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Chapter 5: Problem 20

A rookie quarterback is negotiating his first NFL contract. His opportunity cost is \(10 \%\). He has been offered three possible 4 -year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows: $$\begin{array}{lcccc} & 1 & 2 & 3 & 4 \\\& & & & \\\\\text { Contract 1 } & \$ 3,000,000 & \$ 3,000,000 & \$ 3,000,000 & \$ 3,000,000 \\\\\text { Contract 2 } & \$ 2,000,000 & \$ 3,000,000 & \$ 4,000,000 & \$ 5,000,000 \\\\\text { Contract 3 } & \$ 7,000,000 & \$ 1,000,000 & \$ 1,000,000 & \$ 1,000,000 \end{array}$$ As his adviser, which contract would you recommend that he accept?

Short Answer

Expert verified
Recommend Contract 2 as it has the highest present value.

Step by step solution

01

Calculate Present Value for Contract 1

The Present Value (PV) is calculated using the formula: \[ PV = \sum \frac{C_t}{(1 + r)^t} \]where \(C_t\) is the cash flow at time \(t\), and \(r\) is the opportunity cost or discount rate (10% or 0.10). For Contract 1, the cash flows are consistent at $3,000,000 from years 1 to 4.\[ PV = \frac{3,000,000}{(1 + 0.10)^1} + \frac{3,000,000}{(1 + 0.10)^2} + \frac{3,000,000}{(1 + 0.10)^3} + \frac{3,000,000}{(1 + 0.10)^4} \]Calculating each term:1. \(\frac{3,000,000}{1.1} = 2,727,273\)2. \(\frac{3,000,000}{1.1^2} = 2,479,339\)3. \(\frac{3,000,000}{1.1^3} = 2,253,945\)4. \(\frac{3,000,000}{1.1^4} = 2,048,132\)Adding these values gives the total present value for Contract 1: \( PV \approx 9,508,689 \).
02

Calculate Present Value for Contract 2

Using the same Present Value formula, calculate for Contract 2 as follows:\[ PV = \frac{2,000,000}{(1+0.10)^1} + \frac{3,000,000}{(1+0.10)^2} + \frac{4,000,000}{(1+0.10)^3} + \frac{5,000,000}{(1+0.10)^4} \]Calculating each term:1. \(\frac{2,000,000}{1.1} = 1,818,182\)2. \(\frac{3,000,000}{1.1^2} = 2,479,339\)3. \(\frac{4,000,000}{1.1^3} = 3,004,593\)4. \(\frac{5,000,000}{1.1^4} = 3,413,553\)Adding these values gives the total present value for Contract 2:\( PV \approx 10,715,667 \).
03

Calculate Present Value for Contract 3

Now, calculate using the Present Value formula for Contract 3:\[ PV = \frac{7,000,000}{(1+0.10)^1} + \frac{1,000,000}{(1+0.10)^2} + \frac{1,000,000}{(1+0.10)^3} + \frac{1,000,000}{(1+0.10)^4} \]Calculating each term:1. \(\frac{7,000,000}{1.1} = 6,363,636\)2. \(\frac{1,000,000}{1.1^2} = 826,446\)3. \(\frac{1,000,000}{1.1^3} = 751,315\)4. \(\frac{1,000,000}{1.1^4} = 683,013\)Adding these values gives the total present value for Contract 3:\( PV \approx 8,624,410 \).
04

Compare Present Values and Recommend

Compare the total present values calculated for each contract: - Contract 1: 9,508,689 - Contract 2: 10,715,667 - Contract 3: 8,624,410 The contract with the highest present value is Contract 2, with a present value of 10,715,667. Therefore, it is advisable to recommend the rookie quarterback to accept Contract 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Opportunity Cost
Opportunity cost is a key concept in financial decision-making. Imagine you have two different choices, but you can only pick one. The opportunity cost is the benefit you miss out on by not choosing the next best alternative. It is everything you would have gained by making a different choice.
In financial management, the opportunity cost is often reflected as a percentage, known as the discount rate. It鈥檚 the rate of return you could earn from an alternative investment.
  • For instance, in the exercise above, the opportunity cost is 10%. This indicates that the quarterback could earn a 10% return elsewhere.
  • It helps in evaluating and comparing different cash flows.
Always remembering opportunity cost helps make smarter investment decisions by considering what we are potentially giving up.
The Importance of Discount Rate
The discount rate is crucial in present value calculations. It's the interest rate used to determine the present value of future cash flows. This rate essentially helps bridge the gap between future money and present money.
Why is it important? Here鈥檚 why:
  • A higher discount rate means that the value of future cash flows is lower. So, selecting the right discount rate is essential for accurate evaluations.
  • In the context of the quarterback鈥檚 contracts, a 10% discount rate is used to assess his potential earnings.
Choosing an appropriate discount rate is important since it affects the present value of investments, impacting financial decisions.
Essence of Financial Management
Financial management involves planning, organizing, and controlling financial resources to achieve organizational goals. In our exercise, we're using financial management principles to advise on contract options. Here鈥檚 how it benefits decision-making:
  • It helps balance risk and return by evaluating investments or cash flow like the ones in the contracts.
  • Ensures that financial decisions are aligned with personal or organizational financial goals.
  • Involves using tools like present value calculations to assess the value of future cash flows.
Effective financial management enhances decision-making and maximizes the value of investments or resources over time.
Cash Flow Analysis
Cash flow analysis is an examination of how money moves in and out over a period. It鈥檚 pivotal in understanding how investments, like the quarterback鈥檚 contracts, would fare over time.
This involves several steps:
  • Identifying and analyzing patterns in cash inflows and outflows.
  • Using present value calculations to assess the current worth of future payments as seen with contract evaluations.
  • Evaluating the sufficiency of cash to deal with any liabilities and ensuring sound financial planning.
In our example, understanding each contract's cash flow helps in making informed decisions to maximize the player's earnings over the contract duration.

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Most popular questions from this chapter

What is the present value of a security that will pay \(\$ 5,000\) in 20 years if securities of equal risk pay \(7 \%\) annually?

You want to buy a car, and a local bank will lend you \(\$ 20,000 .\) The loan will be fully amortized over 5 years \((60\) months), and the nominal interest rate will be \(12 \%\) with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR?

UNEVEN CASH FLOW STREAM a. Find the present values of the following cash flow streams at \(8 \%\) compounded annually. $$\begin{array}{lcccccc} & 0 & 1 & 2 & 3 & 4 & 5 \\ & & & & & & & \\\\\text { Stream A } & \$ 0 & \$ 100 & \$ 400 & \$ 400 & \$ 400 & \$ 300 \\ \text { Stream B } & \$ 0 & \$ 300 & \$ 400 & \$ 400 & \$ 400 & \$ 100\end{array}$$ b. What are the PVs of the streams at \(0 \%\) compounded annually?

Your client is 40 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save \(\$ 5,000\) per year; and you advise her to invest it in the stock market, which you expect to provide an average return of \(9 \%\) in the future. a. If she follows your advice, how much money will she have at \(65 ?\) b. How much will she have at \(70 ?\) c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70 . If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age?

What is the present value of a \(\$ 100\) perpetuity if the interest rate is \(7 \% ?\) If interest rates doubled to \(14 \%\), what would its present value be?
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