + [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 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 1 2 Expected cash flow $200,000 ? Present value $500,000 PV = C + [C 1 /(1+r) 1 ] + [C 2 /(1+r) 2 ] PV = 500,000 C = 0 C 1 = 200,000 C 2 = ? r = .10 PV = C + [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 + [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? Step 1: cash flow is $500,000 per year forever with first one in 1 year Step 2A: cash flows can be expressed as taking place annually, so a year is the largest period from this step Step 2B: no compounding period is given Step 2C: the cost of capital no associated time period, so we assume it’s annual Step 2D: the shortest of the periods identified in steps 2A, 2B, and 2C is a year and is the length that each period on the timeline should reflect Step 3: the cost of capital is given as 8.0 percent Time 1 2 3 4 … Cash flow $0 $500,000 $500,000 $500,000 $500,000 … Present value ?...

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