Question

1) You are an investor evaluating a project which is going to take 8 years. The project will pay $500,000 at the beginning of each year starting a year from now. These payments will grow at 2% for the first two years, then 3.5% for the following two years and then stay consistent at 4% until the end of the project. In the last year of the project you will receive a lump sum of $1 million while also paying a lump sum of $200,000. If your expected return on this project is 12.5%, what is the PV of the project?

2) You are 20 years old and anitcipate you will have your first child when you are 25 years old. At 25 years old, you want to save at the end of each month for the next 18 years. You anticipate that when your child goes to college, tuition room and board to be paid at the beginning of each year will cost $20,000. Education inflation is expected to be at 4% each year. If you can earn 8.5% on investments from when you are 25 years until your child completes college and you put $2,000 down at 25 years old as you start investing, how much money in real dollars do you have to save to achieve this goal accounting for education inflation?

Answer 1

Answer:-

Given

Year 0	0	0
Year 1	$ 500000	$ 500000
Year 2	$ 500000 x 1.02	$ 510000
Year 3	$ 500000 x (1.02)2	$ 520200
Year 4	$ 500000 x ( 1.02)2 x 1.035	$ 538407
Year 5	$ 500000 x ( 1.02)2 x (1.035)2	$ 557251
Year 6	$ 500000 x ( 1.02)2 x (1.035)2 x 1.04	$ 579541
Year 7	$ 500000 x ( 1.02)2 x (1.035)2 x (1.04)2	$ 602723
Year 8	$ 500000 x ( 1.02)2 x (1.035)2 x ( 1.04)3	$ 626832

Also we will receive $1 million in 8th year and pay $ 200000 at the end of 8th year

Expected return = discount rate = 12.5 %

NPV = $ 500000 / 1.12 + $ 510000 / 1.12² + $ 520200 / 1.12³ + $ 538407 / 1.12⁴ + $ 557251 / 1.12⁵ + $ 579541 / 1.12⁶ + $ 60223 / 1.12⁷ +$ 626832 / 1.12⁸ + $ 1000000 / 1.12⁸ - $ 200000 / 1.12⁸
NPV = $ 2652566 + $ 1000000 / 1.12⁸ - $ 200000 / 1.12⁸
NPV = $ 2652566 +$ 403877 - $ 80775
NPV = $ 2975668

Therefore the Present value of the project = $ 2975668

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