Question 1

You are considering a job offer. The job offers an annual salary of $42,000, $45,000, and $48,000 a year for the next three years, respectively. The offer also includes a starting bonus of $1,000 payable immediately. What is this offer worth to you today at a discount rate of 5.5%?

Accepted Answer

The present value of the salary for each year and the bonus is calculated using the formula for present value: PV = FV / (1 + r)^n. Summing these values gives the total worth today.

Question 2

You are considering investing $750 in a 10 year annuity. The rate of return you require is 6.5%. What annual cash flow from the annuity will provide the required return?

Accepted Answer

The annual cash flow from the annuity can be calculated using the formula for the present value of an annuity: $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where PV is the present value ($750), PMT is the annual payment, r is the annual interest rate (6.5% or 0.065), and n is the number of periods (10 years). Rearranging the formula to solve for PMT gives: $PMT = PV \times \frac{r}{1 - (1 + r)^{-n}}$. Substituting the given values and solving for PMT gives approximately $104.33.

Question 3

On the day you enter college you borrow $12,000 from your local bank. The terms of the loan include an interest rate of 5.45%. The terms stipulate that the principle is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much will you pay the bank one year after you graduate?

Accepted Answer

The answer of On the day you enter college you...

Question 4

Analysts expect Marble Comics to pay shareholders $1.00 per share annually for the next five years. After that, the dividend will be $1.50 annually forever. Given a discount rate of 10%, what is the value of the stock today?

Accepted Answer

The answer of Analysts expect Marble Comics to pay shareholders...

Question 5

What is the future value in 10 years of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%.

Accepted Answer

The answer of What is the future value in 10...

Question 6

What is the future value of the following cash flows at the end of year 3 if the interest rate is 7.25%? The cash flows occur at the end of each year.

Accepted Answer

The answer of What is the future value of the...

Question 7

Your car dealer is willing to lease you a new car for $199 a month for 72 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 5.45%, what is the current value of the lease?

Accepted Answer

The answer of Your car dealer is willing to lease...

Question 8

Your uncle left you an inheritance in the form of a trust. The trust agreement states that you are to receive $750 each year, starting today and continuing for 25 years. What is the value of this inheritance today if the applicable discount rate is 5.8%?

Accepted Answer

This is an annuity due problem since the payments start today. The present value of an annuity due can be calculated using the formula: $PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)$, where $P$ is the payment amount, $r$ is the discount rate per period, and $n$ is the number of periods. Plugging in the values: $PV = 750 \times \left(\frac{1 - (1 + 0.058)^{-25}}{0.058}\right) \times (1 + 0.058)$, we get a present value of approximately $10,339.26, which matches option C.

Question 9

You are considering a project with the following cash flows:  What is the present value of these cash flows, given an 11% discount rate?

Accepted Answer

The answer of You are considering a project with the...

Question 10

You have a 25-year $400,000 mortgage with a 3.5% rate of interest (compounded monthly) that you make monthly payments on. What is the balance of the loan at the end of year 20?

Accepted Answer

The answer of You have a 25-year $400,000 mortgage with...

Question 11

You are buying a previously owned car today at a price of $4,950. You are paying $750 down in cash and financing the balance for 42 months at 8.45%. What is the amount of each loan payment?

Accepted Answer

To find the monthly loan payment, you can use the formula for calculating loan payments or a financial calculator. The loan amount is $4,950 - $750 = $4,200. The interest rate per month is 8.45% per year, or 8.45/12 = 0.7042% per month. The number of payments is 42 months. Using the formula for an installment loan payment or a financial calculator, you find the monthly payment to be approximately $115.86.

Question 12

You plan on withdrawing quarterly payments for the next ten years and have deposited $350,000 in an account. If the rate of return is 5% compounded quarterly, determine the value of the quarterly withdrawals.

Accepted Answer

The value of the quarterly withdrawals can be calculated using the formula for the present value of an annuity: $P = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)$, where $P$ is the present value ($350,000), $PMT$ is the payment per period (what we're solving for), $r$ is the quarterly interest rate (5% annual rate divided by 4, so 0.0125), and $n$ is the total number of payments (10 years times 4 quarters/year = 40 payments). Rearranging the formula to solve for $PMT$ gives us $PMT = P \times \left( \frac{r}{1 - (1 + r)^{-n}} \right)$. Plugging in the values gives $PMT = 350,000 \times \left( \frac{0.0125}{1 - (1 + 0.0125)^{-40}} \right)$, which calculates to approximately $11,172.50.

