Ask Question
BusinessBusiness
1 June, 04:44

You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $375,000 per year. Thus, in one year, you receive $1.375 million. In two years, you get $1.75 million, and so on. If the appropriate interest rate is 6.5 percent, what is the value of your winnings today?

+2
Answers (1)
  1. 1 June, 07:16
    0
    Total Present value (Sum of all PVs $21,624,467.720

    Explanation:

    The question is asking for the calculation or computation of the total PV of all the payments. This can be derived by summing up the Present Value (PV) of individual cash received.

    Step 1: Calculate the Present Value of each cash payment

    Formula = PV = C0 + C1 / (1+r) 1 + C2 / (1+r) 2 + ... + C n / (1+r) n

    C0, C1 ... Cn = Cash payments for each year for the 10 years

    r = The rate each period ... in the question this is 6.5%

    Step 2: Use the Formula to calculate annual cash payment

    Year Cash payment

    0 $1,000,000

    1 $1,000,000 + $ 375,000 = $1,375,000

    2 $1,375,000 + $ 375000 = $1,750,000

    3 $1,750,000 + $ 375000 = $2,125,000

    4 $2,125,000 + $ 375000 = $2,500,000

    5 $2,500,000 + $ 375000 = $2,875,000

    6 $2,875,000 + $ 375000 = $3,250,000

    7 3,250,000 + $ 375000 = $3,625,000

    8 $3,625,000 + $ 375000 = $4,000,000

    9 4,000,000 + $ 375000 = $4,375,000

    10 $4,375,000 + $ 375000 = $4,750,000

    Step 3: Use the calculated annual cash payments and the formula in step 1 to compute the Total Present Value

    Computation of PV:

    Yr Cash (C) PV Factor PV Factor @ 6.5 % (F) PV (C x F)

    0 1,000,000 1 / (1+0.065) ^0 1 1,000,000

    1 1,375,000 1 / (1+0.065) ^1 0.939 $1,291,079.812

    2 1,750,000 1 / (1+0.065) ^2 0.882 $1,542,903.745

    3 2,125,000 1 / (1+0.065) ^3 0.828 $1,759,179.320

    4 2,500,000 1 / (1+0.065) ^4 0.777 $1,943,307.727

    5 2,875,000 1 / (1+0.065) ^5 0.730 $2,098,407.405

    6 3,250,000 1 / (1+0.065) ^6 0.685 $2,227,335.886

    7 3,625,000 1 / (1+0.065) ^7 0.644 $2,332,710.029

    8 4,000,000 1 / (1+0.065) ^8 0.604 $2,416,924.751

    9 4,375,000 1 / (1+0.065) ^9 0.567 $2,482,170.372

    10 4,750,000 1 / (1+0.065) ^10 0.533 $2,530,448.669

    Total Present value (Sum of all PVs) $21,624,467.720
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $375,000 per year. Thus, ...” in 📘 Business if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers
You Might be Interested in
You get a letter in the mail stating that you have been chosen by the IRS for an audit
Answers (1)
What does a budget account for primarily?
Answers (1)
Three employees of a hardware store damaged a tile floor while moving concrete pavers from their delivery truck to an outdoor patio shop. Many of the pavers were also damaged during the move.
Answers (1)
For a period of time, Energizer batteries used mock commercials for seemingly boring, mundane products. A few seconds into the mock commercial, viewers heard the distinctive drumbeat of the Energizer Bunny before it marched across the screen.
Answers (1)
Yakov hires melina to be his vice president for marketing. the job description is pretty broad but does not include the ability to hire or terminate lower level employees in the marketing division. if melina has this power, it is based on her:
Answers (1)
New Questions in Business
A (n) is the issuer's written promise to pay an amount equaling the par value. The par value is paid at a specified future date. Most often, the issuer is required to make semiannual interest payments.
Answers (1)
The primary goal of the Consumer Financial Protection Bureau is: A To monitor your credit report and ensure your identity and other sensitive data has not been compromised. B To protect against abusive or deceptive debt collection purposes.
Answers (1)
Jake Skinner purchases a big screen TV on credit and will repay the loan with one payment at the end of 90 days. What type of credit did Jake use?
Answers (1)
Which most likely results from producers engaging in specialization? Producers reduce their costs. Producers increase their market share. Producers decrease the materials needed for production. Producers always offer more competitive pricing.
Answers (1)
The workers at State Hospital, a public sector employer, and Acme Inc, a private employer, are subject to speech censorship and arbitrary job termination. Constitutional issues are present only for the State Hospital workers. TrueFalse
Answers (1)
Home » Business » You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $375,000 per year. Thus, in one year, you receive $1.375 million. In two years, you get $1.75 million, and so on.
Sign Up Forgot Password?