Question 1

You are considering a project which will provide annual cash inflows of $4,500, $5,700, and $8,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a 9 percent discount rate?

Accepted Answer

We can use the present value formula to calculate the present value of these cash flows: 
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 
where CF is the cash flow and r is the discount rate. Plugging in the numbers, we get: 
PV = 4,500/(1+0.09)^1 + 5,700/(1+0.09)^2 + 8,000/(1+0.09)^3 
PV = 4,128.44 + 4,721.84 + 6,253.53 
PV = 15,103.81 
Therefore, the present value of the cash flows is $15,103 which is closest to answer choice B.

Question 2

Will has been purchasing $25,000 worth of New Tek stock annually for the past 11 years. His holdings are now worth $598,100. What is his annual rate of return on this stock?

Accepted Answer

The answer of Will has been purchasing $25,000 worth of...

Question 3

Lucas will receive $6,800, $8,700, and $12,500 each year starting at the end of year one. What is the future value of these cash flows at the end of year five if the interest rate is 7 percent?

Accepted Answer

The future value of each cash flow is calculated separately and then summed up. The future value of $6,800 at the end of year five is $6,800 * (1.07)^4, the future value of $8,700 is $8,700 * (1.07)^3, and the future value of $12,500 is $12,500 * (1.07)^2. Adding these values gives the total future value of $33,883.

Question 4

Your local travel agent is advertising an upscale winter vacation package for travel three years from now to Antarctica. The package requires that you pay $25,000 today, $30,000 one year from today, and a final payment of $45,000 on the day you depart three years from today. What is the cost of this vacation in today's dollars if the discount rate is 9.75 percent?

Accepted Answer

The answer of Your local travel agent is advertising an...

Question 5

Today, you turn 23. Your birthday wish is that you will be a millionaire by your 40^th birthday. In an attempt to reach this goal, you decide to save $50 a day, every day until you turn 40. You open an investment account and deposit your first $50 today. What rate of return must you earn to achieve your goal?

Accepted Answer

The answer of Today, you turn 23. Your birthday wish...

Question 6

Blackwell, Inc. has a $75,000 liability it must pay three years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $15,000 each year for the next three years, starting one year from today. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today?

Accepted Answer

The answer of Blackwell, Inc. has a $75,000 liability it...

Question 7

You just signed a consulting contract that will pay you $35,000, $52,000, and $80,000 annually at the end of the next three years, respectively. What is the present value of these cash flows given a 10.5 percent discount rate?

Accepted Answer

The present value of the cash flows is $133,554. This is calculated by taking the sum of the present values of each of the three cash flows. The present value of the first cash flow is $35,000 / (1 + 0.105)^1 = $31,666.67. The present value of the second cash flow is $52,000 / (1 + 0.105)^2 = $42,575.76. The present value of the third cash flow is $80,000 / (1 + 0.105)^3 = $59,311.57. The sum of these three present values is $133,554.

Question 8

You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why?

Accepted Answer

To calculate the net present value (NPV) of the second offer, we need to discount the $70,000 payment two years from today to its present value. Using the given discount rate of 11.5 percent, we can calculate the present value of $70,000 as $51,030. We can then calculate the total NPV of the second offer as $35,000 + $51,030 = $86,030. The NPV of the first offer is simply the offer amount of $89,500. Therefore, the second offer has the larger NPV and should be accepted.

Question 9

You just won a national sweepstakes! For your prize, you opted to receive never-ending payments. The first payment will be $12,500 and will be paid one year from today. Every year thereafter, the payments will increase by 3.5 percent annually. What is the present value of your prize at a discount rate of 8 percent?

Accepted Answer

The answer of You just won a national sweepstakes! For...

Question 10

You are considering changing jobs. Your goal is to work for three years and then return to school full-time in pursuit of an advanced degree. A potential employer just offered you an annual salary of $41,000, $44,000, and $46,000 a year for the next three years, respectively. All salary payments are made as lump sum payments at the end of each year. The offer also includes a starting bonus of $2,500 payable immediately. What is this offer worth to you today at a discount rate of 6.75 percent?

Accepted Answer

The answer of You are considering changing jobs. Your goal...

Question 11

You just settled an insurance claim. The settlement calls for increasing payments over a 10-year period. The first payment will be paid one year from now in the amount of $10,000. The following payments will increase by 4.5 percent annually. What is the value of this settlement to you today if you can earn 8 percent on your investments?

Accepted Answer

The answer of You just settled an insurance claim. The...