Question 13

On the day you enter college, you work out a deal with your local bank such that you borrow $9,600 for four years. The terms of the loan include an interest rate of 5.9%. The terms also stipulate that the principle is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much will you pay the bank one year after you graduate?

Accepted Answer

The total amount paid one year after graduation includes the original principal plus the interest accumulated over five years. The annual interest payment is calculated as $9,600 * 5.9% = $566.40. Over four years in college, this amounts to $566.40 * 4 = $2,265.60 in interest payments. After graduation, the principal of $9,600 is due, along with one more year of interest payment ($566.40), totaling $9,600 + $2,265.60 + $566.40 = $12,432.00. However, the question asks for the amount paid one year after graduation, which includes the principal and the final year's interest, not the total of all interest payments made. Therefore, the correct calculation should be the principal ($9,600) plus one year of interest ($566.40), which equals $10,166.40.

Question 14

You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $15 a month for the next nine months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2% interest per month. How much money are you borrowing?

Accepted Answer

The loan is an annuity due, where payments are made at the beginning of each period. The present value of the loan can be calculated using the formula for the present value of an annuity due: PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r). Here, Pmt = $15, r = 0.02, and n = 9. Calculating this gives approximately $124.88.

Question 15

You are expecting annual cash flows of $80,000 in years 1-5; $95,000 in years 6-20; and $105,000 in years 21-50. If the rate of interest is 10% compounded annually, calculate the future value of this cash flow stream.

Accepted Answer

The future value of each segment of cash flows is calculated separately using the future value of an annuity formula and then summed up. The future value of the first segment (years 1-5) is calculated and compounded to year 50, the second segment (years 6-20) is compounded to year 50, and the third segment (years 21-50) is already at year 50. Summing these gives approximately $105.54 million.

Question 16

Your recently departed rich, eccentric uncle has left for you in his will a large sum of money. Unfortunately, rather than giving you this sum of money immediately, he has instructed the executor of the will to pay you $10,000 in one year. This payment is to grow by 9% each year and to be made each year forever. If the appropriate discount rate is 10%, how much have you actually inherited?

Accepted Answer

The present value of a perpetuity is the annual payment divided by the discount rate minus the growth rate. In this case, the annual payment is $10,000, the discount rate is 10%, and the growth rate is 9%. Therefore, the present value of the inheritance is $10,000 / (0.10 - 0.09) = $1,000,000.

Question 17

You just won the lottery! As your prize you will receive $1,500 a month for ten years. If you can earn 9.3% on your money, what is this prize worth to you today?

Accepted Answer

The answer of You just won the lottery! As your...

Question 18

Angela is able to pay $230 a month for 6 years on a car loan. If the interest rate is 7.9%, how much can she afford to borrow to buy a car?

Accepted Answer

The correct answer is A because $13,154.54 is the amount that Angela can afford to borrow to buy a car. This is calculated using the formula A = P * (r * (1 + r)^n) / ((1 + r)^n - 1), where A is the amount that Angela can afford to borrow, P is the monthly payment, r is the interest rate, and n is the number of months.

Question 19

You need some money today and the only friend you have that has any is your 'miserly' friend. He agrees to loan you the money you need, if you make payments of $20 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5% interest per month. How much money are you borrowing?

Accepted Answer

The answer of You need some money today and the...

Question 20

Mr. Dubofsky just won a "Name That Tune" contest with a grand prize of $250,001. However, the contest stipulates that the winner will receive $100,000 immediately, and $15,000 at the end of each of the next 10 years. Assuming that he can earn 5% on his money, how much has he actually won?

Accepted Answer

To calculate the actual amount Mr. Dubofsky has won, we need to consider the present value of the annuity (the $15,000 payments for 10 years) plus the immediate $100,000 payment. The formula for the present value of an annuity is $PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods.Given:- $P = $15,000$- $r = 5\% = 0.05$- $n = 10$The present value of the annuity (the $15,000 payments) is:$$PV = $15,000 \times \left[\frac{1 - (1 + 0.05)^{-10}}{0.05}\right]$$$$PV = $15,000 \times \left[\frac{1 - (1.05)^{-10}}{0.05}\right]$$$$PV = $15,000 \times 7.7217$$ (using a financial calculator or present value table for the factor)$$PV = $115,826.02$$Adding the immediate $100,000 payment:$$Total = $115,826.02 + $100,000 = $215,826.02$$Therefore, the actual amount Mr. Dubofsky has won, considering the present value of future payments at a 5% interest rate, is $215,826.02.

Quiz 6: Discounted Cash Flow Valuation