Problem 4-40 Calculating Present Values You just won the TVM Lottery. You will r

Question

Problem 4-40 Calculating Present Values You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $530,000 per year. Thus, in one year you receive $1.53 million. In two years, you get $2.06 million, and so on. If the appropriate interest rate is 6.3 percent, what is the present value of your winnings? (Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).)

Present value $

Explanation / Answer

Present Value =

Cash flow in Year 0 = 1,000,000

Cash Flow in Year 1 = 1,530,000

Cash Flow in Year 2 = 2,060,000

and increasing year to year by $ 530,000

Cash Flow in Year 10 =  6,300,000

Present Value = 1,000,000 + [1,530,000 * (1/1.063)] + [2,060,000 * (1/1.063)^2] + [2,590,000 * (1/1.063)^3] + ... + [6,300,000 * (1/1.063)^10]

Present Value = 1,000,000 + 1,439,322.67 + 1,823,058.86 + 2,156,254.26 + 2,443,551.72 + 2,689,221.29 + 2,897,188.11 + 3,071,058.26+ 3,214,142.82 + 3,329,480.17 + 3,419,85.67

Present Value = $ 27,483,134.84

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