Question 12

You are considering two savings options. Both options offer a 7.4 percent rate of return. The first option is to save $900, $2,100, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. If you want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option?

Accepted Answer

The answer of You are considering two savings options. Both...

Question 13

Your father helped you start saving $20 a month beginning on your 5^th birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 17^th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings?

Accepted Answer

This cannot be solved directly, so it's easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that your answer is correct.

Question 14

Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $187,000, $220,000, and $245,000 over the next three years, respectively. After that time, they feel the business will be worthless. Southern Tours has determined that a 13.5 percent rate of return is applicable to this potential acquisition. What is Southern Tours willing to pay today to acquire Holiday Vacations?

Accepted Answer

The answer of Southern Tours is considering acquiring Holiday Vacations....

Question 15

You plan on saving $5,200 this year, nothing next year, and $7,500 the following year. You will deposit these amounts into your investment account at the end of each year. What will your investment account be worth at the end of year three if you can earn 8.5 percent on your funds?

Accepted Answer

The answer of You plan on saving $5,200 this year,...

Question 16

One year ago, Deltona Motor Parts deposited $16,500 in an investment account for the purpose of buying new equipment three years from today. Today, it is adding another $12,000 to this account. The company plans on making a final deposit of $20,000 to the account one year from today. How much will be available when it is ready to buy the equipment, assuming the account pays 5.5 interest?

Accepted Answer

To solve the problem, we need to use the formula for the future value of an annuity:

FV = PMT x (((1 + r)^n) - 1) / r

where:
PMT = the amount of the periodic payments
r = the interest rate per period (in this case, per year)
n = the total number of periods

We can divide the problem into two parts: the first deposit of $16,500 and the subsequent deposits of $12,000 and $20,000.

For the first deposit of $16,500, we need to find the future value in three years, so:

FV1 = 16,500 x (1 + 0.055)^3 = $19,712.92

For the subsequent deposits, we need to find the future value in two years (since we are adding them one year and two years from today, respectively), so:

FV2 = 12,000 x (((1 + 0.055)^2) - 1) / 0.055 = $25,152.97
FV3 = 20,000 x (((1 + 0.055)^1) - 1) / 0.055 = $20,907.40

Finally, we can add up the three future values to find the total:

FV = FV1 + FV2 + FV3 = $19,712.92 + $25,152.97 + $20,907.40 = $65,773.29

Therefore, the best choice is D, $56,792.

Question 17

Miley expects to receive the following payments: Year 1 = $60,000; Year 2 = $35,000; Year 3 = $12,000. All of this money will be saved for her retirement. If she can earn an average of 10.5 percent on her investments, how much will she have in her account 25 years after making her first deposit?

Accepted Answer

The answer of Miley expects to receive the following payments:...

Question 18

A wealthy benefactor just donated some money to the local college. This gift was established to provide scholarships for worthy students. The first scholarships will be granted one year from now for a total of $35,000. Annually thereafter, the scholarship amount will be increased by 5.5 percent to help offset the effects of inflation. The scholarship fund will last indefinitely. What is the value of this gift today at a discount rate of 8 percent?

Accepted Answer

The value of the scholarship fund today can be calculated using the perpetuity formula, which is:

Present value = Annual amount / Discount rate

To use this formula, we need to calculate the first year's scholarship amount, which is $35,000. Then, we can use the given annual increase rate of 5.5% to calculate the scholarship amount in all subsequent years.

Next, we need the discount rate, which is 8%.

Putting it all together, we get:

Present value = $35,000 / (0.08 - 0.055) = $35,000 / 0.025 = $1,400,000

Therefore, the value of the gift today is $1,400,000, which is option D.

Question 19

Your parents have made you two offers. The first offer includes annual gifts of $10,000, $11,000, and $12,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 8 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer?

Accepted Answer

The answer of Your parents have made you two offers....

Question 20

Your grandfather left you an inheritance that will provide an annual income for the next 10 years. You will receive the first payment one year from now in the amount of $4,000. Every year after that, the payment amount will increase by 6 percent. What is your inheritance worth to you today if you can earn 9.5 percent on your investments?

Accepted Answer

The present value of a growing annuity formula is used to calculate the worth of the inheritance today. Using the formula: PV = Pmt * [(1 - (1 + g)^n / (1 + r)^n) / (r - g)], where Pmt = $4,000, g = 6% (0.06), r = 9.5% (0.095), and n = 10, the present value is approximately $31,699.15.

Quiz 6: Discounted Cash Flow Valuation